Multiparameter Persistent Homology for Molecular Property Prediction

TL;DR

This paper introduces a multiparameter persistent homology-based molecular fingerprinting method that captures complex structural features across multiple scales and parameters, improving property prediction interpretability.

Contribution

It presents a novel multiparameter persistent homology approach for molecular fingerprinting, with theoretical stability guarantees and superior performance over traditional methods.

Findings

Effective in predicting molecular properties on multiple datasets.

Provides more comprehensive and interpretable topological features.

Outperforms traditional graph neural networks in certain tasks.

Abstract

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features that exhibit persistence across multiple scales along multiple parameters, such as atomic mass, partial charge, and bond type, and can be further enhanced by incorporating additional parameters like ionization energy, electron affinity, chirality and orbital hybridization. The proposed fingerprinting method provides fresh perspectives on molecular structure that are not easily discernible from single-parameter or single-scale analysis. Besides, in comparison with traditional graph neural networks, multiparameter persistent homology has the advantage of providing a more comprehensive and interpretable characterization of the topology of the molecular data. We have established theoretical stability guarantees for multiparameter persistent homology, and have conducted extensive experiments on the Lipophilicity, FreeSolv, and ESOL datasets to demonstrate its effectiveness in predicting molecular properties.