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Classifying MathML Expressions by Multilayer Perceptron
Abstract
MathML is a standard markup language for describing math expressions. MathML consists of two sets of elements: Presentation Markup and Content Markup. The former is widely used to display math expressions in Web pages, while the latter is more suited to the calculation of math expressions. In this letter, we focus on the former and consider classifying Presentation MathML expressions. Identifying the classes of given Presentation MathML expressions is helpful for several applications, e.g., Presentation to Content MathML conversion, text-to-speech, and so on. We propose a method for classifying Presentation MathML expressions by using multilayer perceptron. Experimental results show that our method classifies MathML expressions with high accuracy.
... Two kinds of markup to describe mathematical expressions are provided by MathML: presentation markup and content markup [6,7]. Mathematical expressions encoded with presentation markup are referred to as presentational expressions (presentation MathML) which focus on the layout of expressions and can preserve the prototypes of operators and operands, but do not contain semantic information. ...
The semantic information of mathematical expressions plays an important role in information retrieval and similarity calculation. However, a large number of presentational expressions in the presentation MathML format contained in electronic scientific documents do not reflect semantic information. It is a shortcut to extract semantic information using the rule mapping method to convert presentational expressions in presentation MathML format into semantic expressions in the content MathML format. However, the conversion result is prone to semantic errors because the expressions in the two formats do not have exact correspondences in grammatical structures and markups. In this study, a Bayesian error correction algorithm is proposed to correct the semantic errors in the conversion results of mathematical expressions based on the rule mapping method. In this study, the expressions in presentation MathML and content MathML in the NTCIR data set are used as the training set to optimize the parameters of the Bayesian model. The expressions in presentation MathML in the documents collected by the laboratory from the CNKI website are used as the test set to test the error correction results. The experimental results show that the average $ {F_1} $ value is 0.239 with the rule mapping method, and the average $ {F_1} $ value is 0.881 with the Bayesian error correction method, with the average error correction rate is 0.853.
Mathematical formulae are essential in science, but face challenges of ambiguity, due to the use of a small number of identifiers to represent an immense number of concepts. Corresponding to word sense disambiguation in Natural Language Processing, we disambiguate mathematical identifiers. By regarding formulae and natural text as one monolithic information source, we are able to extract the semantics of identifiers in a process we term Mathematical Language Processing (MLP). As scientific communities tend to establish standard (identifier) notations, we use the document domain to infer the actual meaning of an identifier. Therefore, we adapt the software development concept of namespaces to mathematical notation. Thus, we learn namespace definitions by clustering the MLP results and mapping those clusters to subject classification schemata. In addition, this gives fundamental insights into the usage of mathematical notations in science, technology, engineering and mathematics. Our gold standard based evaluation shows that MLP extracts relevant identifier-definitions. Moreover, we discover that identifier namespaces improve the performance of automated identifier-definition extraction, and elevate it to a level that cannot be achieved within the document context alone.
We demonstrate searching of mathematical expressions in technical digital libraries on a MREC collection of 439,423 real scientific documents with more than 158 million mathematical formulae. Our solution-the WebMIaS system-allows the retrieval of mathematical expressions written in TEX or MathML. TEX queries are converted on-the-fly into tree representations of Presentation MathML, which is used for indexing. WebMIaS allows complex queries composed of plain text and mathematical formulae, using MIaS (Math Indexer and Searcher), a math aware search engine based on the state-of-the-art system Lucene. MIaS implements proximity math indexing with a subformulae similarity search.
A Long Short-Term Memory (LSTM) network is a type of recurrent neural network
architecture which has recently obtained strong results on a variety of
sequence modeling tasks. The only underlying LSTM structure that has been
explored so far is a linear chain. However, natural language exhibits syntactic
properties that would naturally combine words to phrases. We introduce the
Tree-LSTM, a generalization of LSTMs to tree-structured network topologies.
Tree-LSTMs outperform all existing systems and strong LSTM baselines on two
tasks: predicting the semantic relatedness of two sentences (SemEval 2014, Task
1) and sentiment classification (Stanford Sentiment Treebank).
Text categorization has been a popular research topic for years and has become more or less a practical technology. However, there exists little research on math topic classification. Math documents contain both textual data and math expressions. The text and math can be considered as two related but different views of a math document. The goal of online math topic classification is to automatically categorize a math document containing both mathematical expressions and textual content into an appropriate topic without the need for periodically retraining the classifier. To achieve this, it is essential to have a two-view online classification algorithm, which deals with the textual data view and the math expression view at the same time. In this paper, we propose a novel adaptive two-view online math document classifier based on the Passive Aggressive (PA) algorithm. The proposed approach is evaluated on real world math questions and answers from the Math Overflow question answering system. Compared to the baseline PA algorithm, our method's overall F-measure is improved by up to 3%. The improvement of our algorithm over the plain math expression view is almost 6%.
Tree-structured data are becoming ubiquitous nowadays and manipulating them based on similarity is essential for many applications. The generally accepted similarity measure for trees is the edit distance. Although similarity search has been extensively studied, searching for similar trees is still an open problem due to the high complexity of computing the tree edit distance. In this paper, we propose to transform tree-structured data into an approximate numerical multidimensional vector which encodes the original structure information. We prove that the L1 distance of the corresponding vectors, whose computational complexity is O(|T1| + |T2|), forms a lower bound for the edit distance between trees. Based on the theoretical analysis, we describe a novel algorithm which embeds the proposed distance into a filter-and-refine framework to process similarity search on tree-structured data. The experimental results show that our algorithm reduces dramatically the distance computation cost. Our method is especially suitable for accelerating similarity query processing on large trees in massive datasets.
MathML consists of two sets of elements: Presentation Markup and Content Markup. The former is more widely used to display math expressions in Web pages, while the latter is more suited to the calculation of math expressions. In this paper, we consider classifying math expressions in Presentation Markup. In general, a math expression in Presentation Markup cannot be uniquely converted into the corresponding expression in Content Markup. If the class of a given math expression can be identified automatically, such conversions can be done more appropriately. Moreover, identifying the class of a given math expression is useful for text-to-speech of math expression. In this paper, we propose a method for classifying math expressions in Presentation Markup by using a kind of deep learning; multilayer perceptron. Experimental results show that our method classifies math expressions with high accuracy.
This paper explores the problem of semantic enrichment of mathematical expressions. We formulate this task as the translation of mathematical expressions from presentation markup to content markup. We use MathML, an application of XML, to describe both the structure and content of mathematical notations. We apply a method based on statistical machine translation to extract translation rules automatically. This approach contrasts with previous research, which tends to rely on manually encoded rules. We also introduce segmentation rules used to segment mathematical expressions. Combining segmentation rules and translation rules strengthens the translation system and archives significant improvements over a prior rule-based system. Copyright © 2013 The Institute of Electronics, Information and Communication Engineers.
In this paper, we study how to automatically classify mathematical expressions written in MathML (Mathematical Markup Language). It is an essential preprocess to resolve analysis problems originated from multi-meaning mathematical symbols. We first define twelve equation classes based on chapter information of mathematics textbooks and then conduct various experiments. Experimental results show an accuracy of 94.75%, by employing the feature combination of tags, operators, strings, and "identifier & operator" bigram.
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