Abstract The comparison of three topic modeling methods—LDA, NMF, and BERTopic—was conducted across diverse collections of mathematical articles. In the initial experiment using articles from ‘‘Izvestiya VUZov. Matematika,’’ LDA exhibited superior performance based on the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8391_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{V}\)</EquationSource>  </InlineEquation> Coherence metric, although NMF also yielded commendable results. Conversely, BERTopic’s thematic classes were less interpretable compared to LDA and NMF. In the subsequent experiment, using articles from the same journal but with vocabulary derived from OntoMath<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8391_Article_IEq2.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\({}^{\text{PRO}}\)</EquationSource>  </InlineEquation> ontology concepts, LDA again demonstrated favorable metric results. However, BERTopic showed interpretability of thematic classes comparable to LDA, although this does not correlate with the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8391_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{V}\)</EquationSource>  </InlineEquation> metric. The third experiment, conducted on a combined collection from two journals with vocabulary compiled via frequency truncation and OntoMath<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8391_Article_IEq2.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\({}^{\text{PRO}}\)</EquationSource>  </InlineEquation> ontology concepts, demonstrated the effectiveness of BERTopic in terms of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8391_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_{V}\)</EquationSource>  </InlineEquation> coherence and interpretability. However, NMF also showed high interpretability of the resulting themes. Hence, it is evident that each topic modeling method possesses distinct advantages and constraints depending on the context and assumptions. The choice of data preprocessing method is pivotal, as it significantly impacts modeling outcomes. Additionally, different data preprocessing approaches influence the interpretability of thematic classes for each method.

Comparative Analysis of Methods for Topic Modeling of Mathematical Documents

期刊论文
发表日期：

2025年6月1日

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B. T. Gizatullin,
O. A. Nevzorova

摘要

Abstract

The comparison of three topic modeling methods—LDA, NMF, and BERTopic—was conducted across diverse collections of mathematical articles. In the initial experiment using articles from ‘‘Izvestiya VUZov. Matematika,’’ LDA exhibited superior performance based on the \(C_{V}\) Coherence metric, although NMF also yielded commendable results. Conversely, BERTopic’s thematic classes were less interpretable compared to LDA and NMF.

In the subsequent experiment, using articles from the same journal but with vocabulary derived from OntoMath \({}^{\text{PRO}}\) ontology concepts, LDA again demonstrated favorable metric results. However, BERTopic showed interpretability of thematic classes comparable to LDA, although this does not correlate with the \(C_{V}\) metric.

The third experiment, conducted on a combined collection from two journals with vocabulary compiled via frequency truncation and OntoMath \({}^{\text{PRO}}\) ontology concepts, demonstrated the effectiveness of BERTopic in terms of \(C_{V}\) coherence and interpretability. However, NMF also showed high interpretability of the resulting themes.

Hence, it is evident that each topic modeling method possesses distinct advantages and constraints depending on the context and assumptions. The choice of data preprocessing method is pivotal, as it significantly impacts modeling outcomes. Additionally, different data preprocessing approaches influence the interpretability of thematic classes for each method.