Retrieving documents with mathematical content

Abstract

Many documents with mathematical content are published on the Web, but conventional search engines that rely on keyword search only cannot fully exploit their mathematical information. In particular, keyword search is insufficient when expressions in a document are not annotated with natural keywords or the user cannot describe her query with keywords. Retrieving documents by querying their mathematical content directly is very appealing in various domains such as education, digital libraries, engineering, patent documents, medical sciences, etc. Capturing the relevance of mathematical expressions also greatly enhances document classification in such domains.Unlike text retrieval, where keywords carry enough semantics to distinguish text documents and rank them, math symbols do not contain much semantic information on their own. In fact, mathematical expressions typically consist of few alphabetical symbols organized in rather complex structures. Hence, the structure of an expression, which describes the way such symbols are combined, should also be considered. Unfortunately, there is no standard testbed with which to evaluate the effectiveness of a mathematics retrieval algorithm.In this paper we study the fundamental and challenging problems in mathematics retrieval, that is how to capture the relevance of mathematical expressions, how to query them, and how to evaluate the results. We describe various search paradigms and propose retrieval systems accordingly. We discuss the benefits and drawbacks of each approach, and further compare them through an extensive empirical study.

Semantic Tagging of Mathematical Expressions

“…Presentation-based methods only consider the variables, numbers and operators appearing in an expression, with no idea about the semantic meanings behind the tokens [10,19,20,7]. For example, one can treat the expression as an ordinary sentence in NLP after proper preprocessing.…”

Retrieval of similar chess positions

“…The search problem, however, is closely related to the problem of retrieving approximately matching entities (typically non-text) from a collection, given a query entity (typically also non-text) as an example. Examples of this class of search tasks include content-based image search [18], mathematical equations search [7], searching for the least edit distance reference sentence for example-based machine translation (EBMT) [10], etc. These search tasks differ widely from standard text search in the following ways.…”

“…the minimum number of operations needed to transform a document to the query and vice-versa. For example, the similarity between two mathematical expressions can be computed by the inverse of the edit distance between their parse tree structures [7]. The edit distance metric can, in principle, be applied to the chess position search problem as well, where the distance (inverse similarity) between two positions could be computed by the number of operations required to transform one board position to another.…”

“…Request permissions from permissions@acm.org. SIGIR'14, July [6][7][8][9][10][11]2014 retrieved games can then be used to devise a winning or a game saving strategy in general, and even decide a sequence of the next best moves in particular. Kotov, the Soviet chess grand master, opines that if one can recall similar positions from earlier games, then it is "easier to reach an assessment of how things stand, and to hit upon the correct plan or analyze variations" [8].…”

Rendering expressions to improve accuracy of relevance assessment for math search

“…In 2013 a math retrieval competition was held as part of the NTCIR Workshop [1] and advances have been made in techniques for retrieving expressions by visual appearance [8,9] and operator structure [11]. Work has also begun on integrating search results obtained from independent text and expression indices [11] and creating search interfaces that Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”