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min: A Multimodal Web Interface for Math Search
"... min is a web interface for constructing search queries that include mathematics, using the metaphor of an ‘intelligent’ blackboard. Formulas are entered using a combination of finger/mouse, keyboard, and images, with symbol recognition results shown using translucent overlays above the user’s input. ..."
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min is a web interface for constructing search queries that include mathematics, using the metaphor of an ‘intelligent’ blackboard. Formulas are entered using a combination of finger/mouse, keyboard, and images, with symbol recognition results shown using translucent overlays above the user’s input. At the user’s request, the blackboard is converted to LATEX and inserted in the query string, and the user’s symbols are repositioned and resized on the blackboard to visualize the recognized layout of symbols on baselines (writing lines). Queries may include keywords and multiple LATEX expressions, and be submitted to a variety of search engines (e.g. Springer LATEX Search, Wolfram Alpha). min allows nonexpert users to include math expressions in queries without special codes for mathematical symbols, providing text describing a formula, or requiring the use of a templatebased equation editor.
Segmenting Handwritten Math Symbols Using AdaBoost and MultiScale Shape Context Features
"... Abstract—This paper presents a new symbol segmentation method based on AdaBoost with confidence weighted predictions for online handwritten mathematical expressions. The handwritten mathematical expression is preprocessed and rendered to an image. Then for each stroke, we compute three kinds of shap ..."
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Abstract—This paper presents a new symbol segmentation method based on AdaBoost with confidence weighted predictions for online handwritten mathematical expressions. The handwritten mathematical expression is preprocessed and rendered to an image. Then for each stroke, we compute three kinds of shape context features (stroke pair, local neighborhood and global shape contexts) with different scales, 21 stroke pair geometric features and symbol classification scores for the current stroke and stroke pair. The stroke pair shape context features covers the current stroke and the following stroke in time series. The local neighborhood shape context features includes the current stroke and its three nearest neighbor strokes in distance while the global shape context features covers the expression. Principal component analysis (PCA) is used for dimensionality reduction. We use AdaBoost with confidence weighted predictions for classification. The method does not use any language model. To our best knowledge, there is no previous work which uses shape context features for symbol segmentation. Experiment results show the new symbol segmentation method achieves good recall and precision on the CROHME 2012 dataset. I.
Combining TFIDF Text Retrieval with an Inverted Index over Symbol Pairs in Math Expressions: The Tangent Math Search Engine at NTCIR 2014
"... We report on the system design and NTCIRMath2 task results for the Tangent mathaware search engine. Tangent uses a federated search over two indices: 1) a TFIDF textual search engine (Lucene), and 2) a querybyexpression engine. Querybyexpression is performed using a bagofwords approach wh ..."
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We report on the system design and NTCIRMath2 task results for the Tangent mathaware search engine. Tangent uses a federated search over two indices: 1) a TFIDF textual search engine (Lucene), and 2) a querybyexpression engine. Querybyexpression is performed using a bagofwords approach where expressions are represented by pairs of symbols computed from symbol layout trees (e.g. as expressed in LATEX or Presentation MathML). Extensions to support matrices and prefix subscripts and superscripts are described. Our system produced the highest highly + partially relevant Precision@5 result for the main text/math query task (92%), and the highest Top1 specificitem recall for the Wikipedia querybyexpression subtask (68%). The current implementation is slow and produces large indices for large corpora, but we believe this can be ameliorated. Source code for our system is publicly available.
Rendering Expressions to Improve Accuracy of Relevance Assessment for Math Search
"... Finding ways to help users assess relevance when they search using math expressions is critical for making Mathematical Information Retrieval (MIR) systems easier to use. We designed a study where participants completed search tasks involving mathematical expressions using two different summary st ..."
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Finding ways to help users assess relevance when they search using math expressions is critical for making Mathematical Information Retrieval (MIR) systems easier to use. We designed a study where participants completed search tasks involving mathematical expressions using two different summary styles, and measured response time and relevance assessment accuracy. The control summary style used Google’s regular hit formatting where expressions are presented as text (e.g. in LATEX), while the second summary style renders the math expressions. Participants were undergraduate and graduate students. Participants in the rendered summary style (n = 19) had on average a 17.18 % higher assessment accuracy than those in the nonrendered summary style (n = 19), with no significant difference in response times. Participants in the rendered condition reported having fewer problems reading hits than participants in the control condition. This suggests that users will benefit from search engines that properly render math expressions in their hit summaries.
A ShapeBased Layout Descriptor for Classifying Spatial Relationships in Handwritten Math ABSTRACT
"... We consider the difficult problem of classifying spatial relationships between symbols and subexpressions in handwritten mathematical expressions. We first improve existing geometric features based on bounding boxes and center points, normalizing them using the distance between the centers of the tw ..."
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We consider the difficult problem of classifying spatial relationships between symbols and subexpressions in handwritten mathematical expressions. We first improve existing geometric features based on bounding boxes and center points, normalizing them using the distance between the centers of the two symbols or subexpressions in question. We then propose a novel feature set for layout classification, using polar histograms computed over points in handwritten strokes. A series of experiments are presented in which a Support Vector Machine is used with these new features to classify spatial relationships of five types in the MathBrush corpus (horizontal, superscript, subscript, below, and inside (e.g. in a square root)). The normalized geometric features provide an improvement over previously published results, while the shapebased features provide a natural representation with results comparable to those for the geometric features. Combining the features produced a very small improvement in accuracy.
Baseline ExtractionDriven Parsing of Handwritten Mathematical Expressions
"... We generalize recursive baseline extraction algorithms for symbol layout analysis in math expressions so that handwritten strokes may be provided as input. Specifically, baseline extraction is used for lexical analysis in a modified LL(1) parser, returning a set of candidate symbols when the leftmos ..."
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We generalize recursive baseline extraction algorithms for symbol layout analysis in math expressions so that handwritten strokes may be provided as input. Specifically, baseline extraction is used for lexical analysis in a modified LL(1) parser, returning a set of candidate symbols when the leftmost or next symbol along the current baseline (from lefttoright) is requested by the parser. Candidate symbols are used to produce a forest of parse trees, and the highest ranked parse returned. Hidden Markov Models (HMMs) are used for symbol classification, and horizontal adjacency between symbols is determined using two probabilistic quadratic classifiers, one for ascenders (e.g. ‘A’) and another for centered and descender symbols (e.g. ‘y ’ and ‘x’). The system placed second in the CROHME 2011 handwritten math recognition competition. 1.
Discovering RealWorld Use Cases for a Multimodal Math Search Interface
"... To use math expressions in search, current search engines require knowing expression names or using a structure editor or string encoding (e.g., LaTeX). For mathematical nonexperts, this can lead to an “intention gap ” between the query they wish to express and what the interface will allow them to ..."
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To use math expressions in search, current search engines require knowing expression names or using a structure editor or string encoding (e.g., LaTeX). For mathematical nonexperts, this can lead to an “intention gap ” between the query they wish to express and what the interface will allow them to express. min is a search interface that supports drawing expressions on a canvas using mouse/touch, keyboard and images. We present a user study examining whether min changes search behavior for mathematical nonexperts, and to identify realworld usage scenarios for multimodal math search interfaces. Participants found querybyexpression using handdrawn input useful, and identified scenarios in which they would like to use systems like min such as for locating, editing and sharing complex expressions (e.g., with many Greek letters), and working on complex math problems.
Using Offline Features and Synthetic Data for Online Handwritten Math Symbol Recognition
"... Abstract—We present an approach for online recognition of handwritten math symbols using adaptations of offline features and synthetic data generation. We compare the performance of our approach using four different classification methods: AdaBoost.M1 with C4.5 decision trees, Random Forests and S ..."
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Abstract—We present an approach for online recognition of handwritten math symbols using adaptations of offline features and synthetic data generation. We compare the performance of our approach using four different classification methods: AdaBoost.M1 with C4.5 decision trees, Random Forests and SupportVector Machines with linear and Gaussian kernels. Despite the fact that timing information can be extracted from online data, our feature set is based on shape description for greater tolerance to variations of the drawing process. Our main datasets come from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 and 2013. Class representation bias in CROHME datasets is mitigated by generating samples for underrepresented classes using an elastic distortion model. Our results show that generation of synthetic data for underrepresented classes might lead to improvements of the average perclass accuracy. We also tested our system using the MathBrush dataset achieving a top1 accuracy of 89.87 % which is comparable with the best results of other recently published approaches on the same dataset.
Improving Accuracy of Relevance Assessment for Math Search using
"... am grateful to several people that helped me in different ways in my path to complete this project. I want to thank my advisors for their dedication to the project, and specially Dr. Richard Zanibbi for providing invaluable support and guidance, Dr. Anurag Agarwal for his help in defining first the ..."
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am grateful to several people that helped me in different ways in my path to complete this project. I want to thank my advisors for their dedication to the project, and specially Dr. Richard Zanibbi for providing invaluable support and guidance, Dr. Anurag Agarwal for his help in defining first the problem and then the search tasks and Katherine Zanibbi for informing the initial experimental design. Finally I am want to thank the U.S. Department of State and, more specifically, the Fulbright Scholarship Program for allowing me to pursue my desire to learn more about the HumanComputer Interaction field. iv
Multimodal Mathematical Expressions Recognition: Case of Speech and Handwriting
"... Abstract. In this work, we propose to combine two modalities, handwriting and speech, to build a mathematical expression recognition system. Based on two subsystems which process each modality, we explore various fusion methods to resolve ambiguities which naturally occur independently. The results ..."
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Abstract. In this work, we propose to combine two modalities, handwriting and speech, to build a mathematical expression recognition system. Based on two subsystems which process each modality, we explore various fusion methods to resolve ambiguities which naturally occur independently. The results that are reported on the HAMEX bimodal database show an improvement with respect to a monomodal based system.