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Mapping Chemical Space: Topological Data Analysis of Chemical Latent Space with Mapper

Authors Dhruv Meduri , Chuan-Shen Hu , Cong Shen , Kelin Xia , Bei Wang

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Document Identifiers

Subject Classification

ACM Subject Classification
  • Applied computing → Chemistry
  • Mathematics of computing → Algebraic topology
Keywords
  • Practice of computational topology
  • topological data analysis
  • applications in chemistry
  • mapper algorithm
  • high-dimensional data analysis
  • chemical spaces
  • geometric deep learning
  • latent space geometry

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Abstract

The vast chemical space, encompassing virtually innumerable molecules and materials, presents both immense opportunities and significant challenges. The design and discovery of novel drugs and functional materials may be viewed as a search within this space; however, the sheer scale of potential candidates renders exhaustive exploration infeasible. To address this, we introduce Chemical Mapper, a framework that integrates topological data analysis with deep learning to enable the visual exploration and analysis of chemical latent spaces. At its core, Chemical Mapper employs mapper, a widely used tool in topological data analysis, to investigate the organizational principles of chemical latent spaces defined by molecular representations learned by geometric deep learning models. In doing so, Chemical Mapper not only highlights groups of molecular representations but also uncovers the relationships among them through linkages and branching structures. Our results show that Chemical Mapper reveals intrinsic patterns associated with molecular scaffolds, functional groups, and chemical properties, as well as the structural and functional evolutions of the molecules.

Cite As Get BibTex

Dhruv Meduri, Chuan-Shen Hu, Cong Shen, Kelin Xia, and Bei Wang. Mapping Chemical Space: Topological Data Analysis of Chemical Latent Space with Mapper. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SoCG.2026.78

Author Details

Dhruv Meduri
  • University of Utah, Salt Lake City, UT, USA
Chuan-Shen Hu
  • Nanyang Technological University, Singapore
Cong Shen
  • National University of Singapore, Singapore
Kelin Xia
  • Nanyang Technological University, Singapore
Bei Wang
  • University of Utah, Salt Lake City, UT, USA

Funding

  • Meduri, Dhruv: NSF IIS-2205418 and DMS-2134223.
  • Xia, Kelin: Tier 1 grant RG16/23 and Tier 2 grant MOE-T2EP20125-0004.
  • Wang, Bei: NSF IIS-2205418 and DMS-2134223.

Supplementary Materials

References

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