From cea22c65c09c66a2e5cab3635f0b2fbc142c14f4 Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 21 Dec 2014 17:13:58 +0100 Subject: [PATCH] documents/write-math-ba-paper: Initial commit --- documents/write-math-ba-paper/Makefile | 12 + documents/write-math-ba-paper/README.md | 21 + documents/write-math-ba-paper/glossary.tex | 73 + documents/write-math-ba-paper/variables.tex | 12 + .../write-math-ba-paper.bib | 1711 +++++++++++++++++ .../write-math-ba-paper.tex | 313 +++ 6 files changed, 2142 insertions(+) create mode 100644 documents/write-math-ba-paper/Makefile create mode 100644 documents/write-math-ba-paper/README.md create mode 100644 documents/write-math-ba-paper/glossary.tex create mode 100644 documents/write-math-ba-paper/variables.tex create mode 100644 documents/write-math-ba-paper/write-math-ba-paper.bib create mode 100644 documents/write-math-ba-paper/write-math-ba-paper.tex diff --git a/documents/write-math-ba-paper/Makefile b/documents/write-math-ba-paper/Makefile new file mode 100644 index 0000000..ae2a003 --- /dev/null +++ b/documents/write-math-ba-paper/Makefile @@ -0,0 +1,12 @@ +DOKUMENT = write-math-ba-paper +make: + pdflatex -shell-escape $(DOKUMENT).tex -interaction=batchmode -output-format=pdf # aux-files for makeindex / makeglossaries + makeglossaries $(DOKUMENT) + bibtex $(DOKUMENT) + pdflatex -shell-escape $(DOKUMENT).tex -interaction=batchmode -output-format=pdf # include index + pdflatex -shell-escape $(DOKUMENT).tex -interaction=batchmode -output-format=pdf # include symbol table + pdflatex -shell-escape $(DOKUMENT).tex -interaction=batchmode -output-format=pdf # include symbol table + make clean + +clean: + rm -rf $(TARGET) *.class *.html *.log *.aux *.out *.thm *.idx *.toc *.ind *.ilg figures/torus.tex *.glg *.glo *.gls *.ist *.xdy *.fdb_latexmk *.bak *.blg *.bbl *.glsdefs *.acn *.acr *.alg *.nls *.nlo *.bak *.pyg *.lot *.lof diff --git a/documents/write-math-ba-paper/README.md b/documents/write-math-ba-paper/README.md new file mode 100644 index 0000000..e453a4b --- /dev/null +++ b/documents/write-math-ba-paper/README.md @@ -0,0 +1,21 @@ +## TODO + +### Preprocessing +* Scale-and-shift +* linear interpolation +* connect strokes +* Douglas-Peucker + +### Features +* coordinates +* ink +* stroke count +* aspect ratio + +### Training +* learning rate +* momentum +* Supervised layer-wise pretraining + + +* Check abstract! \ No newline at end of file diff --git a/documents/write-math-ba-paper/glossary.tex b/documents/write-math-ba-paper/glossary.tex new file mode 100644 index 0000000..30ffb11 --- /dev/null +++ b/documents/write-math-ba-paper/glossary.tex @@ -0,0 +1,73 @@ +%!TEX root = thesis.tex +%Term definitions +\newacronym{ANN}{ANN}{artificial neural network} +\newacronym{CSR}{CSR}{cursive script recognition} +\newacronym{DTW}{DTW}{dynamic time warping} +\newacronym{GTW}{GTW}{greedy time warping} +\newacronym{HMM}{HMM}{hidden Markov model} +\newacronym{HWR}{HWR}{handwriting recognition} +\newacronym{HWRT}{HWRT}{handwriting recognition toolkit} +\newacronym{MLP}{MLP}{multilayer perceptron} +\newacronym{MSE}{MSE}{mean squared error} +\newacronym{OOV}{OOV}{out of vocabulary} +\newacronym{TDNN}{TDNN}{time delay neural network} +\newacronym{PCA}{PCA}{principal component analysis} +\newacronym{LDA}{LDA}{linear discriminant analysis} +\newacronym{CROHME}{CROHME}{Competition on Recognition of Online Handwritten Mathematical Expressions} +\newacronym{GMM}{GMM}{Gaussian mixture model} +\newacronym{SVM}{SVM}{support vector machine} +\newacronym{PyPI}{PyPI}{Python Package Index} +\newacronym{CFM}{CFM}{classification figure of merit} +\newacronym{CE}{CE}{cross entropy} +\newacronym{GPU}{GPU}{graphics processing unit} +\newacronym{CUDA}{CUDA}{Compute Unified Device Architecture} +\newacronym{SLP}{SLP}{supervised layer-wise pretraining} + +% Term definitions +\newglossaryentry{Detexify}{name={Detexify}, description={A system used for +on-line handwritten symbol recognition which is described in \cite{Kirsch}}} + +\newglossaryentry{epoch}{name={epoch}, description={During iterative training of a neural network, an \textit{epoch} is a single pass through the entire training set, followed by testing of the verification set.\cite{Concise12}}} + +\newglossaryentry{hypothesis}{ + name={hypothesis}, + description={The recognition results which a classifier returns is called a hypothesis. In other words, it is the \enquote{guess} of a classifier}, + plural=hypotheses +} + +\newglossaryentry{reference}{ + name={reference}, + description={Labeled data is used to evaluate classifiers. Those labels are called references}, +} + +\newglossaryentry{YAML}{name={YAML}, description={YAML is a human-readable data format that can be used for configuration files}} +\newglossaryentry{MER}{name={MER}, description={An error measure which combines symbols to equivalence classes. It was introduced on \cpageref{merged-error-introduction}}} + +\newglossaryentry{JSON}{name={JSON}, description={JSON, short for JavaScript Object Notation, is a language-independent data format that can be used to transmit data between a server and a client in web applications}} + +\newglossaryentry{hyperparamter}{name={hyperparamter}, description={A +\textit{hyperparamter} is a parameter of a neural net, that cannot be learned, +but has to be chosen}, symbol={\ensuremath{\theta}}} + +\newglossaryentry{learning rate}{name={learning rate}, description={A factor $0 \leq \eta \in \mdr$ that affects how fast new weights are learned. $\eta=0$ means that no new data is learned}, symbol={\ensuremath{\eta}}} % Andrew Ng: \alpha + +\newglossaryentry{learning rate decay}{name={learning rate decay}, description={The learning rate decay $0 < \alpha \leq 1$ is used to adjust the learning rate. After each epoch the learning rate $\eta$ is updated to $\eta \gets \eta \times \alpha$}, symbol={\ensuremath{\eta}}} + +\newglossaryentry{preactivation}{name={preactivation}, description={The preactivation of a neuron is the weighted sum of its input, before the activation function is applied}} + +\newglossaryentry{stroke}{name={stroke}, description={The path the pen took from +the point where the pen was put down to the point where the pen was lifted first}} + +\newglossaryentry{line}{name={line}, description={Geometric object that is infinitely long +and defined by two points.}} + +\newglossaryentry{line segment}{name={line segment}, description={Geometric object that has finite length +and defined by two points.}} + +\newglossaryentry{symbol}{name={symbol}, description={An atomic semantic entity. A more detailed description can be found in \cref{sec:what-is-a-symbol}}} + +\newglossaryentry{weight}{name={weight}, description={A +\textit{weight} is a parameter of a neural net, that can be learned}, symbol={\ensuremath{\weight}}} + +\newglossaryentry{control point}{name={control point}, description={A +\textit{control point} is a point recorded by the input device.}} \ No newline at end of file diff --git a/documents/write-math-ba-paper/variables.tex b/documents/write-math-ba-paper/variables.tex new file mode 100644 index 0000000..081426b --- /dev/null +++ b/documents/write-math-ba-paper/variables.tex @@ -0,0 +1,12 @@ +\newcommand{\totalCollectedRecordings}{166898} % ACTUALITY +\newcommand{\detexifyCollectedRecordings}{153423} +\newcommand{\trainingsetsize}{134804} +\newcommand{\validtionsetsize}{15161} +\newcommand{\testsetsize}{17012} +\newcommand{\totalClasses}{1111} +\newcommand{\totalClassesAnalyzed}{369} +\newcommand{\totalClassesAboveFifty}{680} +\newcommand{\totalClassesNotAnalyzedBelowFifty}{431} +\newcommand{\detexifyPercentage}{$\SI{91.93}{\percent}$} +\newcommand{\recordingsWithDots}{$\SI{2.77}{\percent}$} % excluding i,j, ... +\newcommand{\recordingsWithDotsSizechange}{$\SI{0.85}{\percent}$} % excluding i,j, ... \ No newline at end of file diff --git a/documents/write-math-ba-paper/write-math-ba-paper.bib b/documents/write-math-ba-paper/write-math-ba-paper.bib new file mode 100644 index 0000000..222ae22 --- /dev/null +++ b/documents/write-math-ba-paper/write-math-ba-paper.bib @@ -0,0 +1,1711 @@ +% This file was created with JabRef 2.10b2. +% Encoding: UTF-8 + + +@InProceedings{Aguilar2012, + Title = {ExpressMatch: A System for Creating Ground-Truthed Datasets of Online Mathematical Expressions}, + Author = {Aguilar, F.D.J. and Hirata, N. S T}, + Booktitle = {Document Analysis Systems (DAS), 2012 10th IAPR International Workshop on}, + Year = {2012}, + Month = {March}, + Pages = {155-159}, + + Abstract = {In recognition domains, publicly available ground-truthed datasets are essential to perform effective performance evaluation and comparison of existing methods and systems. However, in the field of online handwritten mathematical expression recognition, datasets are quite scarce and their creation is one of the current challenging issues. In this paper, we present Express Match, a system designed to help creation and management of online mathematical expression datasets with ground-truth data. In this system, handwritten model expressions can be input and manually annotated with ground-truth data, transcriptions of these expressions can be automatically annotated by matching them to the respective models. Additional metadata can also be attached to each sample expression. To test the system, a dataset consisting of 56 model expressions and 910 sample expressions with a total of 20,010 symbols, written by 25 different writers, has been created. This dataset, as well as Express Match, will be made publicly available.}, + Doi = {10.1109/DAS.2012.38}, + File = {:/var/www/write-math/papers/expressmatch-a-system-for-creating-ground-truthed-datasets-of-online-mathematical-expressions.pdf:PDF}, + Keywords = {handwriting recognition;mathematics computing;ExpressMatch;ground truthed datasets;online handwritten mathematical expression recognition;performance comparison;performance evaluation;Computational modeling;Data models;Handwriting recognition;Integrated circuit modeling;Labeling;Performance evaluation;Writing;ground-truthed dataset;online mathematical expressions;performance evaluation}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.23} +} + +@InProceedings{Alvarez, + Title = {Printed and Handwritten Digits Recognition Using Neural Networks}, + Author = {Daniel Cruces Álvarez and O Martín Rodríguez and Xulio Fernández Hermida}, + Booktitle = {The Proceedings of The Ninth International Conference on Signal Processing Applications \& Technology}, + Year = {1998}, + + Address = {525 Market Street, Suite 500, San Francisco, CA 94105}, + Month = {9}, + Pages = {839--843}, + Volume = {I}, + + Abstract = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.5854&rep=rep1&type=pdf}, + Comment = {* Only about offline recognition * Refinement network for ambiguous situations (first network may reject classification in case of ambiguity)}, + Doi = {10.1.1.141.5854}, + Ee = {http%3A%2F%2Fwww.gpi.tsc.uvigo.es%2Fpub%2Fpapers%2Ficsp98_1.pdf}, + File = {:/var/www/write-math/papers/printed-and-handwritten-digits-recognition-using-neural-networks-10.1.1.141.5854.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.5854&rep=rep1&type=pdf} +} + +@Article{Arakaw83, + Title = {On-line recognition of handwritten characters -- {A}lphanumerics, {H}iragana, {K}atakana, {K}anji}, + Author = {Hiroki Arakawa}, + Journal = {Pattern Recognition }, + Year = {1983}, + Number = {1}, + Pages = {9 - 21}, + Volume = {16}, + + Abstract = {An on-line recognition system for handwritten characters is proposed. Fourier coefficients of pen-point movement loci relating to strokes are utilized as feature vectors of handwritten characters. A method based on a Bayesian decision rule tested with an experimental simulator. It is revealed that the method is effective for cursive handwritten characters, such as alphanumerics and Japanese characters. }, + Doi = {http://dx.doi.org/10.1016/0031-3203(83)90003-1}, + File = {:/var/www/write-math/papers/on-line-recognition-of-handwritten-characters-alphanumerics-hiragana-katakana-kanji.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {On-line recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://www.sciencedirect.com/science/article/pii/0031320383900031} +} + +@Article{Awal2014, + Title = {A global learning approach for an online handwritten mathematical expression recognition system }, + Author = {Ahmad-Montaser Awal and Harold Mouchère and Christian Viard-Gaudin}, + Journal = {Pattern Recognition Letters }, + Year = {2014}, + Note = {Frontiers in Handwriting Processing }, + Number = {0}, + Pages = {68 - 77}, + Volume = {35}, + + Abstract = {Abstract Despite the recent advances in handwriting recognition, handwritten two-dimensional (2D) languages are still a challenge. Electrical schemas, chemical equations and mathematical expressions (MEs) are examples of such 2D languages. In this case, the recognition problem is particularly difficult due to the two dimensional layout of the language. This paper presents an online handwritten mathematical expression recognition system that handles mathematical expression recognition as a simultaneous optimization of expression segmentation, symbol recognition, and 2D structure recognition under the restriction of a mathematical expression grammar. The originality of the approach is a global strategy allowing learning mathematical symbols and spatial relations directly from complete expressions. A new contextual modeling is proposed for combining syntactic and structural information. Those models are used to find the most likely combination of segmentation/recognition hypotheses proposed by a 2D segmentation scheme. Thus, models are based on structural information concerning the symbol layout. The system is tested with a new public database of mathematical expressions which was used in the \{CHROME\} competition. We have also produced a large base of semi-synthetic expressions which are used to train and test the global learning approach. We obtain very promising results on both synthetic and real expressions databases, as well as in the recent \{CHROME\} competition. }, + Comment = {http://dl.acm.org/citation.cfm?id=2543356}, + Doi = {http://dx.doi.org/10.1016/j.patrec.2012.10.024}, + File = {:/var/www/write-math/papers/a-global-learning-approach-for-an-online-handwritten-mathematical-expression-recognition-system.pdf:PDF}, + ISSN = {0167-8655}, + Keywords = {Handwriting recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.23}, + Url = {http://www.sciencedirect.com/science/article/pii/S0167865512003546} +} + +@Article{Becker72, + Title = {Pattern Recognition Using Dynamic Pictorial Information}, + Author = {Peter W. Becker AND Knud A. Nielsen}, + Journal = {Systems, Man and Cybernetics, IEEE Transactions on}, + Year = {1972}, + + Month = {July}, + Number = {3}, + Pages = {434-437}, + Volume = {SMC-2}, + + Doi = {10.1109/TSMC.1972.4309141}, + File = {:/var/www/write-math/papers/pattern-recognition-using-dynamic-pictorial-information.pdf:PDF}, + ISSN = {0018-9472}, + Keywords = {Character recognition;Computer graphics;Computer interfaces;Laboratories;Man machine systems;Pattern recognition;Postal services;Problem-solving;Sorting;Telephony}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://ieeexplore.ieee.org/xpl/abstractKeywords.jsp?arnumber=4309141} +} + +@Article{Belaid1984, + Title = {A Syntactic Approach for Handwritten Mathematical Formula Recognition}, + Author = {Belaid, Abdelwaheb and Haton, J-P}, + Journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on}, + Year = {1984}, + + Month = {Jan}, + Number = {1}, + Pages = {105-111}, + Volume = {PAMI-6}, + + Abstract = {Mathematical formulas are good examples of two-dimensional patterns as well as pictures or graphics. The use of syntactic methods is useful for interpreting such complex patterns. In this paper we propose a system for the interpretation of 2-D mathematic formulas based on a syntactic parser. This system is able to recognize a large class of 2-D mathematic formulas written on a graphic tablet. It starts the parsing by localization of the ``principal'' operator in the formula and attempts to partition it into subexpressions which are similarly analyzed by looking for a starting character. The generalized parser used in the system has been developed in our group for continuous speech recognition and picture interpretation.}, + Doi = {10.1109/TPAMI.1984.4767483}, + File = {:/var/www/write-math/papers/a-syntactic-approach-.pdf:PDF}, + ISSN = {0162-8828}, + Keywords = {Application software;Artificial intelligence;Character recognition;Graphics;Handwriting recognition;Mathematics;Partitioning algorithms;Pattern recognition;Production;Speech recognition;Graphic tablet;hand written characters;hand-drawing segmentation;mathematic formulas interpretation;primitives;structural recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.08.25} +} + +@TechReport{Bengio2009, + Title = {Learning Deep Architectures for AI}, + Author = {Yoshua Bengio}, + Institution = {Université de Montréal}, + Year = {2009}, + + File = {:var/www/write-math/papers/learining-deep-architectures-for-ai.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.17}, + Url = {http://www.iro.umontreal.ca/~lisa/pointeurs/TR1312.pdf} +} + +@Article{Bengio95, + Title = {LeRec: A NN/HMM Hybrid for On-line Handwriting Recognition}, + Author = {Bengio, Yoshua and LeCun, Yann and Nohl, Craig and Burges, Chris}, + Journal = {Neural Comput.}, + Year = {1995}, + + Month = nov, + Number = {6}, + Pages = {1289--1303}, + Volume = {7}, + + Acmid = {211711}, + Address = {Cambridge, MA, USA}, + Comment = {On-line recognition; convolution network, output of this network is put into a HMM which produces word scores "AMAP" representation that should "preserve the pictorial nature of handwriting"}, + Doi = {10.1162/neco.1995.7.6.1289}, + File = {:/var/www/write-math/papers/leRec-bengio-95.pdf:PDF}, + ISSN = {0899-7667}, + Issue_date = {Nov. 1995}, + Numpages = {15}, + Owner = {Martin Thoma}, + Publisher = {MIT Press}, + Timestamp = {2014.06.18}, + Url = {http://dx.doi.org/10.1162/neco.1995.7.6.1289} +} + +@Book{Bishop06, + Title = {Pattern Recognition and Machine Learning (Information Science and Statistics)}, + Author = {Christopher M. Bishop}, + Publisher = {Springer-Verlag New York, Inc.}, + Year = {2006}, + + Address = {Secaucus, NJ, USA}, + + Comment = {ISBN 978-0-387-31073-2}, + File = {:/var/www/write-math/papers/Pattern-Recognition-and-Machine-Learning-Christophe-M-Bishop.pdf:PDF}, + ISBN = {0387310738}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.17} +} + +@Book{bishop2007, + Title = {Pattern Recognition and Machine Learning}, + Author = {Bishop, Christopher M and others}, + Editor = {Michael Jordan}, + Publisher = {Springer Science+Business Media}, + Year = {2006}, + Volume = {1}, + + ISBN = {0387310738}, + Keywords = {algorithms machinelearning patternrecognition statistics}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.03} +} + +@InBook{Blostein, + Title = {Recognition of Mathematical Notation}, + Author = {Dorothea Blostein AND Ann Grbavec}, + Chapter = {22}, + Pages = {583--599}, + Publisher = {World Scientific Publishing Co. Pte. Ltd.}, + Year = {1997}, + + Comment = {ISBN 981-02-2270-X}, + File = {:/var/www/write-math/papers/recognition-of-mathematical-notation-blostein96recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://www.cs.ucf.edu/courses/cap5937/fall2007/readings/blostein96recognition.pdf} +} + +@Book{Concise12, + Title = {Concise Dictionary of Mathematics}, + Author = {Editorial Board}, + Editor = {unknown}, + Publisher = {V\&S Publishers}, + Year = {2012}, + + ISBN = {9789381588833}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.16}, + Url = {http://books.google.de/books?id=7OqVdc2LGSUC} +} + +@Article{Bozinovic1989, + Title = {Off-line cursive script word recognition}, + Author = {Bozinovic, R.M. and Srihari, S.N.}, + Journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on}, + Year = {1989}, + + Month = {Jan}, + Number = {1}, + Pages = {68-83}, + Volume = {11}, + + Abstract = {Cursive script word recognition is the problem of transforming a word from the iconic form of cursive writing to its symbolic form. Several component processes of a recognition system for isolated offline cursive script words are described. A word image is transformed through a hierarchy of representation levels: points, contours, features, letters, and words. A unique feature representation is generated bottom-up from the image using statistical dependences between letters and features. Ratings for partially formed words are computed using a stack algorithm and a lexicon represented as a trie. Several novel techniques for low- and intermediate-level processing for cursive script are described, including heuristics for reference line finding, letter segmentation based on detecting local minima along the lower contour and areas with low vertical profiles, simultaneous encoding of contours and their topological relationships, extracting features, and finding shape-oriented events. Experiments demonstrating the performance of the system are also described}, + Doi = {10.1109/34.23114}, + File = {:/var/www/write-math/papers/offline-cursive-script-word-recognition.pdf:PDF}, + ISSN = {0162-8828}, + Keywords = {character recognition;picture processing;statistical analysis;character recognition;feature representation;letter segmentation;lexicon;local minima;offline cursive script word recognition;stack algorithm;word image;Computer science;Encoding;Event detection;Feature extraction;Image analysis;Image segmentation;Postal services;Text recognition;Velocity measurement;Writing}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.01}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=23114} +} + +@Article{Brown83, + Title = {Preprocessing Techniques for Cursive Script Word Recognition}, + Author = {M. K. Brown and S. Ganapathy}, + Journal = {Pattern Recognition}, + Year = {1983}, + Number = {5}, + Pages = {447--458}, + Volume = {16}, + + File = {:/var/www/write-math/papers/preprocessing-techniques-for-cursive-script-word-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://deepblue.lib.umich.edu/bitstream/handle/2027.42/25418/0000867.pdf?sequence=1} +} + +@Article{Brown1964, + Title = {On-Line Computer Recognition of Handprinted Characters}, + Author = {Brown, Richard M.}, + Journal = {Electronic Computers, IEEE Transactions on}, + Year = {1964}, + + Month = {Dec}, + Number = {6}, + Pages = {750-752}, + Volume = {EC-13}, + + Abstract = {Not Available}, + Doi = {10.1109/PGEC.1964.263937}, + File = {:/var/www/write-math/papers/on-line-computer-recognition-of-handprinted-characters.pdf:PDF}, + ISSN = {0367-7508}, + Keywords = {Character recognition;Concurrent computing;Handwriting recognition;Inspection;Iterative algorithms;Labeling;Noise generators;Noise level;Parallel processing;Roads}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.01}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4038313} +} + +@InProceedings{Burges92, + Title = {Shortest path segmentation: a method for training a neural network to recognize character strings}, + Author = {Burges, C. J C and Matan, O. and Le Cun, Y. and Denker, J.S. and Jackel, L.D. and Stenard, C.E. and Nohl, C.R. and Ben, J. I.}, + Booktitle = {Neural Networks, 1992. IJCNN., International Joint Conference on}, + Year = {1992}, + Month = {Jun}, + Pages = {165-172 vol.3}, + Volume = {3}, + + Abstract = {The authors describe a method which combines dynamic programming and a neural network recognizer for segmenting and recognizing character strings. The method selects the optimal consistent combination of cuts from a set of candidate cuts generated using heuristics. The optimal segmentation is found by representing the image, the candidate segments, and their scores as a graph in which the shortest path corresponds to the optimal interpretation. The scores are given by neural net outputs for each segment. A significant advantage of the method is that the labor required to segment images manually is eliminated. The system was trained on approximately 7000 unsegmented handwritten zip codes provided by the United States Postal Service. The system has achieved a per-zip-code raw recognition rate of 81% on a 2368 handwritten zip-code test set}, + Doi = {10.1109/IJCNN.1992.227175}, + File = {:/var/www/write-math/papers/shortest-path-segmentation-a-method-for-training-a-neural-network-to-recognize-character-strings.pdf:PDF}, + Keywords = {dynamic programming;heuristic programming;image segmentation;learning (artificial intelligence);neural nets;optical character recognition;character string recognition;dynamic programming;heuristics;neural network training;optimal segmentation;postcodes;shortest path segmentation;unsegmented handwritten zip codes;Character generation;Character recognition;Computer errors;Computer science;Dynamic programming;Error correction codes;Image segmentation;Neural networks;Postal services;System testing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27} +} + +@Article{Burr1983, + Title = {Designing a Handwriting Reader}, + Author = {Burr, D.J.}, + Journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on}, + Year = {1983}, + + Month = {Sept}, + Number = {5}, + Pages = {554-559}, + Volume = {PAMI-5}, + + Abstract = {Computer recognition of cursive handwriting is complisated by the lack of letter separation. In an attempt to gain insight on the cursive problem, the simpler problem of recognizing separated hand-written letters is addressed here. A warp-based character matching technique is employed with dictionary lookup, using a 16 000 word vocabulary. Cooperative users achieve high recognition accuracy with this on-line system, which is easily tailored to the individual. Possible extensions to cursive writing are discussed.}, + Doi = {10.1109/TPAMI.1983.4767435}, + File = {:/var/www/write-math/papers/designing-a-handwriting-reader.pdf:PDF}, + ISSN = {0162-8828}, + Keywords = {Biomedical image processing;Computer errors;Handwriting recognition;Image analysis;Image processing;Iris;Logic;Pattern recognition;Public healthcare;Taxonomy;Cursive handwriting;dictionary lookup;dynamic programming;large vocabulary;polygonal curves;shape matching;text recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.30}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=4767435} +} + +@MastersThesis{Buyubayrak, + Title = {Online Handwritten Mathematical Expression Recognition}, + Author = {Hakan Buyubayrak}, + School = {Graduate School of Engineering and Natural Sciences, Sabanci University}, + Year = {2005}, + + File = {:/var/www/write-math/papers/online-handwritten-mathematical-expression-recognition.dvi:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04} +} + +@Book{Campbell08, + Title = {Biology}, + Author = {Neil A. Campbell and Jane B. Reece and Lisa A. Urry and Michael L. Cain and Steven A. Wasserman and Peter V. Minorsky and Robert B. Jackson}, + Editor = {Beth Wilbur}, + Publisher = {Pearson}, + Year = {2008}, + Edition = {8}, + + ISBN = {978-0-8053-6844-4}, + Owner = {Martin Thoma}, + Timestamp = {2014.11.04} +} + +@TechReport{Chan99, + Title = {Error Detection, Error Correction and Performance Evaluation}, + Author = {Kam-fai Chan and Dit-yan Yeung}, + Institution = {Hong Kong University of Science \& Technology}, + Year = {1999}, + + Abstract = {Automatic recognition of on-line mathematical expressions is di$cult especially when there exist errors. In this paper, we incorporate an error detection and correction mechanism into a parser developed previously by us based on de"nite clause grammar (DCG). The resulting system can handle lexical, syntactic and some semantic errors. The recognition speed for 600 commonly seen expressions is quite acceptable, ranging from 0.73 to 6 s per expression on a modest workstation. In addition, we propose a performance evaluation scheme which can be used to demonstrate the e!ectiveness of both the symbol recognition and structural analysis stages by a single measure. � 2001 Pattern}, + Booktitle = {On-Line Mathematical Expression Recognition, Pattern Recognition}, + File = {:/var/www/write-math/papers/error-detection-error-correction.pdf:PDF}, + Owner = {Martin Thoma}, + Pages = {1671168--4}, + Timestamp = {2014.06.04} +} + +@Misc{Chan, + Title = {Mathematical expression recognition: a survey}, + + Author = {Kam-Fai Chan AND Dit-Yan Yeung}, + Month = {02}, + Year = {2000}, + + File = {:/var/www/write-math/papers/mathematical-expression-recognition-a-survey.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://download.springer.com/static/pdf/846/art%253A10.1007%252FPL00013549.pdf?auth66=1402077129_0c1c3125818bb41d9c06ccecdb9985aa&ext=.pdf} +} + +@InProceedings{Dimond1958, + Title = {Devices for Reading Handwritten Characters}, + Author = {Dimond, T. L.}, + Booktitle = {Papers and Discussions Presented at the December 9-13, 1957, Eastern Joint Computer Conference: Computers with Deadlines to Meet}, + Year = {1958}, + + Address = {New York, NY, USA}, + Pages = {232--237}, + Publisher = {ACM}, + Series = {IRE-ACM-AIEE '57 (Eastern)}, + + Acmid = {1457765}, + Doi = {10.1145/1457720.1457765}, + File = {:/var/www/write-math/papers/devices-for-reading-handwritten-characters.pdf:PDF}, + Location = {Washington, D.C.}, + Numpages = {6}, + Owner = {Martin Thoma}, + Timestamp = {2014.08.14}, + Url = {http://doi.acm.org/10.1145/1457720.1457765} +} + +@Book{Duda2001, + Title = {Pattern Classification}, + Author = {Richard O. Duda AND Peter E. Hart AND David G. Stork}, + Publisher = {John Wiley \& Sons}, + Year = {2001}, + + Owner = {Martin Thoma}, + Timestamp = {2014.10.17} +} + +@Book{Ertel2009, + Title = {Grundkurs Künstliche Intelligenz: eine praxisorientierte Einführung}, + Author = {Ertel, Wolfgang}, + Editor = {Mast, Florian}, + Publisher = {Vieweg + Teubner}, + Year = {2009}, + + Address = {Wiesbaden}, + Edition = {Second}, + Number = {ISBN 978-3-8348-0783-0}, + + Abstract = {Einführung - Intelligente Agenten - Logikbasiertes Schließen - Problemlösen und Suche - Schließen mit Unsicherheit (Bayes-Netze, Methode der Maximalen Entropie) - Maschinelles Lernen - Neuronale Netze - Lernen durch Verstärkung - Lösungen zu den Übungsaufgaben}, + Added-at = {2010-02-09T21:40:24.000+0100}, + Biburl = {http://www.bibsonomy.org/bibtex/257f5840932ca168f64a89d573f43683f/kw}, + File = {:/var/www/write-math/papers/ertel-kibuch-folien.pdf:PDF}, + Interhash = {42b5abee09b26d2cd96567b7ed8b3d24}, + Intrahash = {57f5840932ca168f64a89d573f43683f}, + Keywords = {ai kuenstlicheintelligenz lecture}, + Owner = {Martin Thoma}, + Pages = {342}, + Timestamp = {2010-02-09T21:40:24.000+0100}, + Url = {http://d-nb.info/994758561} +} + +@Misc{Garain, + Title = {Recognition of Online Handwritten Mathematical Expressions}, + + Author = {Utpal Garain AND B. B. Chaudhuri}, + Month = {12}, + Year = {2004}, + + File = {:/var/www/write-math/papers/recognition-of-online-handwritten-mathematical-expressions.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01356025} +} + +@InCollection{Garcia, + Title = {Using a Generic Document Recognition Method for Mathematical Formulae Recognition}, + Author = {Pascal Garcia AND Bertrand Coüasnon}, + Booktitle = {Graphics Recognition Algorithms and Applications}, + Publisher = {Springer Berlin Heidelberg}, + Year = {2002}, + Editor = {Dorothea Blostein and Young-Bin Kwon}, + Pages = {236-244}, + Series = {Lecture Notes in Computer Science}, + Volume = {2390}, + + Doi = {10.1007/3-540-45868-9_20}, + File = {:/var/www/write-math/papers/using-a-generic-document-recognition-method-for-mathematical-formulae-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://dx.doi.org/10.1007/3-540-45868-9_20} +} + +@Misc{Genoe, + Title = {A Purely Online Approach to Mathematical Expression Recognition}, + + Author = {Ray Genoe AND John A. Fitzgerald AND Tahar Kechadi}, + Year = {2006}, + + File = {:/var/www/write-math/papers/a-purely-online-approach-to-mathematical-expression-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04} +} + +@InProceedings{Groner66, + Title = {Real-time Recognition of Handprinted Text}, + Author = {Groner, Gabriel F.}, + Booktitle = {Proceedings of the November 7-10, 1966, Fall Joint Computer Conference}, + Year = {1966}, + + Address = {New York, NY, USA}, + Pages = {591--601}, + Publisher = {ACM}, + Series = {AFIPS '66 (Fall)}, + + Acmid = {1464355}, + Doi = {10.1145/1464291.1464355}, + File = {:/var/www/write-math/papers/real-time-recognition-of-handprinted-text.pdf:PDF}, + Location = {San Francisco, California}, + Numpages = {11}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://doi.acm.org/10.1145/1464291.1464355} +} + +@InProceedings{Guerfali95, + Title = {The Delta LogNormal theory for the generation and modeling of cursive characters}, + Author = {Guerfali, W. and Plamondon, R.}, + Booktitle = {Document Analysis and Recognition, 1995., Proceedings of the Third International Conference on}, + Year = {1995}, + Month = {Aug}, + Pages = {495-498 vol.1}, + Volume = {1}, + + Abstract = {We exploit the Delta LogNormal theory, a powerful tool for the generation and modeling of rapid movements to generate curvilinear strokes and constituting letters that respect both the dynamics and the appearance of movements made by a human. A theoretical analysis of the effects of the various parameters of the model is carried out: first, to reduce the size of the representation space of the letter models; and second, to select the parameters that constitute the optimal conditions for representing various symbols}, + Doi = {10.1109/ICDAR.1995.599042}, + File = {:/var/www/write-math/papers/the-delta-lognormal-theory-for-the-generation-and-modeling-of-cursive-characters.pdf:PDF}, + Keywords = {character sets;log normal distribution;Delta LogNormal theory;constituting letters;cursive characters;curvilinear strokes;letter models;optimal conditions;representation space;Angular velocity;Character generation;Context modeling;Delay effects;Humans;Information analysis;Neuromuscular;Psychology;Shape;Timing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10}, + Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=599042} +} + +@Article{Guerfali93, + Title = {Normalizing and Restoring On-Line Handwriting}, + Author = {Wacef Guerfali AND Réjean Plamondon}, + Journal = {Pattern Recognition}, + Year = {1993}, + Number = {3}, + Pages = {419--431}, + Volume = {26}, + + Abstract = {Preprocessing and normalization techniques for on-line handwriting analysis are crucial steps that usually compromise the success of recognition algorithms. These steps are often neglected and presented as solved problems, but this is far from the truth. An overview is presented of the principal on-line techniques for handwriting preprocessing and word normalization, covering the major difficulties encountered and the various approaches usually used to resolve these problems. Some measurable definitions for handwriting characteristics are proposed, such as baseline orientation, character slant and handwriting zones. These definitions are used to measure and quantify the performance of the normalization algorithms. An approach to enhancing and restoring handwriting text is also presented, and an objective evaluation of all the processing results.}, + File = {:/var/www/write-math/papers/normalizing-and-restoring-on-line-handwriting.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10}, + Url = {http://dx.doi.org/10.1016/0031-3203(93)90169-W} +} + +@Article{Guyon91, + Title = {Design of a neural network character recognizer for a touch terminal}, + Author = {I. Guyon and P. Albrecht and Y. Le Cun and J. Denker and W. Hubbard}, + Journal = {Pattern Recognition }, + Year = {1991}, + Number = {2}, + Pages = {105 - 119}, + Volume = {24}, + + Abstract = {We describe a system which can recognize digits and uppercase letters handprinted on a touch terminal. A character is input as a sequence of [x(t), y(t)] coordinates, subjected to very simple preprocessing, and then classified by a trainable neural network. The classifier is analogous to “time delay neural networks” previously applied to speech recognition. The network was trained on a set of 12,000 digits and uppercase letters, from approximately 250 different writers, and tested on 2500 such characters from other writers. Classification accuracy exceeded 96% on the test examples.}, + Comment = {Great paper!}, + Doi = {http://dx.doi.org/10.1016/0031-3203(91)90081-F}, + File = {:/var/www/write-math/papers/design-of-a-neural-network-character-recognizer-for-a-touch-termina.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {Character recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.18}, + Url = {http://www.sciencedirect.com/science/article/pii/003132039190081F} +} + +@InProceedings{Hampshire1989, + Title = {A novel objective function for improved phoneme recognition using time delay neural networks}, + Author = {Hampshire, J.B., II and Waibel, A.H.}, + Booktitle = {Neural Networks, 1989. IJCNN., International Joint Conference on}, + Year = {1989}, + Pages = {235-241 vol.1}, + + Abstract = {The authors present single- and multispeaker recognition results for the voiced stop consonants /b, d, g/ using time-delay neural networks (TDNN), a new objective function for training these networks, and a simple arbitration scheme for improved classification accuracy. With these enhancements a median 24% reduction in the number of misclassifications made by TDNNs trained with the traditional backpropagation objective function is achieved. This redundant results in /b, d, g/ recognition rates that consistently exceed 98% for TDNNs trained with individual speakers; it yields a 98.1% recognition rate for a TDNN trained with three male speakers.<>}, + Doi = {10.1109/IJCNN.1989.118586}, + File = {:var/www/write-math/papers/a-novel-objective-function-for-improved-phoneme-recognition-using-time-delay-neural-networks.pdf:PDF}, + Keywords = {neural nets;speech recognition;arbitration scheme;classification accuracy;male speakers;misclassifications;multispeaker recognition;objective function;phoneme recognition;recognition rate;single speaker;time delay neural networks;voiced stop consonants;Neural networks;Speech recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.22}, + Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=118586} +} + +@Article{Hanaki76, + Title = {An on-line character recognition aimed at a substitution for a billing machine keyboard }, + Author = {Shin-ichi Hanaki and Tsutomu Temma and Hiroshi Yoshida}, + Journal = {Pattern Recognition }, + Year = {1976}, + Note = {Pattern Recognition Society Monographs }, + Number = {2}, + Pages = {63 - 71}, + Volume = {8}, + + Abstract = {An on-line character recognition system was developed which recognized small sized characters, whose typical height was 4 mm, with a recognition rate of 98%. The system features programming flexibility and modifying a recognition logic. It was made possible by the scheme whereby proposition-test sequences were separated into both an assembly of tree node data and test subroutines. A demonstration system was also developed which enters personal data into a computer by recognizing hand-printed characters. The whole system showed a feasible substitution for a billing machine keyboard in data entry applications. }, + Doi = {http://dx.doi.org/10.1016/0031-3203(76)90034-0}, + File = {:/var/www/write-math/papers/an-on-line-character-recognition-aimed-at-asubstitution-for-a-billing-machine-keyboard.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {On-line recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://www.sciencedirect.com/science/article/pii/0031320376900340} +} + +@Article{Hanaki80, + Title = {On-line recognition of handprinted Kanji characters}, + Author = {Shin-ichi Hanaki and Takemi Yamazaki}, + Journal = {Pattern Recognition }, + Year = {1980}, + Number = {6}, + Pages = {421 - 429}, + Volume = {12}, + + Abstract = {Difficulties in Kanji (Chinese character) recognition stem from its large character set (about 5000 characters) and the large number of strokes (up to about sixty) in each character. The paper describes a preliminary approach to this Kanji recognition problem. In the present method, a handprinted Kanji character is coded into a symbol string using the binary relation between stroke and reference zone. Two symbol string recognition methods are proposed and investigated; the direct matching recognition (DMR) method and the unit structure recognition (USR) method. The \{DMR\} method worked efficiently for characters which have up to five strokes. The \{USR\} method represents Kanji characters with a structural unit combination. This method worked efficiently for multi-stroke characters and greatly reduced dictionary update labor. }, + Doi = {http://dx.doi.org/10.1016/0031-3203(80)90018-7}, + File = {:/var/www/write-math/papers/on-line-recognition-of-handprinte-kanji-characters.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {Character recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.01}, + Url = {http://www.sciencedirect.com/science/article/pii/0031320380900187} +} + +@Article{Harmon1972, + Title = {Automatic recognition of print and script}, + Author = {Harmon, Leon D.}, + Journal = {Proceedings of the IEEE}, + Year = {1972}, + + Month = {Oct}, + Number = {10}, + Pages = {1165-1176}, + Volume = {60}, + + Abstract = {A deceptively simple kind of optical pattern recognition deals with print and script. What seemed at one time to be a fairly easy problem area in automated reading of line-like patterns has turned out to be difficult and expensive. The evolution and present state of the art of machine recognition of print and script is examined. On-hand systems relieve large amounts of human drudgery, and both theory and engineering design have advanced greatly in response to pressures caused by our paper explosion. But major problems of cost and effectiveness still exist.}, + Doi = {10.1109/PROC.1972.8878}, + File = {:/var/www/write-math/papers/automatic-recognition-of-print-and-script.pdf:PDF}, + ISSN = {0018-9219}, + Keywords = {Character recognition;Costs;Design engineering;Explosions;Humans;Optical character recognition software;Optical noise;Optical sensors;Pattern recognition;Power generation economics}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.30}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=1450808} +} + +@Book{Haykin98, + Title = {Neural Networks: A Comprehensive Foundation}, + Author = {Haykin, Simon}, + Publisher = {Prentice Hall PTR}, + Year = {1998}, + + Address = {Upper Saddle River, NJ, USA}, + Edition = {2nd}, + + Comment = {ISBN 978-0131471399}, + File = {:/var/www/write-math/papers/neural-networks-and-learning-machines-3rd_edition_contents.pdf:PDF}, + ISBN = {0132733501}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.17} +} + +@InProceedings{Hild93, + Title = {Connected Letter Recognition with a Multi-State Time Delay Neural Network}, + Author = {Hermann Hild and Alex Waibel}, + Booktitle = {In 3rd European Conference on Speech, Communication and Technology (EUROSPEECH) 93}, + Year = {1993}, + Pages = {1481--1484}, + Publisher = {Morgan Kaufman}, + + File = {:/var/www/write-math/papers/620-connected-letter-recognition-with-a-multi-state-time-delay-neural-network.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://isl.anthropomatik.kit.edu/downloads/0712-1_Kopie_.pdf} +} + +@Article{Hinton1989, + Title = {Connectionist Learning Procedures}, + Author = {Hinton, G. E.}, + Journal = {Artif. Intell.}, + Year = {1989}, + + Month = sep, + Number = {1-3}, + Pages = {185--234}, + Volume = {40}, + + Acmid = {74812}, + Address = {Essex, UK}, + Doi = {10.1016/0004-3702(89)90049-0}, + File = {:var/www/write-math/papers/connectionist-learning-procedures.pdf:PDF}, + ISSN = {0004-3702}, + Issue_date = {Sep. 1989}, + Numpages = {50}, + Owner = {Martin Thoma}, + Publisher = {Elsevier Science Publishers Ltd.}, + Timestamp = {2014.10.22}, + Url = {http://dx.doi.org/10.1016/0004-3702(89)90049-0} +} + +@InCollection{Hu1995, + Title = {Invariant features for HMM based on-line handwriting recognition}, + Author = {Hu, Jianying and Brown, MichaelK. and Turin, William}, + Booktitle = {Image Analysis and Processing}, + Publisher = {Springer Berlin Heidelberg}, + Year = {1995}, + Editor = {Braccini, Carlo and DeFloriani, Leila and Vernazza, Gianni}, + Pages = {588-593}, + Series = {Lecture Notes in Computer Science}, + Volume = {974}, + + Doi = {10.1007/3-540-60298-4_318}, + File = {:/var/www/write-math/papers/invariant-features-for-hmm-based-on-line-handwriting-recognition.pdf:PDF}, + ISBN = {978-3-540-60298-9}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.17}, + Url = {http://dx.doi.org/10.1007/3-540-60298-4_318} +} + +@InProceedings{IWFHR94, + Title = {Handwriting recognition with hidden {M}arkov models and grammatical constraints}, + Author = {Jianying Hu AND Michael K. Brown AND William Turin}, + Booktitle = {In Proceedings of the Fourth International Workshop on Frontiers in Handwriting Recognition}, + Year = {1994}, + + File = {:/var/www/write-math/papers/iwfhr94.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.30}, + Url = {http://www.bell-labs.com/user/jianhu/papers/iwfhr94.ps} +} + +@InCollection{Huang06, + Title = {An {HMM-SNN} Method for Online Handwriting Symbol Recognition}, + Author = {Huang, B.Q. and Kechadi, M.-T.}, + Booktitle = {Image Analysis and Recognition}, + Publisher = {Springer Berlin Heidelberg}, + Year = {2006}, + Editor = {Campilho, Aurélio and Kamel, Mohamed}, + Pages = {897-905}, + Series = {Lecture Notes in Computer Science}, + Volume = {4142}, + + Abstract = {This paper presents a combined approach for online handwriting symbols recognition. The basic idea of this approach is to employ a set of left-right HMMs to generate a new feature vector as input, and then use SNN as a classifier to finally identify unknown symbols. The new feature vector consists of global features and several pairs of maximum probabilities with their associated different model labels for an observation pattern. A recogniser based on this method inherits the practical and dynamical modeling abilities from HMM, and robust discriminating ability from SNN for classification tasks. This hybrid technique also reduces the dimensions of feature vectors significantly, complexity, and solves size problem when using only SNN. The experimental results show that this approach outperforms several classifiers reported in recent research, and can achieve recognition rates of 97.41%, 91.81% and 91.63% for digits and upper/lower case characters respectively on the UNIPEN database benchmarks.}, + Comment = {Seems to explain the HMM / NN approach pretty well (p. 899f) HMMs are used to generate a new (fixed-length) features for NN.}, + Doi = {10.1007/11867661_81}, + File = {:/var/www/write-math/papers/an-hmm-snn-method-for-online-handwriting-symbol-recognition.pdf:PDF}, + ISBN = {978-3-540-44894-5}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10}, + Url = {http://dx.doi.org/10.1007/11867661_81} +} + +@InCollection{Huang09, + Title = {Preprocessing Techniques for Online Handwriting Recognition}, + Author = {Huang, Bing Quan and Zhang, Y.B. and Kechadi, M.-T.}, + Booktitle = {Intelligent Text Categorization and Clustering}, + Publisher = {Springer Berlin Heidelberg}, + Year = {2009}, + Chapter = {Preprocessing Techniques for Online Handwriting Recognition}, + Editor = {Nedjah, Nadia and de Macedo Mourelle, Luiza and Kacprzyk, Janusz and França, FelipeM.G. and de De Souza, AlbertoFerreira}, + Pages = {25--45}, + Series = {Studies in Computational Intelligence}, + Volume = {164}, + + Abstract = {As a general first step in a recognition system, preprocessing plays a very important role and can directly affect the recognition performance. This Chapter proposes a new preprocessing technique for online handwriting. The approach is to first remove the hooks of the strokes by using changed-angle threshold with length threshold, then filter the noise by using a smoothing technique, which is the combination of the Cubic Spline and the equal-interpolation methods. Finally, the handwriting is normalised. Section 2.1 introduces the problems and the related techniques of the preprocessing for online handwritten data. Section 2.2 describes our preprocessing approach for online handwritten data. The experimental results with discussions are showed in Section 2.3. The summary of this chapter is given in the last section.}, + Comment = {ISBN 978-3-540-85643-6, ISBN 978-3-540-85644-3}, + Doi = {10.1007/978-3-540-85644-3_2}, + File = {:/var/www/write-math/papers/preprocessing-techniques-for-online-handwriting-recognition.pdf:PDF}, + ISBN = {978-3-540-85643-6}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.09}, + Url = {http://dx.doi.org/10.1007/978-3-540-85644-3_2} +} + +@Article{Ikeda81, + Title = {On-line recognition of hand-written characters utilizing positional and stroke vector sequences }, + Author = {Katsuo Ikeda and Takashi Yamamura and Yasumasa Mitamura and Shiokazu Fujiwara and Yoshiharu Tominaga and Takeshi Kiyono}, + Journal = {Pattern Recognition }, + Year = {1981}, + Number = {3}, + Pages = {191 - 206}, + Volume = {13}, + + Abstract = {An on-line recognition method for hand-written characters utilizing stroke vector sequences and a positional vector sequence has been developed. The number of target characters is about 2000, and fairly good recognition scores have been attained. Our scheme uses the number of strokes as the primary parameter. We employ three types of recognition strategy depending on the number of strokes. The general stroke vector sequence method, devised to analyze the shape, can represent both skeleton and local characteristics by a small amount of information; and the restricted dynamic programming method is effective to determine the shape of a stroke. The similarity of two shapes and the complexity of a stroke have been introduced to reduce the dictionary size and the processing time, respectively. }, + Doi = {http://dx.doi.org/10.1016/0031-3203(81)90096-0}, + File = {:/var/www/write-math/papers/on-line-recognition-of-hand-written-characters-utilizing-positional-and-stroke-vector-sequences.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {Recognition of hand-written characters}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://www.sciencedirect.com/science/article/pii/0031320381900960} +} + +@Article{Impedovo1976, + Title = {Real-Time Recognition of Handwritten Numerals}, + Author = {Impedovo, S. and Marangelli, B. and Plantamura, V. L.}, + Journal = {Systems, Man and Cybernetics, IEEE Transactions on}, + Year = {1976}, + + Month = {Feb}, + Number = {2}, + Pages = {145-148}, + Volume = {SMC-6}, + + Abstract = {Some experiments on the recognition of handwritten numerals are reported. A device affording real-time recognition, independent of the constraints usually required of the writer, has been used. The procedure implemented is also described.}, + Doi = {10.1109/TSMC.1976.5409186}, + File = {:/var/www/write-math/papers/real-time-recognition-of-handwritten-numerals.pdf:PDF}, + ISSN = {0018-9472}, + Keywords = {Distributed computing;Handwriting recognition;Image edge detection;Image recognition;Laboratories;Least squares methods;Logic;Physics computing;Scanning electron microscopy;Uncertainty}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.07}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5409186} +} + +@InProceedings{Manke01, + Title = {Online handwriting recognition: the {NP}en++ recognizer}, + Author = {S. Jaeger AND Stefan Manke AND J. Reichert AND Alex Waibel}, + Booktitle = {International Journal on Document Analysis and Recognition}, + Year = {2001}, + Pages = {169--180}, + + File = {:/var/www/write-math/papers/npen-art%3A10.1007%2FPL00013559.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04} +} + +@InProceedings{Manke00, + Title = {{NP}en++: An On-Line Handwriting Recognition System}, + Author = {S. Jaeger and Stefan Manke and Alex Waibel}, + Booktitle = {in 7th International Workshop on Frontiers in Handwriting Recognition}, + Year = {2000}, + Pages = {249--260}, + + File = {:/var/www/write-math/papers/npen-IWFHR_stephen1.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://isl.anthropomatik.kit.edu/cmu-kit/IWFHR_stephen1.pdf} +} + +@Misc{LaViola, + Title = {MathPad: A System for the Creation and Exploration of Mathematical Sketches}, + + Author = {Joseph J. LaViola Jr. AND Robert C. Zeleznik}, + Year = {2004}, + + File = {:/var/www/write-math/papers/mathpad.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://www.cs.uml.edu/~holly/teaching/91550/spring2011/LaViola-Jr-2004.pdf} +} + +@InProceedings{Khotanzad, + Title = {Hand Written Digit Recognition Using Combination of Neural Network Classifiers}, + Author = {A. Khotanzad and C. Chung}, + Booktitle = {Image Analysis and Interpretation, 1998 IEEE Southwest Symposium on}, + Year = {1998}, + Month = {4}, + Pages = {168-173}, + + Abstract = {A new classification scheme for handwritten digit recognition is proposed. The method is based on combining the decisions of two multi-layer perceptron (MLP) artificial neural network classifiers operating on two different feature types. The first feature set is defined on the pseudo Zernike moments of the image whereas the second feature type is derived from the shadow code of the image using a newly defined projection mask. A MLP network is employed to perform the combination task. The performance is tested on a data base of 15000 samples and the advantage of the combination approach is demonstrated.}, + Doi = {10.1109/IAI.1998.666880}, + File = {:/var/www/write-math/papers/handwritten-digit-recognition-using-combination-of-neural-network-classifiers.pdf:PDF}, + Keywords = {character recognition;feature extraction;image classification;multilayer perceptrons;artificial neural network;decision combination;feature set;handwritten digit recognition;image classification scheme;multilayer perceptron;neural network classifiers;projection mask;pseudo Zernike moments;shadow code;Artificial neural networks;Feature extraction;Feedforward systems;Handwriting recognition;Multilayer perceptrons;Neural networks;Pattern classification;Pattern recognition;Shape;Testing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=666880} +} + +@MastersThesis{Kirsch, + Title = {Detexify: Erkennung handgemalter {L}a{T}e{X}-Symbole}, + Author = {Daniel Kirsch}, + School = {Westfälische Wilhelms-Universität Münster}, + Year = {2010}, + Month = {10}, + Type = {Diploma thesis}, + + File = {:/var/www/write-math/papers/detexify-thesis.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://danielkirs.ch/thesis.pdf} +} + +@InProceedings{Koschinski95, + Title = {Segmentation and recognition of symbols within handwritten mathematical expressions}, + Author = {Koschinski, M. and Winkler, H.-J. and Lang, M.}, + Booktitle = {Acoustics, Speech, and Signal Processing, 1995. ICASSP-95., 1995 International Conference on}, + Year = {1995}, + Month = {May}, + Pages = {2439-2442 vol.4}, + Volume = {4}, + + Abstract = {An efficient on-line recognition system for symbols within handwritten mathematical expressions is proposed. The system is based on the generation of a symbol hypotheses net and the classification of the elements within the net. The final classification is done by calculating the most probable path through the net under regard of the stroke group probabilities and the probabilities obtained by the symbol recognizer based on hidden Markov models}, + Doi = {10.1109/ICASSP.1995.479986}, + File = {:/var/www/write-math/papers/segmentation-and-recognition-of-symbols-within-handwritten-mathematical-expressions.pdf:PDF}, + ISSN = {1520-6149}, + Keywords = {handwriting recognition;hidden Markov models;image classification;mathematics;probability;classification;handwritten mathematical expressions;hidden Markov models;most probable path;on-line recognition system;stroke group probabilities;symbol hypotheses net;symbol recognizer;Data preprocessing;Electronic switching systems;Handwriting recognition;Hidden Markov models;Probability;Smoothing methods;Writing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.12} +} + +@InProceedings{Kosmala98, + Title = {Recognition Of On-Line Handwritten Formulas}, + Author = {Andreas Kosmala and Gerhard Rigoll}, + Booktitle = {In Proceedings of the Sixth International Workshop on Frontiers in Handwriting Recognition}, + Year = {1998}, + Pages = {219--228}, + + Doi = {10.1.1.41.9056}, + File = {:/var/www/write-math/papers/iwfhr98_formula.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.12}, + Url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.9056} +} + +@InProceedings{Kosmala11, + Title = {On-Line Handwritten Formula Recognition using Hidden {M}arkov Models and Context Dependent Graph Grammars}, + Author = {Andreas Kosmala AND Gerhard Rigoll AND Stéphane Lavirotte AND Lo¨ıc Pottier}, + Booktitle = {Proceedings of the Fifth Internation Conference on Document Analysis and Recognition ({ICDAR})}, + Year = {1999}, + Pages = {107--110}, + + File = {:/var/www/write-math/papers/online-handwritten-formula-recognition-using-hidden-markov-models-and-cdgg-kosmala-rigoll-etal_1999.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://hal.inria.fr/docs/00/56/46/45/PDF/kosmala-rigoll-etal_1999.pdf} +} + +@InProceedings{MacLean06, + Title = {A preliminary report on the MathBrush pen-math system}, + Author = {George Labahn AND Scott MacLean AND Mirette Marzouk AND Ian Rutherford AND David Tausky}, + Booktitle = {Maple 2006 Conference}, + Year = {2006}, + Pages = {162--178}, + + File = {:/var/www/write-math/papers/math-brush-paper.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://cs.uwaterloo.ca/~glabahn/Papers/MathBrush-1.pdf} +} + +@Misc{Lagaris1997, + Title = {Artificial Neural Networks for Solving Ordinary and Partial Differential Equations}, + + Author = {I. E. Lagaris and A. Likas and D. I. Fotiadis}, + HowPublished = {arXiv:physics/9705023v1}, + Month = {05}, + Year = {1997}, + + Eprint = {arXiv:physics/9705023}, + File = {:var/www/write-math/papers/artificial-neural-networks-for-solving-ordinary-and-partial-differential-equations.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.22}, + Url = {http://arxiv.org/abs/physics/9705023} +} + +@MastersThesis{Lapointe, + Title = {Issues in Performance Evaluation of Mathematical Notation Recognition Systems}, + Author = {Adrien Lapointe}, + School = {School of Computing, Queen’s University, Kingston, Ontario, Canada}, + Year = {2008}, + Month = {05}, + + File = {:/var/www/write-math/papers/issues-in-performance-evaluation-of-mathematical-notation-recognition-systems.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.23}, + Url = {https://qspace.library.queensu.ca/bitstream/1974/1218/1/Lapointe_Adrien_200805_MSc.pdf} +} + +@InProceedings{Lapointe2009, + Title = {Issues in Performance Evaluation: A Case Study of Math Recognition}, + Author = {Lapointe, A and Blostein, D.}, + Booktitle = {10th International Conference on Document Analysis and Recognition, 2009. ICDAR '09.}, + Year = {2009}, + Month = {July}, + Pages = {1355-1359}, + + Abstract = {Performance evaluation of document recognition systems is a difficult and practically important problem. Issues arise in defining requirements, in characterizing the systempsilas range of inputs and outputs, in interpreting published performance evaluation results, in reproducing performance evaluation experiments, in choosing training and test data, and in selecting performance metrics. We discuss these issues in the context of evaluating systems for recognition of mathematical expressions. Excellent progress has been made in the theory and practice of performance evaluation, but many open problems remain.}, + Doi = {10.1109/ICDAR.2009.247}, + File = {:/var/www/write-math/papers/issues-in-performance-evaluation-a-case-study-of-math-recognition.pdf:PDF}, + ISSN = {1520-5363}, + Keywords = {document image processing;software metrics;software performance evaluation;document recognition system;mathematical expression recognition;performance evaluation;performance metrics selection;Measurement;Performance analysis;Performance evaluation;Scattering;Software design;System testing;Text analysis;Typesetting;Uncertainty;User interfaces;performance evaluation;recognition of math notation}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.23} +} + +@Article{Li98, + Title = {Segmentation and reconstruction of on-line handwritten scripts}, + Author = {Xiaolin Li and Marc Parizeau and Réjean Plamondon}, + Journal = {Pattern Recognition }, + Year = {1998}, + Number = {6}, + Pages = {675 - 684}, + Volume = {31}, + + Abstract = {On-line handwritten scripts consist of sequences of components that are pen tip traces from pen-down to pen-up positions. This paper presents a segmentation and reconstruction procedure which segments components of a script into sequences of static strokes, and then reconstructs the script from these sequences. The segmentation is based on the extrema of curvature and inflection points in individual components. The static strokes are derived from the delta log-normal model of handwriting generation and are used in component representation and reconstruction. The performance of the procedure is measured in terms of root-mean-square reconstruction error and data compression rate. }, + Doi = {http://dx.doi.org/10.1016/S0031-3203(97)00086-1}, + File = {:/var/www/write-math/papers/segmentation-and-reconstruction-of-on-line-handwritten-scripts.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {Delta log-normal model}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10}, + Url = {http://www.sciencedirect.com/science/article/pii/S0031320397000861} +} + +@Article{Lindgren1965, + Title = {Machine recognition of human language Part III - Cursive script recognition}, + Author = {Lindgren, Nilo}, + Journal = {Spectrum, IEEE}, + Year = {1965}, + + Month = {May}, + Number = {5}, + Pages = {104-116}, + Volume = {2}, + + Abstract = {Not Available}, + Doi = {10.1109/MSPEC.1965.5212951}, + File = {:/var/www/write-math/papers/machine-recognition-of-human-language-iii.pdf:PDF}, + ISSN = {0018-9235}, + Keywords = {Assembly;Automatic speech recognition;Character recognition;Handwriting recognition;Human factors;Ink;Optical character recognition software;Pattern recognition;Speech recognition;Writing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.30}, + Url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5212951} +} + +@MastersThesis{Littin95, + Title = {Mathematical expression recognition: Parsing pen/tablet input in real-time using LR techniques.}, + Author = {Richard Henry Littin}, + School = {University of Waikato}, + Year = {1995}, + Month = {3}, + + Owner = {Martin Thoma}, + Timestamp = {2014.06.06} +} + +@Book{Lodish08, + Title = {Molecular Cell Biology}, + Author = {Harvey Lodish and Arnold Berk and Chris A. Kaiser and Monty Krieger and Matthew P. Scott and Anthony Bretscher and Hidde Ploegh and Paul Matsudaira}, + Editor = {Katherine Ahr}, + Publisher = {W. H. Freeman and Company}, + Year = {2008}, + Edition = {6}, + + ISBN = {978-0-7167-7601-7}, + Owner = {Martin Thoma}, + Timestamp = {2014.11.04} +} + +@Misc{Loosli2005, + Title = {Training Invariant Support Vector Machines using Selective Sampling}, + + Author = {Gaëlle Loosli and Stéphane Canu and Léon Bottou}, + Year = {2005}, + + Abstract = {(author?) [3] describe the efficient online LASVM algorithm using selective sampling. On the other hand, (author?) [24] propose a strategy for handling invariance in SVMs, also using selective sampling. This paper combines the two approaches to build a very large SVM. We present state-of-the-art results obtained on a handwritten digit recognition problem with 8 millions points on a single processor. This work also demonstrates that online SVMs can effectively handle really large databases.}, + Doi = {10.1.1.104.7028}, + File = {:/var/www/write-math/papers/training-invariant-svms-using-selective-sampling.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.02}, + Url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.7028} +} + +@TechReport{MacLean10, + Title = {Recognizing handwritten mathematics via fuzzy parsing}, + Author = {Scott MacLean AND George Labahn}, + Institution = {School of Computer Science, University of Waterloo}, + Year = {2010}, + + File = {:/var/www/write-math/papers/math-reco.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://cs.uwaterloo.ca/~smaclean/math-reco.pdf} +} + +@Misc{MacLean10fuzzy, + Title = {A new approach for recognizing handwritten mathematics using relational grammars and fuzzy sets}, + + Author = {Scott MacLean and George Labahn}, + Month = {07}, + Year = {2010}, + + Abstract = {We present a new approach for parsing two- dimensional input using relational grammars and fuzzy sets. A fast, incremental parsing algorithm is devel- oped, motivated by the two-dimensional structure of written mathematics. The approach reports all identifi- able parses of the input. The parses are represented as a fuzzy set, in which the membership grade of a parse measures the similarity between it and the handwrit- ten input. To identify and report parses efficiently, we adapt and apply existing techniques such as rectangular partitions and shared parse forests, and introduce new ideas such as relational classes and interchangeability. We also present a correction mechanism which allows users to navigate parse results and choose the correct interpretation in case of recognition errors or ambigu- ity. Such corrections are incorporated into subsequent incremental recognition results. Finally, we include two empirical evaluations of our recognizer. One uses a novel user-oriented correction count metric, while the other replicates the CROHME 2011 math recognition con- test. Both evaluations demonstrate the effectiveness of our proposed approach.}, + Doi = {10.1007/s10032-012-0184-x}, + File = {:/var/www/write-math/papers/fuzzy-parsing.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://cs.uwaterloo.ca/~glabahn/Papers/fuzzy.pdf} +} + +@InCollection{Manke95, + Title = {The Use of Dynamic Writing Information in a Connectionist On-Line Cursive Handwriting Recognition System}, + Author = {Stefan Manke and Michael Finke and Alex Waibel}, + Booktitle = {Advances in Neural Information Processing Systems 7}, + Publisher = {MIT Press}, + Year = {1995}, + Editor = {G. Tesauro and D.S. Touretzky and T.K. Leen}, + Pages = {1093--1100}, + + Abstract = {In this paper we present NPen ++ , a connectionist system for writer independent, large vocabulary on-line cursive handwriting recognition. This system combines a robust input representation, which preserves the dynamic writing information, with a neural network architecture, a so called Multi-State Time Delay Neural Network (MS-TDNN), which integrates recognition and segmentation in a single framework. Our preprocessing transforms the original coordinate sequence into a (still temporal) sequence of feature vectors, which combine strictly local features, like curvature or writing direction, with a bitmap-like representation of the coordinate 's proximity. The MS-TDNN architecture is well suited for handling temporal sequences as provided by this input representation. Our system is tested both on writer dependent and writer independent tasks with vocabulary sizes ranging from 400 up to 20,000 words. For example, on a 20,000 word vocabulary we achieve word recognition rates up to 88.9%...}, + File = {:/var/www/write-math/papers/908-the-use-of-dynamic-writing-information-in-a-connectionist-on-line-cursive-handwriting-recognition-system.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://isl.anthropomatik.kit.edu/cmu-kit/downloads/The_Use_of_Dynamic_Writing_Information_in_a_Connectionist_On-Line_Cursive_Handwriting_Recognition_System(3).pdf} +} + +@Misc{Manke96, + Title = {A Fast Search Technique for Large Vocabulary On-Line Handwriting Recognition}, + + Author = {Stefan Manke and Michael Finke and Alex Waibel}, + Year = {1996}, + + Abstract = {State-of-the-art on-line handwriting recognition systems should be able to handle dictionary sizes of at least 25,000 words or more to be useful for real-world applications. Using dictionaries of this size requires fast search techniques to achieve reasonable recognition times. In this paper we present a search approach yielding recognition times, which are virtually independent of the dictionary size. This approach combines a tree representation of the dictionary with efficent pruning techniques to reduce the search space without loosing much recognition performance compared to a flat exhaustive search through all words in the dictionary. The tree search with pruning is about 15 times faster than a flat search and allows us to run the NPen++ on-line handwriting recognition system in real-time with dictionary sizes up to 100,000 words.}, + File = {:/var/www/write-math/papers/npen-CP_1996_01_A_Fast_Search_Technique_for_Large_Vocabulary_On-Line_Handwriting_Recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://isl.anthropomatik.kit.edu/cmu-kit/downloads/CP_1996_01_A_Fast_Search_Technique_for_Large_Vocabulary_On-Line_Handwriting_Recognition.pdf} +} + +@InProceedings{Manke94, + Title = {Combining Bitmaps with Dynamic Writing Information for On-Line Handwriting Recognition}, + Author = {Stefan Manke and Michael Finke and Alex Waibel}, + Booktitle = {Proceedings of the ICPR-94}, + Year = {1994}, + Pages = {596--598}, + + Abstract = {Writer independent, large vocabulary on-line handwriting recognition systems require robust input representations, which make optimal use of the dynamic writing information, i.e. the temporal ordering of the sampled data points. In this paper we describe an input representation for cursive handwriting, which combines this dynamic writing information with static bitmaps used in optical character recognition. This input representation is used with a connectionist recognizer, which is well suited for handling temporal sequences of patterns as provided by this kind of input representation. Our system has been tested on different cursive handwriting recognition tasks with vocabulary sizes up to 20000 words. We achieve recognition rates up to 99.5% on writer independent, single character recognition tasks and up to 98.1% on writer dependent, cursive handwriting tasks. 1 Introduction Several different preprocessing techniques both for optical character recognition (OCR) and on-line character...}, + File = {:/var/www/write-math/papers/1994_Combining_Bitmaps_With_Dynamic_Writing_Information_For_On-Line_Handwriting_Recognition_Reihenfolge.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04} +} + +@InProceedings{Martin1971, + Title = {Computer Input/Output of Mathematical Expressions}, + Author = {Martin, William A.}, + Booktitle = {Proceedings of the Second ACM Symposium on Symbolic and Algebraic Manipulation}, + Year = {1971}, + + Address = {New York, NY, USA}, + Pages = {78--89}, + Publisher = {ACM}, + Series = {SYMSAC '71}, + + Acmid = {806270}, + Doi = {10.1145/800204.806270}, + File = {:/var/www/write-math/papers/computer-input-output-of-mathematical-expressions.pdf:PDF}, + Location = {Los Angeles, California, USA}, + Numpages = {12}, + Owner = {Martin Thoma}, + Timestamp = {2014.08.25}, + Url = {http://doi.acm.org/10.1145/800204.806270} +} + +@Article{McCulloch1943, + Title = {A logical calculus of the ideas immanent in nervous activity}, + Author = {McCulloch, Warren S. and Pitts, Walter}, + Journal = {The bulletin of mathematical biophysics}, + Year = {1943}, + Number = {4}, + Pages = {115-133}, + Volume = {5}, + + Doi = {10.1007/BF02478259}, + File = {:var/www/write-math/papers/a-logical-calculus-of-the-ideas-immanent-in-nervous-activity.pdf:PDF}, + ISSN = {0007-4985}, + Language = {English}, + Owner = {Martin Thoma}, + Publisher = {Kluwer Academic Publishers}, + Timestamp = {2014.10.22}, + Url = {http://dx.doi.org/10.1007/BF02478259} +} + +@Book{Mitchell97, + Title = {Machine learning}, + Author = {Tom M. Mitchell}, + Publisher = {McGraw-Hill}, + Year = {1997}, + Series = {McGraw Hill series in computer science}, + + Bibsource = {DBLP, http://dblp.uni-trier.de}, + Comment = {ISBN: 0-07-042807-7}, + File = {:/var/www/write-math/papers/machine-learning-tom-mitchell.pdf:PDF}, + ISBN = {978-0-07-042807-2}, + Owner = {Martin Thoma}, + Pages = {I-XVII, 1-414}, + Timestamp = {2014.06.17} +} + +@InProceedings{Mitoma05, + Title = {Online character recognition based on elastic matching and quadratic discrimination}, + Author = {Mitoma, H. and Uchida, S. and Sakoe, H.}, + Booktitle = {Eighth International Conference on Document Analysis and Recognition, 2005.}, + Year = {2005}, + Month = {Aug}, + Pages = {36-40 Vol. 1}, + + Abstract = {We try to link elastic matching with a statistical discrimination framework to overcome the overfitting problem which often degrades the performance of elastic matching-based online character recognizers. In the proposed technique, elastic matching is used just as an extractor of a feature vector representing the difference between input and reference patterns. Then quadratic discrimination is performed under the assumption that the feature vector is governed by a Gaussian distribution. The result of a recognition experiment on UNIPEN database (Train-R01/V07, 1a) showed that the proposed technique can attain a high recognition rate (97.95%) and outperforms a recent elastic matching-based recognizer.}, + Doi = {10.1109/ICDAR.2005.178}, + File = {:/var/www/write-math/papers/online-character-recognition-based-on-elastic-matching-and-quadratic-discrimination.pdf:PDF}, + ISSN = {1520-5263}, + Keywords = {Gaussian distribution;feature extraction;handwritten character recognition;pattern matching;statistical analysis;Gaussian distribution;UNIPEN database;elastic matching;feature vector;online character recognition;overfitting problem;quadratic discrimination;statistical discrimination framework;Character recognition;Cost function;Covariance matrix;Degradation;Gaussian distribution;Hidden Markov models;Optimal matching;Pattern matching;Pattern recognition;Spatial databases}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27} +} + +@TechReport{Moreira95, + Title = {Neural Networks with Adaptive Learning Rate and Momentum Terms}, + Author = {Miguel Moreira and Emile Fiesler}, + Institution = {Institut Dalle Molle D’Intelligence Artificielle Perceptive}, + Year = {1995}, + + Address = {Martigny, Switzerland}, + Month = {10}, + Note = {CASE POSTALE 609 - 1920 MARTIGNY - VALAIS - SUISSE TELEPHONE : ++41 26 22.76.64 - FAX : ++41 26 22.78.18 E-MAIL : IDIAP@IDIAP.CH}, + Number = {Idiap-RR-04-1995}, + + File = {:/var/www/write-math/papers/idiap-technical-report-neural-networks-with-adaptive-learning-rate-and-momentum-terms.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.16}, + Url = {http://publications.idiap.ch/index.php/publications/show/124} +} + +@InProceedings{Morita02, + Title = {An HMM-MLP hybrid system to recognize handwritten dates}, + Author = {Morita, M. and Oliveira, L.S. and Sabourin, R. and Bortolozzi, F. and Suen, C.Y.}, + Booktitle = {IJCNN '02. Proceedings of the 2002 International Joint Conference on Neural Networks, 2002.}, + Year = {2002}, + Pages = {867-872}, + Volume = {1}, + + Abstract = {Presents an HMM-MLP hybrid system to process complex date images written on Brazilian bank cheques. The system first segments implicitly a date image into sub-fields through the recognition process based on an HMM approach. Afterwards, a recognition and verification strategy is proposed to recognize the three obligatory date sub-fields (day, month and year) using different classifiers. Markovian and neural approaches have been adopted to recognize and verify words and strings of digits respectively. We also introduce the concept of meta-classes of digits, which is used to reduce the lexicon size of the day and year and improve the precision of their segmentation and recognition. Experiments show interesting results on date recognition}, + Doi = {10.1109/IJCNN.2002.1005588}, + File = {:/var/www/write-math/papers/an-hmm-mlp-hybrid-system-to-recognize-handwritten-dates.pdf:PDF}, + ISSN = {1098-7576}, + Keywords = {handwritten character recognition;hidden Markov models;image segmentation;multilayer perceptrons;Brazilian bank cheques;HMM-MLP hybrid system;complex date images;handwritten dates recognition;lexicon size;segmentation;verification strategy;Character recognition;Cities and towns;Handwriting recognition;Hidden Markov models;Image analysis;Image recognition;Image segmentation;Machine intelligence;Particle separators;Text recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10} +} + +@InProceedings{Mouchere2012, + Title = {ICFHR 2012 Competition on Recognition of On-Line Mathematical Expressions (CROHME 2012)}, + Author = {Mouchere, H. and Viard-Gaudin, C. and Kim, D.H. and Kim, J.H. and Garain, U.}, + Booktitle = {International Conference on Frontiers in Handwriting Recognition (ICFHR), 2012}, + Year = {2012}, + Month = {Sept}, + Pages = {811--816}, + + Abstract = {This paper presents an overview of the second Competition on Recognition of Online Handwritten Mathematical Expressions, CROHME 2012. The objective of the contest is to identify current advances in mathematical expression recognition using common evaluation performance measures and datasets. This paper describes the contest details including the evaluation measures used as well as the performance of the 7 submitted systems along with a short description of each system. Progress as compared to the 1st version of CROHME is also documented.}, + Doi = {10.1109/ICFHR.2012.215}, + File = {:/var/www/write-math/papers/Mouchere2012_CROHME.pdf:PDF}, + Keywords = {handwritten character recognition;mathematics computing;CROHME 2012;Competition on Recognition of Online Handwritten Mathematical Expressions;evaluation performance measure;mathematical expression recognition;Handwriting recognition;Competition;Math Recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.09.26}, + Url = {http://hal.archives-ouvertes.fr/docs/00/71/78/50/PDF/Mouchere2012_CROHME.pdf} +} + +@InProceedings{Mouchere2011, + Title = {CROHME2011: Competition on Recognition of Online Handwritten Mathematical Expressions}, + Author = {Mouchere, H. and Viard-Gaudin, C. and Dae Hwan Kim and Jin Hyung Kim and Garain, U.}, + Booktitle = {International Conference on Document Analysis and Recognition (ICDAR), 2011}, + Year = {2011}, + Month = {Sept}, + Pages = {1497--1500}, + + Abstract = {A competition on recognition of online handwritten mathematical expressions is organized. Recognition of mathematical expressions has been an attractive problem for the pattern recognition community because of the presence of enormous uncertainties and ambiguities as encountered during parsing of the two-dimensional structure of expressions. The goal of this competition is to bring out a state of the art for the related research. Three labs come together to organize the event and six other research groups participated the competition. The competition defines a standard format for presenting information, provides a training set of 921 expressions and supplies the underlying grammar for understanding the content of the training data. Participants were invited to submit their recognizers which were tested with a new set of 348 expressions. Systems are evaluated based on four different aspects of the recognition problem. However, the final rating of the systems is done based on their correct expression recognition accuracies. The best expression level recognition accuracy (on the test data) shown by the competing systems is 19.83% whereas a baseline system developed by one of the organizing groups reports an accuracy 22.41% on the same data set.}, + Comment = {ISSN: 1520-5363}, + Doi = {10.1109/ICDAR.2011.297}, + Keywords = {handwriting recognition;handwritten character recognition;pattern recognition;expression level recognition accuracy;mathematical expression recognition;online handwritten recognition;pattern recognition;Accuracy;Communities;Grammar;Handwriting recognition;Ink;Organizing;Training;Mathematical expressions;Online handwriting;evaluation;symbol recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.09.26}, + Url = {http://hal.archives-ouvertes.fr/docs/00/61/52/16/PDF/CROHME_CRC511.pdf} +} + +@InProceedings{Mouchere2013, + Title = {{ICDAR} 2013 {CROHME}: Third International Competition on Recognition of Online Handwritten Mathematical Expressions}, + Author = {Mouchere, H. and Viard-Gaudin, C. and Zanibbi, R. and Garain, U. and Dae Hwan Kim and Jin Hyung Kim}, + Booktitle = {12th International Conference on Document Analysis and Recognition (ICDAR), 2013}, + Year = {2013}, + Month = {Aug}, + Pages = {1428-1432}, + + Abstract = {We report on the third international Competition on Handwritten Mathematical Expression Recognition (CROHME), in which eight teams from academia and industry took part. For the third CROHME, the training dataset was expanded to over 8000 expressions, and new tools were developed for evaluating performance at the level of strokes as well as expressions and symbols. As an informal measure of progress, the performance of the participating systems on the CROHME 2012 data set is also reported. Data and tools used for the competition will be made publicly available.}, + Doi = {10.1109/ICDAR.2013.288}, + File = {:/var/www/write-math/papers/CROHME2013.pdf:PDF}, + ISSN = {1520-5363}, + Keywords = {handwritten character recognition;mathematics computing;CROHME 2012 data set;ICDAR 2013 CROHME;online handwritten mathematical expression recognition;performance evaluation;training dataset;Grammar;Handwriting recognition;Layout;Mathematical model;Training;Training data;competition;evaluation metric;mathematical expression recognition;on-line handwrting recongition}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.03}, + Url = {http://www.isical.ac.in/~crohme/CROHME2013.pdf} +} + +@InProceedings{Ng2004, + Title = {Feature Selection, L1 vs. L2 Regularization, and Rotational Invariance}, + Author = {Ng, Andrew Y.}, + Booktitle = {Proceedings of the Twenty-first International Conference on Machine Learning}, + Year = {2004}, + + Address = {New York, NY, USA}, + Pages = {78--}, + Publisher = {ACM}, + Series = {ICML '04}, + + Acmid = {1015435}, + Doi = {10.1145/1015330.1015435}, + File = {:var/www/write-math/papers/feature-selection-l1-vs-l2-regularization-and-rotational-invariance.pdf:PDF}, + ISBN = {1-58113-838-5}, + Location = {Banff, Alberta, Canada}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.23}, + Url = {http://doi.acm.org/10.1145/1015330.1015435} +} + +@Article{1982, + Title = {On-Line Recognition of Handwritten Characters by Approximating Each Stroke with Several Points}, + Author = {Kazumi Odaka and Hiroki Arakawa and Isao Masuda}, + Journal = {Systems, Man and Cybernetics, IEEE Transactions on}, + Year = {1982}, + + Month = {Nov}, + Number = {6}, + Pages = {898-903}, + Volume = {12}, + + Doi = {10.1109/TSMC.1982.4308924}, + File = {:/var/www/write-math/papers/on-line-recognition-of-handwritten-characters-by-approximating-each-stroke-with-several-points.pdf:PDF}, + ISSN = {0018-9472}, + Keywords = {Character recognition;Decision trees;Handwriting recognition;Information processing;Interpolation;Noise measurement;Observability;Pattern recognition;Speech recognition;Testing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27} +} + +@Article{Powers1973, + Title = {Pen direction sequences in character recognition }, + Author = {V. Michael Powers}, + Journal = {Pattern Recognition }, + Year = {1973}, + Number = {4}, + Pages = {291 - 302}, + Volume = {5}, + + Abstract = {A descriptive, generative model of the pen direction sequences measured during the hand drawing of characters is shown to be useful in recognition. Preprocessing and classification procedures are based on the properties of the model. Results are presented from tests with a realization of these methods as a real time recognition system running in a small computer. }, + Doi = {http://dx.doi.org/10.1016/0031-3203(73)90022-8}, + File = {:/var/www/write-math/papers/pen-direction-sequences-in-character-recognition.pdf:PDF}, + ISSN = {0031-3203}, + Keywords = {Descriptive model}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.07}, + Url = {http://www.sciencedirect.com/science/article/pii/0031320373900228} +} + +@InProceedings{Rabiner89, + Title = {A Tutorial on Hidden {M}arkov Models and Selected Applications in Speech Recognition}, + Author = {Lawrence R. Rabiner}, + Booktitle = {PROCEEDINGS OF THE IEEE}, + Year = {1989}, + Month = {2}, + Number = {2}, + Pages = {257--286}, + Volume = {77}, + + File = {:/var/www/write-math/papers/a-tutorial-on-hidden-markov-models-and-selected-applications-in-speech-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.10}, + Url = {http://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf} +} + +@Article{Rosenblatt58, + Title = {The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain}, + Author = {Frank Rosenblatt}, + Journal = {Psychological Review}, + Year = {1958}, + Number = {6}, + Pages = {386--408}, + Volume = {65}, + + Booktitle = {Brain Theory}, + Doi = {10.1007/978-3-642-70911-1_20}, + Editor = {Palm, Günther and Aertsen, Ad}, + ISBN = {978-3-642-70913-5}, + Language = {English}, + Owner = {Martin Thoma}, + Publisher = {Springer Berlin Heidelberg}, + Timestamp = {2014.10.22}, + Url = {http://dx.doi.org/10.1007/978-3-642-70911-1_20} +} + +@Book{Russell04, + Title = {Künstliche Intelligenz. Ein moderner Ansatz}, + Author = {Russell, Stuart J. and Norvig, Peter}, + Publisher = {Pearson Studium}, + Year = {2004}, + Edition = {2., überarb. A.}, + + Added-at = {2010-09-09T13:26:52.000+0200}, + Asin = {3827370892}, + Biburl = {http://www.bibsonomy.org/bibtex/2390ffc27ec121f3f153cd77418b2d8d6/kw}, + Description = {Amazon.de: Künstliche Intelligenz. Ein moderner Ansatz: Bücher: Stuart J. Russell,Peter Norvig}, + Ean = {9783827370891}, + File = {:/var/www/write-math/papers/kuenstliche-intelligenz-norvig.pdf:PDF}, + Interhash = {0e204744acacd79a68a874a3babd0695}, + Intrahash = {390ffc27ec121f3f153cd77418b2d8d6}, + ISBN = {3827370892}, + Keywords = {ai bought ki künstlicheintelligenz}, + Owner = {Martin Thoma}, + Timestamp = {2010-09-09T13:26:52.000+0200}, + Url = {http://www.amazon.de/gp/redirect.html%3FASIN=3827370892%26tag=ws%26lcode=xm2%26cID=2025%26ccmID=165953%26location=/o/ASIN/3827370892%253FSubscriptionId=13CT5CVB80YFWJEPWS02} +} + +@InProceedings{ICASSP-94, + Title = {On-Line Cursive Script Recognition using Time Delay Neural Networks and Hidden {M}arkov Models}, + Author = {M. Schenkely and I. Guyonz and D. Hendersonz}, + Booktitle = {1994 IEEE International Conference on Acoustics, Speech, and Signal Processing.}, + Year = {1994}, + Month = {4}, + Pages = {637--640}, + Volume = {ii}, + + Comment = {ISSN 1520-6149}, + Doi = {10.1109/ICASSP.1994.389575}, + File = {:/var/www/write-math/papers/on_line_cursive_script_recognition_using_time_delay_neural_networks.pdf:PDF}, + Keywords = {backpropagation;character recognition;delays;feature extraction;feedforward neural nets;hidden Markov models;multilayer perceptrons;natural language interfaces;search problems;a posteriori probabilities;cursive script;dictionary search;feature vectors;geometrical normalization scheme;global word score;hand-print;handwriting recognition;hidden Markov models;online cursive script recognition;pen trajectory information;shared weight;time delay neural networks;touch sensitive pad;unconstrained cursive words;word dictionary;writer independent system;Character recognition;Computer aided manufacturing;Computer interfaces;Delay effects;Dictionaries;Handwriting recognition;Hidden Markov models;Keyboards;Neural networks;Writing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.16}, + Url = {http://pdf.aminer.org/003/076/160/on_line_cursive_script_recognition_using_time_delay_neural_networks.pdf} +} + +@InProceedings{Schoelkopf1996, + Title = {Incorporating Invariances in Support Vector Learning Machines}, + Author = {Bernhard Schölkopf and Chris Burges and Vladimir Vapnik}, + Booktitle = {Artificial Neural Networks -- ICANN 96}, + Year = {1996}, + Editor = {von der Malsburg, Christoph and von Seelen, Werner and Vorbrüggen, JanC. and Sendhoff, Bernhard}, + Pages = {47--52}, + Publisher = {Springer Berlin Heidelberg}, + Series = {Lecture Notes in Computer Science}, + Volume = {1112}, + + Doi = {10.1007/3-540-61510-5_12}, + File = {:/var/www/write-math/papers/incorporating-invariances-in-svms.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.02}, + Url = {http://link.springer.com/chapter/10.1007/3-540-61510-5_12} +} + +@InProceedings{Shah07, + Title = {Handwritten Digit Recognition Using Image Processing and Neural Networks}, + Author = {Faisal Tehseen Shah AND Kamran Yousaf}, + Booktitle = {Proceedings of the World Congress on Engineering 2007 Vol I}, + Year = {2007}, + Month = {7}, + Organization = {International Association of Engineers}, + Pages = {648--651}, + Publisher = {Newswood Limited}, + Volume = {1}, + + File = {:/var/www/write-math/papers/handwritten-digit-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://www.iaeng.org/publication/WCE2007/WCE2007_pp648-651.pdf} +} + +@Article{Shlens2014, + Title = {A Tutorial on Principal Component Analysis}, + Author = {Jonathon Shlens}, + Journal = {CoRR}, + Year = {2014}, + Volume = {abs/1404.1100}, + + Abstract = {Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. This manuscript crystallizes this knowledge by deriving from simple intuitions, the mathematics behind PCA. This tutorial does not shy away from explaining the ideas informally, nor does it shy away from the mathematics. The hope is that by addressing both aspects, readers of all levels will be able to gain a better understanding of PCA as well as the when, the how and the why of applying this technique.}, + Bibsource = {dblp computer science bibliography, http://dblp.org}, + Biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/Shlens14}, + File = {:/var/www/write-math/papers/a-tutorial-on-pricipal-component-analysis.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {Fri, 03 Oct 2014 10:36:32 +0200}, + Url = {http://arxiv.org/abs/1404.1100} +} + +@InProceedings{Smithies99, + Title = {A Handwriting-based Equation Editor}, + Author = {Smithies, Steve and Novins, Kevin and Arvo, James}, + Booktitle = {Proceedings of the 1999 Conference on Graphics Interface '99}, + Year = {1999}, + + Address = {San Francisco, CA, USA}, + Pages = {84--91}, + Publisher = {Morgan Kaufmann Publishers Inc.}, + + Abstract = {Current equation editing systems rely on either textbased equation description languages or on interactive construction by means of structure templates and menus. These systems are often tedious to use, even for experts, because the user is forced to "parse" the expressions mentally before they are entered. This step is not normally part of the process of writing equations on paper or on a whiteboard. We describe a prototype equation editor that is based on handwriting recognition and automatic equation parsing. It is coupled with a user interface that incorporates a set of simple procedures for correcting errors made by the automatic interpretation. Although some correction by the user is typically necessary before the formula is recognized, we have found that the system is simpler and more natural to use than systems based on specialized languages or template-based interaction.}, + Acmid = {351660}, + File = {:/var/www/write-math/papers/a-handwriting-based-equation-editor.pdf:PDF}, + ISBN = {1-55860-632-7}, + Keywords = {equation editing, equation parsing, handwriting recognition, human-computer interaction, pen-based computing, pen-based input}, + Location = {Kingston, Ontario, Canada}, + Numpages = {8}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://dl.acm.org/citation.cfm?id=351631.351660} +} + +@Book{Division87, + Title = {Speed, Accuracy, Flexibility Trade-offs in On-line Character Recognition}, + Author = {C. C. Tappert}, + Publisher = {IBM T.J. Watson Research Center}, + Year = {1987}, + Series = {Research report}, + + File = {:/var/www/write-math/papers/speed-accuracy-and-flexibility-trade-offs-in-online-character-recognition.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.27}, + Url = {http://books.google.com/books?id=5br\_HAAACAAJ} +} + +@Article{Tappert2007, + Title = {English language handwriting recognition interfaces}, + Author = {Charles C. Tappert and Sung-Hyuk Cha}, + Journal = {Text entry systems: Mobility, accessibility, universality}, + Year = {2007}, + Pages = {123--137}, + + File = {:/var/www/write-math/papers/english-language-handwriting-recognition-interfaces.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.07.02}, + Url = {http://csis.pace.edu/ctappert/papers/handwriting-chapter6.pdf} +} + +@Article{Tappert90, + Title = {The State of the Art in Online Handwriting Recognition}, + Author = {Tappert, C. C. and Suen, C. Y. and Wakahara, T.}, + Journal = {IEEE Trans. Pattern Anal. Mach. Intell.}, + Year = {1990}, + + Month = {8}, + Number = {8}, + Pages = {787--808}, + Volume = {12}, + + Acmid = {83137}, + Address = {Washington, DC, USA}, + Comment = {http://kanjiteacher.googlecode.com/svn/Non-Code/Papers/HWR/tappert1990_pen-tappert_TheStateArtHandWriting.pdf This article sums up work done before. It is explicitly about on-line handwriting recognition}, + Doi = {10.1109/34.57669}, + File = {:/var/www/write-math/papers/tappert1990_pen-tappert_TheStateArtHandWriting.pdf:PDF}, + ISSN = {0162-8828}, + Issue_date = {August 1990}, + Keywords = {character recognition, digitizer technology, offline recognition, online handwriting recognition, postprocessing, preprocessing, shape recognition, user interfaces}, + Numpages = {22}, + Owner = {Martin Thoma}, + Publisher = {IEEE Computer Society}, + Timestamp = {2014.06.17}, + Url = {http://dx.doi.org/10.1109/34.57669} +} + +@InProceedings{Thombre, + Title = {Neural Network Approach to Recognize Online Handwriting Script}, + Author = {Deepali Thombre and Toran Verma}, + Booktitle = {IJECT}, + Year = {2011}, + Number = {4}, + Volume = {2}, + + Abstract = {Online handwriting recognition of English script is a difficult problem since it is naturally both cursive and unconstrained The analysis of English script is further complicated in comparison to Latin script due to obligatory dots/stokes that are placed above or below most letters. This paper introduces a kohonen neural network (KNN). We want to do single character recognition using a Kohonen neural network fed by down sampled images to accomplish this task.}, + Comment = {ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)}, + File = {:/var/www/write-math/papers/neural-network-approach-to-recognize-online-handwriting-script.pdf:PDF}, + Keywords = {Neural Network}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.18}, + Url = {http://iject.org/archives/vol-2-issue-4/} +} + +@InProceedings{Toyozumi, + Title = {A System for Real-time Recognition of Handwritten Mathematical Formulas}, + Author = {Kenichi Toyozumi AND Takahiro Suzuki}, + Booktitle = {Document Analysis and Recognition, 2001. Proceedings. Sixth International Conference on}, + Year = {2001}, + Pages = {1059--1063}, + + Doi = {10.1109/ICDAR.2001.953948}, + File = {:/var/www/write-math/papers/a-system-for-real-time-recognition-of-handwritten-mathematical-formulas.pdf:PDF}, + Keywords = {computer peripheral equipment;handwritten character recognition;mathematics computing;real-time systems;user interfaces;LATEX source code;data tablet;handwritten mathematical formulas;matrix structures;real-time recognition;Application software;Character recognition;Graphical user interfaces;Handwriting recognition;Keyboards;Mice;Real time systems;Target recognition;Typesetting;Writing}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {http://ir.nul.nagoya-u.ac.jp/jspui/bitstream/2237/6867/1/newsystemfor_1059.pdf} +} + +@InProceedings{Vincent2008, + Title = {Extracting and Composing Robust Features with Denoising Autoencoders}, + Author = {Vincent, Pascal and Larochelle, Hugo and Bengio, Yoshua and Manzagol, Pierre-Antoine}, + Booktitle = {Proceedings of the 25th International Conference on Machine Learning}, + Year = {2008}, + + Address = {New York, NY, USA}, + Pages = {1096--1103}, + Publisher = {ACM}, + Series = {ICML '08}, + + Acmid = {1390294}, + Doi = {10.1145/1390156.1390294}, + File = {:var/www/write-math/papers/extracting-and-composing-robust-features-with-denoising-autoencoders.pdf:PDF}, + ISBN = {978-1-60558-205-4}, + Location = {Helsinki, Finland}, + Numpages = {8}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.22}, + Url = {http://doi.acm.org/10.1145/1390156.1390294} +} + +@InProceedings{Vinyals2011, + Title = {Comparing multilayer perceptron to Deep Belief Network Tandem features for robust ASR}, + Author = {Vinyals, O. and Ravuri, S.V.}, + Booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on}, + Year = {2011}, + Month = {May}, + Pages = {4596-4599}, + + Abstract = {In this paper, we extend the work done on integrating multilayer perceptron (MLP) networks with HMM systems via the Tandem approach. In particular, we explore whether the use of Deep Belief Networks (DBN) adds any substantial gain over MLPs on the Aurora2 speech recognition task under mismatched noise conditions. Our findings suggest that DBNs outperform single layer MLPs under the clean condition, but the gains diminish as the noise level is increased. Furthermore, using MFCCs in conjunction with the posteriors from DBNs outperforms merely using single DBNs in low to moderate noise conditions. MFCCs, however, do not help for the high noise settings.}, + Doi = {10.1109/ICASSP.2011.5947378}, + File = {:var/www/write-math/papers/comparing-mlp-to-deep-belief-network-tandem-features-for-robust-asr.pdf:PDF}, + ISSN = {1520-6149}, + Keywords = {belief networks;hidden Markov models;multilayer perceptrons;speech recognition;DBN;HMM system;MLP network;belief network tandem feature;deep belief network;mismatched noise conditions;multilayer perceptron;robust ASR;speech recognition;Accuracy;Mel frequency cepstral coefficient;Noise measurement;Signal to noise ratio;Speech recognition;Training;Automatic Speech Recognition;Deep Belief Network;Multilayer Perceptron}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.17}, + Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5947378} +} + +@InProceedings{Visvalingam1990, + Title = {The Douglas-Peucker Algorithm for Line Simplification: Re-evaluation through Visualization}, + Author = {Visvalingam, Mahes and Whyatt, J Duncan}, + Booktitle = {Computer Graphics Forum}, + Year = {1990}, + Number = {3}, + Organization = {Wiley Online Library}, + Pages = {213--225}, + Volume = {9}, + + File = {:var/www/write-math/papers/speeding-up-the-douglas-peucker-line-simplification-algorithm.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.22}, + Url = {http://www.bowdoin.edu/~ltoma/teaching/cs350/spring06/Lecture-Handouts/hershberger92speeding.pdf} +} + +@InProceedings{Wiesler2014, + Title = {RASR/NN: The RWTH neural network toolkit for speech recognition}, + Author = {Wiesler, S. and Richard, A. and Golik, P. and Schluter, R. and Ney, H.}, + Booktitle = {Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on}, + Year = {2014}, + Month = {May}, + Pages = {3281-3285}, + + Abstract = {This paper describes the new release of RASR - the open source version of the well-proven speech recognition toolkit developed and used at RWTH Aachen University. The focus is put on the implementation of the NN module for training neural network acoustic models. We describe code design, configuration, and features of the NN module. The key feature is a high flexibility regarding the network topology, choice of activation functions, training criteria, and optimization algorithm, as well as a built-in support for efficient GPU computing. The evaluation of run-time performance and recognition accuracy is performed exemplary with a deep neural network as acoustic model in a hybrid NN/HMM system. The results show that RASR achieves a state-of-the-art performance on a real-world large vocabulary task, while offering a complete pipeline for building and applying large scale speech recognition systems.}, + Doi = {10.1109/ICASSP.2014.6854207}, + File = {:var/www/write-math/papers/rasrnn-the-rwth-neural-network-toolkit-for-speech-recognition.pdf:PDF}, + Keywords = {graphics processing units;hidden Markov models;neural nets;optimisation;public domain software;speech recognition;telecommunication computing;telecommunication network topology;GPU computing;NN module;RASR-NN;RWTH Aachen University;RWTH neural network toolkit;activation functions;code configuration;code design;code features;hybrid NN-HMM system;network topology;open source version;optimization;run-time performance;speech recognition;training criteria;training neural network acoustic models;Acoustics;Graphics processing units;Hidden Markov models;Neural networks;Speech;Speech recognition;Training;GPU;RASR;acoustic modeling;neural networks;open source;speech recognition}, + Owner = {Martin Thoma}, + Timestamp = {2014.10.17}, + Url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6854207} +} + +@InProceedings{Zanibbi01, + Title = {Aiding Manipulation of Handwritten Mathematical Expressions through Style-Preserving Morphs}, + Author = {Katherine Zanibbi and Kevin Novins and James Arvo}, + Booktitle = {In Proceedings of Graphics Interface 2001}, + Year = {2001}, + Pages = {127--134}, + + Abstract = {We describe a technique for enhancing a user's ability to manipulate hand-printed symbolic information by automatically improving legibility and simultaneously providing immediate feedback on the system's current structural interpretation of the information. Our initial application is a handwriting-based equation editor. Once the user has written a formula, the individual hand-drawn symbols can be gradually translated and scaled to closely approximate their relative positions and sizes in a corresponding typeset version. These transformations preserve the characteristics, or style, of the original userdrawn symbols. In applying this style-preserving morph, the system improves the legibility of the user-drawn symbols by correcting alignment and scaling, and also reveals the baseline structure of the symbols that has been inferred by system. We performed a preliminary user study that indicates that this new method of feedback is a useful addition to a conventional interpretive interface. We believe this is because the style preserving morph makes it easier to understand the correspondence between the original input and interpreted output than methods that radically change the appearance of the original input. Key words: formula entry, math recognition, mental map, morphing, pen-based computing, user feedback. 1}, + File = {:/var/www/write-math/papers/aiding-manipulation-of-handwritten-math-expressions-through-style-preserving-morphs.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://ritdml.rit.edu/bitstream/handle/1850/7922/RZanibbiConfProc06-2001.pdf?sequence=1} +} + +@Misc{Blostein02, + Title = {Recognizing Mathematical Expressions Using Tree Transformation}, + + Author = {Richard Zanibbi AND Dorothea Blostein}, + Month = {11}, + Year = {2002}, + + File = {:/var/www/write-math/papers/recognizing-mathematical-expressions-using-tree-transfromations.pdf:PDF}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://ritdml.rit.edu/bitstream/handle/1850/7732/RZanibbiArticle11-2002.pdf?sequence=1&origin=publication_detail} +} + +@InProceedings{Blostein01, + Title = {Baseline Structure Analysis of Handwritten Mathematics Notation}, + Author = {Richard Zanibbi AND Dorothea Blostein AND James R. Cordy}, + Booktitle = {Sixth International Conference on Document Analysis and Recognition.}, + Year = {2001}, + Pages = {768--773}, + + Doi = {10.1109/ICDAR.2001.953892}, + File = {:/var/www/write-math/papers/baseline-structure-analysis-of-handwritten-mathematics-notation.pdf:PDF}, + Keywords = {grammars;handwritten character recognition;trees (mathematics);baseline structure analysis;dialects;handwritten mathematics notation;handwritten notation;image partitioning;mathematics notation;nested baselines;parsing;robust method;search functions;semantics;syntax;tree transformations;typeset mathematics;Handwriting recognition;Image analysis;Image converters;Image recognition;Information science;Mathematics;Minimization methods;Robustness;Stochastic processes;Typesetting}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.04}, + Url = {https://ritdml.rit.edu/bitstream/handle/1850/7906/RZanibbiConfProc09-2001.pdf?sequence=6} +} + +@Other{Deeplearning, + Title = {Deep Learning… moving beyond shallow machine learning since 2006!}, + Owner = {Martin Thoma}, + Timestamp = {2014.06.17}, + Url = {http://www.deeplearning.net/tutorial/} +} + +@Misc{Deeplearning-Denoising-AE, + Title = {Denoising Autoencoders (dA)}, + + Owner = {Martin Thoma}, + Timestamp = {2014.10.23}, + Url = {http://deeplearning.net/tutorial/dA.html} +} + +@Misc{deeplearningweights, + Title = {Going from logistic regression to MLP}, + + Owner = {Martin Thoma}, + Timestamp = {2014.10.30}, + Url = {http://www.deeplearning.net/tutorial/mlp.html#going-from-logistic-regression-to-mlp} +} + +@Misc{newbob-icis, + Title = {The training performed by qnstrn}, + Month = {08}, + Year = {2000}, + + Owner = {Martin Thoma}, + Timestamp = {2014.10.17}, + Url = {http://www1.icsi.berkeley.edu/Speech/faq/nn-train.html} +} + +@Misc{Thoma:2014, + Title = {On-line Recognition of Handwritten Mathematical Symbols}, + + Author = {Martin Thoma}, + Month = nov, + Year = {2014}, + School = "Karlsruhe Institute of Technology", + Address = "Karlsruhe, Germany", + Type = "{B.S. Thesis}", + + Keywords = {handwriting recognition; on-line; machine learning; + artificial neural networks; mathematics; classification; + supervised learning; MLP; multilayer perceptrons; hwrt; + write-math}, + Timestamp = {2014.06.07}, + Url = {http://martin-thoma.com/write-math} +} \ No newline at end of file diff --git a/documents/write-math-ba-paper/write-math-ba-paper.tex b/documents/write-math-ba-paper/write-math-ba-paper.tex new file mode 100644 index 0000000..f10cd3f --- /dev/null +++ b/documents/write-math-ba-paper/write-math-ba-paper.tex @@ -0,0 +1,313 @@ +\documentclass[9pt,technote]{IEEEtran} +\usepackage{amssymb, amsmath} % needed for math +\usepackage{hyperref} % links im text +\usepackage{parskip} +\usepackage{csquotes} +\usepackage{braket} +\usepackage[noadjust]{cite} +\usepackage[nameinlink,noabbrev]{cleveref} % has to be after hyperref, ntheorem, amsthm +\usepackage[binary-units]{siunitx} +\sisetup{per-mode=fraction,binary-units=true} +\DeclareSIUnit\pixel{px} +\usepackage{glossaries} +\loadglsentries[main]{glossary} +\makeglossaries + +\title{On-line Recognition of Handwritten Mathematical Symbols} +\author{Martin Thoma} + +\hypersetup{ + pdfauthor = {Martin Thoma}, + pdfkeywords = {Mathematics,Symbols,recognition}, + pdftitle = {On-line Recognition of Handwritten Mathematical Symbols} +} +\include{variables} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Begin document % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} +\maketitle +\begin{abstract} +Writing mathematical formulas with \LaTeX{} is easy as soon as one is used to +commands like \verb+\alpha+ and \verb+\propto+. However, for people who have +never used \LaTeX{} or who don't know the English name of the command, it can +be difficult to find the right command. Hence the automatic recognition of +handwritten mathematical symbols is desirable. This paper presents a system +which uses the pen trajectory to classify handwritten symbols. Five +preprocessing steps, one data multiplication algorithm, five features and five +variants for multilayer Perceptron training were evaluated using $\num{166898}$ +recordings which were collected with two crowdsourcing projects. The evaluation +results of these 21~experiments were used to create an optimized recognizer +which has a TOP1 error of less than $\SI{17.5}{\percent}$ and a TOP3 error of +$\SI{4.0}{\percent}$. This is an improvement of $\SI{18.5}{\percent}$ for the +TOP1 error and $\SI{29.7}{\percent}$ for the TOP3 error compared to the +baseline system. +\end{abstract} + +\section{Introduction} +On-line recognition makes use of the pen trajectory. This means the data is +given as groups of sequences of tuples $(x, y, t) \in \mathbb{R}^3$, where +each group represents a stroke, $(x, y)$ is the position of the pen on a canvas +and $t$ is the time. One handwritten symbol in the described format is called +a \textit{recording}. Recordings can be classified by making use of +this data. One classification approach assigns a probability to each class +given the data. The classifier can be evaluated by using recordings which +were classified by humans and were not used by to train the classifier. The +set of those recordings is called \textit{testset}. Then +the TOP-$n$ error is defined as the fraction of the symbols where the correct +class was not within the top $n$ classes of the highest probability. + +Various systems for mathematical symbol recognition with on-line data have been +described so far~\cite{Kosmala98,Mouchere2013}, but most of them have neither +published their source code nor their data which makes it impossible to re-run +experiments to compare different systems. This is unfortunate as the choice of +symbols is cruicial for the TOP-$n$ error. For example, the symbols $o$, $O$, +$\circ$ and $0$ are very similar and systems which know all those classes will +certainly have a higher TOP-$n$ error than systems which only accept one of +them. + +Daniel Kirsch describes in~\cite{Kirsch} a system which uses time warping to +classify on-line handwritten symbols and claimes to achieve a TOP3 error of +less than $\SI{10}{\percent}$ for a set of $\num{100}$~symbols. He also +published his data, which was collected by a crowd-sourcing approach via +\url{http://detexify.kirelabs.org}, on +\url{https://github.com/kirel/detexify-data}. Those recordings as well as +some recordings which were collected by a similar approach via +\url{http://write-math.com} were used to train and evaluated different +classifiers. A complete description of all involved software, data, +presentations and experiments is listed in~\cite{Thoma:2014}. + +\section{Steps in Handwriting Recognition} +The following steps are used in all classifiers which are described in the +following: + +\begin{enumerate} + \item \textbf{Preprocessing}: Recorded data is never perfect. Devices have + errors and people make mistakes while using devices. To tackle + these problems there are preprocessing algorithms to clean the data. + The preprocessing algorithms can also remove unnecessary variations of + the data that do not help classify but hide what is important. + Having slightly different sizes of the same symbol is an example of such a + variation. Nine preprocessing algorithms that clean or normalize + recordings are explained in + \cref{sec:preprocessing}. + \item \textbf{Data multiplication}: Learning algorithms need lots of data + to learn internal parameters. If there is not enough data available, + domain knowledge can be considered to create new artificial data from + the original data. In the domain of on-line handwriting recognition + data can be multiplied by adding rotated variants. + \item \textbf{Segmentation}: The task of formula recognition can eventually + be reduced to the task of symbol recognition combined with symbol + placement. Before symbol recognition can be done, the formula has + to be segmented. As this paper is only about single-symbol + recognition, this step will not be further discussed. + \item \textbf{Feature computation}: A feature is high-level information + derived from the raw data after preprocessing. Some systems like + Detexify, which was presented in~\cite{Kirsch}, simply take the + result of the preprocessing step, but many compute new features. This + might have the advantage that less training data is needed since the + developer can use knowledge about handwriting to compute highly + discriminative features. Various features are explained in + \cref{sec:features}. + \item \textbf{Feature enhancement}: Applying PCA, LDA, or + feature standardization might change the features in ways that could + improve the performance of learning algorithms. +\end{enumerate} + +After these steps, we are faced with a classification learning task which consists of +two parts: +\begin{enumerate} + \item \textbf{Learning} parameters for a given classifier. This process is + also called \textit{training}. + \item \textbf{Classifying} new recordings, sometimes called + \textit{evaluation}. This should not be confused with the evaluation + of the classification performance which is done for multiple + topologies, preprocessing queues, and features in \Cref{ch:Evaluation}. +\end{enumerate} + +Two fundamentally different systems for classification of time series data were +evaluated. One uses greedy time warping, which has a very easy, fast learning +algorithm which only stores some of the seen training examples. The other one is +based on neural networks, taking longer to train, but is much faster in +recognition and also leads to better recognition results. + +\section{Algorithms} +\subsection{Preprocessing}\label{sec:preprocessing} +Preprocessing in symbol recognition is done to improve the quality and +expressive power of the data. It should make follow-up tasks like segmentation +and feature extraction easier, more effective or faster. It does so by resolving +errors in the input data, reducing duplicate information and removing irrelevant +information. + +The preprocessing algorithms fall in two groups: Normalization and noise +reduction algorithms. + +The most important normalization algorithm in single-symbol recognition is +\textit{scale-and-shift}. It scales the recording so that +its bounding box fits into a unit square. As the aspect ratio of a recording +is almost never 1:1, only one dimension will fit exactly in the unit square. +Then there are multiple ways how to shift the recording. For this paper, it was +chosen to shift the bigger dimension to fit into the $[0,1] \times [0,1]$ unit +square whereas the smaller dimension is centered in the $[-1,1] \times [-1,1]$ +square. + +Another normalization preprocessing algorithm is resampling. As the data points +on the pen trajectory are generated asynchronously and with different +time-resolutions depending on the used hardware and software, it is desirable +to resample the recordings to have points spread equally in time for every +recording. This was done with linear interpolation of the $(x,t)$ and $(y,t)$ +sequences and getting a fixed number of equally spaced samples. + +\textit{Connect strokes} is a noise reduction algorithm. It happens sometimes +that the hardware detects that the user lifted the pen where he certainly +didn't do so. This can be detected by measuring the distance between the end of +one stroke and the beginning of the next stroke. If this distance is below a +threshold, then the strokes are connected. + +Due to a limited resolution of the recording device and due to erratic +handwriting, the pen trajectory might not be smooth. One way to smooth is +calculating a weighted average and replacing points by the weighted average of +their coordinate and their neighbors coordinates. Another way to do smoothing +would be to reduce the number of points with the Douglas-Peucker algorithm to +the most relevant ones and then interpolate those points. The Douglas-Peucker +stroke simplification algorithm is usually used in cartography to simplify the +shape of roads. The Douglas-Peucker algorithm works recursively to find a +subset of control points of a stroke that is simpler and still similar to the +original shape. The algorithm adds the first and the last point $p_1$ and $p_n$ +of a stroke to the simplified set of points $S$. Then it searches the control +point $p_i$ in between that has maximum distance from the \gls{line} $p_1 p_n$. +If this distance is above a threshold $\varepsilon$, the point $p_i$ is added +to $S$. Then the algorithm gets applied to $p_1 p_i$ and $p_i p_n$ recursively. +Pseudocode of this algorithm is on \cpageref{alg:douglas-peucker}. It is +described as \enquote{Algorithm 1} in~\cite{Visvalingam1990} with a different +notation. + +\subsection{Features}\label{sec:features} +Features can be global, that means calculated for the complete recording or +complete strokes. Other features are calculated for single points on the +pen trajectory and are called \textit{local}. + +Global features are the \textit{number of strokes} in a recording, the +\textit{aspect ratio} of the bounding box of a recordings bounding box or the +\textit{ink} being used for a recording. The ink feature gets calculated by +measuring the length of all strokes combined. The re-curvature, which was +introduced in~\cite{Huang06}, is defined as +\[\text{re-curvature}(stroke) := \frac{\text{height}(stroke)}{\text{length}(stroke)}\] +and a stroke-global feature. + +The most important local feature is the coordinate of the point itself. +Speed, curvature and a local small-resolution bitmap around the point, which +was introduced by Manke et al. in~\cite{Manke94} are other local features. + +\subsection{Multilayer Perceptrons}\label{sec:mlp-training} +\Glspl{MLP} are explained in detail in~\cite{Mitchell97}. They can have +different numbers of hidden layers, the number of neurons per layer and the +activation functions can be varied. The learning algorithm is parameterized by +the learning rate $\eta$, the momentum $\alpha$ and the number of epochs. The +learning of \glspl{MLP} can be executed in various different ways, for example +with layer-wise supversided pretraining which means if a three layer \gls{MLP} +of the topology $160:500:500:500:369$ should get trained, at first a \gls{MLP} +with one hidden layer ($160:500:369$) is trained. Then the output layer is +discarded, a new hidden layer and a new output layer is added and it is trained +again. Then we have a $160:500:500:369$ \gls{MLP}. The output layer is +discarded again, a new hidden layer is added and a new output layer is added +and the training is executed again. + +\section{Evaluation}\label{ch:Evaluation} +In order to evaluate the effect of different preprocessing algorithms, features +and adjustments in the \gls{MLP} training and topology, the following baseline +system was used: + +Scale the recording to fit into a unit square while keeping the aspect ratio, +shift it into $[-1,1] \times [-1,1]$ as described in \cref{sec:preprocessing}, +resample it with linear interpolation to get 20~points per stroke, spaced +evenly in time. Take the first 4~strokes with 20~points per stroke and +2~coordinates per point as features, resulting in 160~features which is equal +to the number of input neurons. If a recording has less than 4~strokes, the +remaining features were filled with zeroes. + +All experiments were evaluated with four baseline systems $B_i$, $i \in \Set{1, +2, 3, 4}$, where $i$ is the number of hidden layers as different topologies +could have a severe influence on the effect of new features or preprocessing +steps. Each hidden layer in all evaluated systems has $500$ neurons. + +Each \gls{MLP} was trained with a learning rate of $\eta = 0.1$ and a momentum +of $\alpha = 0.1$. The activation function of every neuron is + +%TODO: Evaluation randomnes +%TODO: + +\section{Conclusion} +The aim of this bachelor's thesis was to build a recognition system that +can recognize many mathematical symbols with low error rates as well as to +evaluate which preprocessing steps and features help to improve the recognition +rate. + +All recognition systems were trained and evaluated with +$\num{\totalCollectedRecordings{}}$ recordings for \totalClassesAnalyzed{} +symbols. These recordings were collected by two crowdsourcing projects +(\href{http://detexify.kirelabs.org/classify.html}{Detexify} and +\href{write-math.com}{write-math.com}) and created with various devices. While +some recordings were created with standard touch devices such as tablets and +smartphones, others were created with the mouse. + +\Glspl{MLP} were used for the classification task. Four baseline systems with +different numbers of hidden layers were used, as the number of hidden layer +influences the capabilities and problems of \glspl{MLP}. Furthermore, an error +measure MER was defined, which takes the top three \glspl{hypothesis} of the classifier, +merges symbols such as \verb+\sum+ ($\sum$) and \verb+\Sigma+ ($\Sigma$) to +equivalence classes, and then calculates the error. + +All baseline systems used the same preprocessing queue. The recordings were +scaled to fit into a unit square, shifted to $(0,0)$, resampled with linear +interpolation so that every stroke had exactly 20~points which are spread +equidistant in time. The 80~($x,y$) coordinates of the first 4~strokes were used +to get exactly $160$ input features for every recording. The baseline systems +$B_2$ has a MER error of $\SI{5.67}{\percent}$. + +Three variations of the scale and shift algorithm, wild point filtering, stroke +connect, weighted average smoothing, and Douglas-Peucker smoothing were +evaluated. The evaluation showed that the scale and shift algorithm is extremely +important and the connect strokes algorithm improves the classification. All +other preprocessing algorithms either diminished the classification performance +or had less influence on it than the random initialization of the \glspl{MLP} +weights. + +Adding two slightly rotated variants for each recording and hence tripling the +training set made the systems $B_3$ and $B_4$ perform much worse, but improved +the performance of the smaller systems. + +The global features re-curvature, ink, stoke count and aspect ratio improved the +systems $B_1$--$B_3$, whereas the stroke center point feature made $B_2$ perform +worse. + +The learning rate and the momentum were evaluated. A learning rate of $\eta=0.1$ +and a momentum of $\alpha=0.9$ gave the best results. Newbob training lead to +much worse recognition rates. Denoising auto-encoders were evaluated as one way +to use pretraining, but by this the error rate increased notably. However, +supervised layer-wise pretraining improved the performance decidedly. + +The stroke connect algorithm was added to the preprocessing steps of the +baseline system as well as the re-curvature feature, the ink feature, the number +of strokes and the aspect ratio. The training setup of the baseline system was +changed to supervised layer-wise pretraining and the resulting model was trained +with a lower learning rate again. This optimized recognizer $B_{2,c}'$ had a MER +error of $\SI{3.96}{\percent}$. This means that the MER error dropped by over +$\SI{30}{\percent}$ in comparison to the baseline system $B_2$. + +A MER error of $\SI{3.96}{\percent}$ makes the system usable for symbol lookup. +It could also be used as a starting point for the development of a +multiple-symbol classifier. + +The aim of this bachelor's thesis was to develop a symbol recognition system +which is easy to use, fast and has high recognition rates as well as evaluating +ideas for single symbol classifiers. Some of those goals were reached. The +recognition system $B_{2,c}'$ evaluates new recordings in a fraction of a second +and has acceptable recognition rates. Many variations algorithms were evaluated. +However, there are still many more algorithms which could be evaluated and, at +the time of this work, the best classifier $B_{2,c}'$ is not publicly available. + +\bibliographystyle{IEEEtranSA} +\bibliography{write-math-ba-paper} +\end{document}