Mathematical Information Retrieval Research Articles

A Multi-Modal Retrieval Model for Mathematical Expressions Based on ConvNeXt and Hesitant Fuzzy Set

Mathematical expression retrieval is an essential component of mathematical information retrieval. Current mathematical expression retrieval research primarily targets single modalities, particularly text, which can lead to the loss of structural information. On the other hand, multimodal research has demonstrated promising outcomes across different domains, and mathematical expressions in image format are adept at preserving their structural characteristics. So we propose a multi-modal retrieval model for mathematical expressions based on ConvNeXt and HFS to address the limitations of single-modal retrieval. For the image modal, mathematical expression retrieval is based on the similarity of image features and symbol-level features of the expression, where image features of the expression image are extracted by ConvNeXt, while symbol-level features are obtained by the Symbol Level Features Extraction (SLFE) module. For the text modal, the Formula Description Structure (FDS) is employed to analyze expressions and extract their attributes. Additionally, the application of the Hesitant Fuzzy Set (HFS) theory facilitates the computation of hesitant fuzzy similarity between mathematical queries and candidate expressions. Finally, Reciprocal Rank Fusion (RRF) is employed to integrate rankings from image modal and text modal retrieval, yielding the ultimate retrieval list. The experiment was conducted on the publicly accessible ArXiv dataset (containing 592,345 mathematical expressions) and the NTCIR-mair-wikipedia-corpus (NTCIR) dataset.The MAP@10 values for the multimodal RRF fusion approach are recorded as 0.774. These substantiate the efficacy of the multi-modal mathematical expression retrieval approach based on ConvNeXt and HFS.

Caching and Reproducibility: Making Data Science Experiments Faster and FAIRer.

Small to medium-scale data science experiments often rely on research software developed ad-hoc by individual scientists or small teams. Often there is no time to make the research software fast, reusable, and open access. The consequence is twofold. First, subsequent researchers must spend significant work hours building upon the proposed hypotheses or experimental framework. In the worst case, others cannot reproduce the experiment and reuse the findings for subsequent research. Second, suppose the ad-hoc research software fails during often long-running computational expensive experiments. In that case, the overall effort to iteratively improve the software and rerun the experiments creates significant time pressure on the researchers. We suggest making caching an integral part of the research software development process, even before the first line of code is written. This article outlines caching recommendations for developing research software in data science projects. Our recommendations provide a perspective to circumvent common problems such as propriety dependence, speed, etc. At the same time, caching contributes to the reproducibility of experiments in the open science workflow. Concerning the four guiding principles, i.e., Findability, Accessibility, Interoperability, and Reusability (FAIR), we foresee that including the proposed recommendation in a research software development will make the data related to that software FAIRer for both machines and humans. We exhibit the usefulness of some of the proposed recommendations on our recently completed research software project in mathematical information retrieval.

A Hybrid Model Combining Formulae with Keywords for Mathematical Information Retrieval

Formula retrieval is an important research topic in Mathematical Information Retrieval (MIR). Most studies have focused on formula comparison to determine the similarity between mathematical documents. However, two similar formulae may appear in entirely different knowledge domains and have different meanings. Based on N-ary Tree-based Formula Embedding Model (NTFEM, our previous work in [Y. Dai, L. Chen, and Z. Zhang, An N-ary tree-based model for similarity evaluation on mathematical formulae, in Proc. 2020 IEEE Int. Conf. Systems, Man, and Cybernetics, 2020, pp. 2578–2584.], we introduce a new hybrid retrieval model, NTFEM-K, which combines formulae with their surrounding keywords for more accurate retrieval. By using keywords extraction technology, we extract keywords from context, which can supplement the semantic information of the formula. Then, we get the vector representations of keywords by FastText N-gram embedding model and the vector representations of formulae by NTFEM. Finally, documents are sorted according to the similarity between keywords, and then the ranking results are optimized by formula similarity. For performance evaluation, NTFEM-K is not only compared with NTFEM but also hybrid retrieval models combining formulae with long text and hybrid retrieval models combining formulae with their keywords using other keyword extraction algorithms. Experimental results show that the accuracy of top-10 results of NTFEM-K is at least 20% higher than that of NTFEM and can be 50% in some specific topics.

Embedding and generalization of formula with context in the retrieval of mathematical information

Retrieval of mathematical information from scientific documents is one of the crucial tasks. Numerous Mathematical Information Retrieval (MIR) systems have been developed, which mainly focus on the improvement over the indexing and the searching mechanism, the poor results obtained for evaluation measures depict major limitations of such systems. These enhance the scope of improvement and new innovations through the inclusion of functionalities, which can resolve the challenges of MIR system. Further, to improve the performance of the MIR systems, this paper proposed a formula embedding and generalization approach with the context, in addition to innovative relevance measurement technique. In this approach, documents are preprocessed by the document preprocessor module and extracted the formulas in Presentation MathML format with their context. The formula embedding and generalization modules of the proposed approach formed the binary vectors where ‘1’ represents the presence, and ‘0’ represents the absence of a particular entity in a formula, and subsequently, the vectors of formulas with context are indexed by the indexer. The innovative relevance measurement technique of the proposed approach ranked those documents first, which are retrieved by both formula embedding and generalization modules as compared to the individual one. The proposed approach has been tested on the MathTagArticles of Wikipedia of NTCIR-12, and the obtained results verify the significance of the context of the formula and the dissimilarity factor in the retrieval of mathematical information.

Math-word embedding in math search and semantic extraction

Word embedding, which represents individual words with semantically fixed-length vectors, has made it possible to successfully apply deep learning to natural language processing tasks such as semantic role-modeling, question answering, and machine translation. As math text consists of natural text, as well as math expressions that similarly exhibit linear correlation and contextual characteristics, word embedding techniques can also be applied to math documents. However, while mathematics is a precise and accurate science, it is usually expressed through imprecise and less accurate descriptions, contributing to the relative dearth of machine learning applications for information retrieval in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in word embedding, it is worthwhile to explore their use and effectiveness in math information retrieval tasks, such as math language processing and semantic knowledge extraction. In this paper, we explore math embedding by testing it on several different scenarios, namely, (1) math-term similarity, (2) analogy, (3) numerical concept-modeling based on the centroid of the keywords that characterize a concept, (4) math search using query expansions, and (5) semantic extraction, i.e., extracting descriptive phrases for math expressions. Due to the lack of benchmarks, our investigations were performed using the arXiv collection of STEM documents and carefully selected illustrations on the Digital Library of Mathematical Functions (DLMF: NIST digital library of mathematical functions. Release 1.0.20 of 2018-09-1, 2018). Our results show that math embedding holds much promise for similarity, analogy, and search tasks. However, we also observed the need for more robust math embedding approaches. Moreover, we explore and discuss fundamental issues that we believe thwart the progress in mathematical information retrieval in the direction of machine learning.

SciMath: A Mathematical Information Retrieval System using Signature Based B Tree Indexing

Given a mathematical query, traditional text retrieval systems are not very effective in retrieving mathematical information from scientific documents. This paper presents the design and implementation of a new mathematical information retrieval (MIR) system: SciMath, which can take a mathematical formulae as a query and retrieve the relevant scientific documents consisting the relevant mathematical contents based on a B-Tree indexing scheme. The proposed system is then compared with two classical math-aware search engines to prove its effectiveness.

Binary vector transformation of math formula for mathematical information retrieval

Binary vector transformation of math formula for mathematical information retrieval

Mathematical Document Retrieval System based on Signature Hashing

Scientific documents and magazines involve large number of mathematical expressions and formulas along with text. The continuous growth of such documents necessitates the requirement of developing specialized tools and techniques, which could handle and analyse mathematical expressions and formulas. Mathematical expressions and formulae are highly structured and quite different from traditional text. Due to which conventional text retrieval system performs poorly in retrieving scientific documents based on mathematical expression formulated as a query. Mathematical information retrieval is concerned with finding information in documents that include mathematics. To address the challenges posed by mathematical formulae as compared to text, this paper aims to construct a math aware search engine, which can retrieve relevant scientific documents based on a mathematical query. A novel signature based hashing scheme to index raw mathematical web documents is proposed in this paper, which can also take mathematical notational equivalences into account. The proposed system demonstrates better precision and stability of the ranked results when compared with other related state-of-the-art math aware search engines.

Improving the representation and conversion of mathematical formulae by considering their textual context.

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial for communicating information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.

Access to all components of scanned mathematical documents by vision-impaired students

ABSTRACTVision-impaired people access documents using screen readers. Electronic documents may contain non-textual components, non-linear components, and multidimensional components, such as mathematical expressions and graphs. These components create a number of accessibility issues for those who use screen readers as assistive technology. The research presented here describes mathematical information retrieval, and accessible and navigable representation of mathematical function graphs as solutions to these issues. Additionally, this research study is about how to present course materials to vision-impaired students, and is not about how to teach them. The system shows promise, given an initial evaluation by a vision-impaired person, and an encouraging review by three blind professionals. The next step is to perform a full evaluation of the system employing a larger number of vision-impaired students.