Martin Líška

The art of mathematics retrieval

The design and architecture of MIaS (Math Indexer and Searcher), a system for mathematics retrieval is presented, and design decisions are discussed. We argue for an approach based on Presentation MathML using a similarity of math subformulae. The system was implemented as a math-aware search engine based on the state-of-the-art system Apache Lucene. Scalability issues were checked against more than 400,000 arXiv documents with 158 million mathematical formulae. Almost three billion MathML subformulae were indexed using a Solr-compatible Lucene.

Indexing and Searching Mathematics in Digital Libraries

This paper surveys approaches and systems for searching mathematical formulae in mathematical corpora and on the web. The design and architecture of our MIaS (Math Indexer and Searcher) system is presented, and our design decisions are discussed in detail. An approach based on PresentationMathML using a similarity of math subformulae is suggested and verified by implementing it as a math-aware search engine based on the state-of-the-art system, Apache Lucene. Scalability issues were checked based on 324,000 real scientific documents from arXiv archive with 112 million mathematical formulae. More than two billions MathML subformulae were indexed using our Solr-compatible Lucene extension.

Combining Text and Formula Queries in Math Information Retrieval: Evaluation of Query Results Merging Strategies

Specific to Math Information Retrieval is combining text with mathematical formulae both in documents and in queries. Rigorous evaluation of query expansion and merging strategies combining math and standard textual keyword terms in a query are given. It is shown that techniques similar to those known from textual query processing may be applied in math information retrieval as well, and lead to a cutting edge performance. Striping and merging partial results from subqueries is one technique that improves results measured by information retrieval evaluation metrics like Bpref.

Math Indexer and Searcher Web Interface

We are designing and developing a web user interface for digital mathematics libraries called WebMIaS. It allows queries to be expressed by mathematicians through a faceted search interface. Users can combine standard textual autocompleted keywords with keywords in the form of mathematical formulae in LaTeX or MathML formats. Formulae are shown rendered by the web browser on-the-fly for users’ feedback. We describe WebMIaS design principles and our experiences deploying in the European Digital Mathematics Library (EuDML). We further describe the issues addressed by formulae canonicalization and by extending the MIaS indexing engine with Content MathML support.

Enhancing Mathematics Information Retrieval

Mathematics Information Retrieval (MIR) is a domain specific branch of Information Retrieval. MIR is a broad term for all the activities related to obtaining information from a collection of resources and answering an information need that involves mathematics in the form of math expressions and formulae. MIR is very important for Digital Mathematics Libraries (DMLs) which gather mathematically oriented documents in which users need to search and navigate effectively. A concrete implementation usually means a search engine that is able to answer a query composed of mathematical expressions as well as standard textual keywords searching through a collection with a substantial amount of mathematics. There are several research groups that aim at creating well performing and usable math search engine. Our group located at the Faculty of Informatics, Masaryk University, develops Math Indexer and Searcher (MIaS) [2] – a math-aware search engine, currently deployed in EuDML (European Digital Mathematics Library). To the best of my knowledge, it is the only deployment of a MIR system in such a scale. Other deployments, e.g. DML-CZ, are planned.