Michal Růžička

Petr Sojka, Michal Růžička, Vít Novotný

Digital mathematical libraries (DMLs) such as arXiv, Numdam, and EuDML contain mainly documents from STEM fields, where mathematical formulae are often more important than text for understanding. Conventional information retrieval (IR) systems are unable to represent formulae and they are therefore ill-suited for math information retrieval (MIR). To fill the gap, we have developed, and open-sourced the MIaS MIR system. MIaS is based on the full-text search engine Apache Lucene. On top of text retrieval, MIaS also incorporates a set of tools for preprocessing mathematical formulae. We describe the design of the system and present speed, and quality evaluation results. We show that MIaS is both efficient, and effective, as evidenced by our victory in the NTCIR-11 Math-2 task.

Michal Růžička, Petr Sojka

In this paper, we investigate mathematical content representations suitable for the automated classification of and the similarity search in STEM documents using standard machine learning algorithms: the Latent Dirichlet Allocation (LDA) and the Latent Semantic Indexing (LSI). The methods are evaluated on a subset of arXiv.org papers with the Mathematics Subject Classification (MSC) as a reference classification and using the standard precision/recall/F1-measure metrics. The results give insight into how different math representations may influence the performance of the classification and similarity search tasks in STEM repositories. Non-surprisingly, machine learning methods are able to grab distributional semantics from textual tokens. A proper selection of weighted tokens representing math may improve the quality of the results slightly. A structured math representation that imitates successful text-processing techniques with math is shown to yield better results than flat TeX tokens.

Jan Rygl, Jan Pomikálek, Radim Řehůřek et al.

Vector representations and vector space modeling (VSM) play a central role in modern machine learning. We propose a novel approach to `vector similarity searching' over dense semantic representations of words and documents that can be deployed on top of traditional inverted-index-based fulltext engines, taking advantage of their robustness, stability, scalability and ubiquity. We show that this approach allows the indexing and querying of dense vectors in text domains. This opens up exciting avenues for major efficiency gains, along with simpler deployment, scaling and monitoring. The end result is a fast and scalable vector database with a tunable trade-off between vector search performance and quality, backed by a standard fulltext engine such as Elasticsearch. We empirically demonstrate its querying performance and quality by applying this solution to the task of semantic searching over a dense vector representation of the entire English Wikipedia.

Martin Líška, Petr Sojka, Michal Růžička

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.