  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.
