# The Geometric Structure of Topic Models

arXiv: https://arxiv.org/abs/2403.03607 · HTML: https://mlsanity.com/paper/2403.03607/

## Key facts

- Cited by 1 papers in the map (data through 7 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Construction of the Literature Graph in Semantic Scholar](https://mlsanity.com/paper/1805.02262/) (2018)
- [Is Automated Topic Model Evaluation Broken?: The Incoherence of Coherence](https://mlsanity.com/paper/2107.02173/) (2021)
- [An Analysis of the t-SNE Algorithm for Data Visualization](https://mlsanity.com/paper/1803.01768/) (2018)
- [On the Lattice of Conceptual Measurements](https://mlsanity.com/paper/2012.05267/) (2020)
- [Knowledge Cores in Large Formal Contexts](https://mlsanity.com/paper/2002.11776/) (2020)
- [Sentiment Analysis and Topic Modeling for COVID-19 Vaccine Discussions](https://mlsanity.com/paper/2111.04415/) (2021)
- [Topic Space Trajectories: A case study on machine learning literature](https://mlsanity.com/paper/2010.12294/) (2020)
- [Quantifying the Conceptual Error in Dimensionality Reduction](https://mlsanity.com/paper/2106.06815/) (2021)
- [Conceptual Views on Tree Ensemble Classifiers](https://mlsanity.com/paper/2302.05270/) (2023)
- [Exploring Scale-Measures of Data Sets](https://mlsanity.com/paper/2102.02576/) (2021)
- [Research Topic Flows in Co-Authorship Networks](https://mlsanity.com/paper/2206.07980/) (2022)
- [Ordinal Motifs in Lattices](https://mlsanity.com/paper/2304.04827/) (2023)
- [Automatic Textual Explanations of Concept Lattices](https://mlsanity.com/paper/2304.08093/) (2023)

## Built on by (most cited first, 1 of 1)

- [Conceptual Topic Aggregation](https://mlsanity.com/paper/2506.22309/) (2025)

## Abstract (arXiv)

Topic models are a popular tool for clustering and analyzing textual data. They allow texts to be classified on the basis of their affiliation to the previously calculated topics. Despite their widespread use in research and application, an in-depth analysis of topic models is still an open research topic. State-of-the-art methods for interpreting topic models are based on simple visualizations, such as similarity matrices, top-term lists or embeddings, which are limited to a maximum of three dimensions. In this paper, we propose an incidence-geometric method for deriving an ordinal structure from flat topic models, such as non-negative matrix factorization. These enable the analysis of the topic model in a higher (order) dimension and the possibility of extracting conceptual relationships between several topics at once. Due to the use of conceptual scaling, our approach does not introduce any artificial topical relationships, such as artifacts of feature compression. Based on our findings, we present a new visualization paradigm for concept hierarchies based on ordinal motifs. These allow for a top-down view on topic spaces. We introduce and demonstrate the applicability of our approach based on a topic model derived from a corpus of scientific papers taken from 32 top machine learning venues.