An Approach to Mathematical Search Through Query Formulation and Data Normalization

Miner, Robert R.; Munavalli, Rajesh

doi:10.1007/978-3-540-73086-6_27

Cited by 54 publications

(41 citation statements)

References 4 publications

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“…The MathWebSearch interface shown in Figure 5a [78], provides templates for structures such as fractions and summations; text representing these operations is inserted into the query using a mouse click. In the Mathdex system, users can enter expressions using a graphical equation editor similar to the editors provided in word-processing programs [104].…”

mentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

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Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with wide-spread availability of Optical Character Recognition (OCR) and text-based search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.

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mentioning

confidence: 99%

Recognition and retrieval of mathematical expressions

Zanibbi

Blostein

2011

IJDAR

234

112

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“…Uses of normalisation include: repairing of broken XML/MathML generated by automatic conversion tools [MM07] (e.g. when the structure imposed by <mrows> is not compatible with the mathematical structure); removal of information that does not contribute to the semantics like comments, layout elements A normalised formula can be quite different from the original one, and that can be a symptom that the formula is not significant.…”

Section: Modular Enhancement Techniquesmentioning

confidence: 99%

A Survey on Retrieval of Mathematical Knowledge

Guidi

Coen

2016

Math.Comput.Sci.

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Abstract. We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques. Purpose Driven Taxonomy of Retrieval ProblemsRetrieval of mathematical knowledge is always presented as the low hanging fruit of Mathematical Knowledge Management, and it has been addressed in several papers by people coming either from the formal methods or from the information retrieval community. The problem being resistant to classical content search techniques [LRG13], it is usually addressed combining a small set of new ideas and techniques that are recurrent in the literature. Despite the amount of work, however, there is not a single solution that is the clearly winning on the others, nor convincing unbiased benchmarks to compare solutions. Some authors like [KK07] also suggest that the community should first better understand the actual needs of mathematicians from an unbiased perspective to improve the MKM technology as a whole. In this paper we collect a hopefully comprehensive bibliography, and we roughly classify the papers according to novel taxonomies both for the problems and the techniques employed. The only other surveys on the same topic are [AZ04], now outdated and focused mostly on (European) research projects that contributed to the topic in the 6th Framework Programme, [ZB12], which covers less literature in much greater detail without attempting a classification, [L13], which is focused on evaluation of mathematics retrieval, and [L10], which is written in Slovak.We begin our discussion with a purpose driven taxonomy made of three different retrieval problems that deal with mathematical knowledge. Each problem is characterised by its own set of expectations and constraints, and adopting a solution to another problem may be infeasible or yield poor results. In the next sections we classify the papers according to an encoding based taxonomy (presentation vs content vs semantics) and to a taxonomy of techniques employed. Finally we point to the rich literature relative to the problem of ranking, and we touch the problem of evaluation of systems. We conclude with some notes on the availability of math retrieval systems.⋆ The final publication is available at http://link.springer.com.

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“…The approaches that consist in applying textual search methods by linearizing expressions [12] cannot correctly account for the nested structure of expressions, and for the issue of bound variables [16]. When looking for integrals in x whose body contains x 2 , a textual search would have false positives such as 2x dx = x 2 + c (x 2 is not in the scope of ), and would have false negatives such as y 2 − y dy (y instead of x).…”

Section: Query Languagesmentioning

confidence: 99%

“…For example, it should be possible to describe a theorem by its author, its discovery date, its informal description as a text, and its formal description as a mathematical expression, all in RDF. An expected advantage of the formal representation of expressions is the ability to search those expressions by their content, which is a problem that has been studied in mathematical search [3,6,16,12,1]. For example, we may wish to retrieve all expressions that are an integral in some variable x and whose body contains x 2 as a sub-expression.…”

Section: Introductionmentioning

confidence: 99%

An RDF Design Pattern for the Structural Representation and Querying of Expressions

Ferré

2016

Lecture Notes in Computer Science

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Abstract. Expressions, such as mathematical formulae, logical axioms, or structured queries, account for a large part of human knowledge. It is therefore desirable to allow for their representation and querying with Semantic Web technologies. We propose an RDF design pattern that fulfills three objectives. The first objective is the structural representation of expressions in standard RDF, so that expressive structural search is made possible. We propose simple Turtle and SPARQL abbreviations for the concise notation of such RDF expressions. The second objective is the automated generation of expression labels that are close to usual notations. The third objective is the compatibility with existing practice and legacy data in the Semantic Web (e.g., SPIN, OWL/RDF). We show the benefits for RDF tools to support this design pattern with the extension of SEWELIS, a tool for guided exploration and edition, and its application to mathematical search.

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An Approach to Mathematical Search Through Query Formulation and Data Normalization

Cited by 54 publications

References 4 publications

Recognition and retrieval of mathematical expressions

Recognition and retrieval of mathematical expressions

A Survey on Retrieval of Mathematical Knowledge

An RDF Design Pattern for the Structural Representation and Querying of Expressions

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