Persistent Cohomology for Data With Multicomponent Heterogeneous Information.

Area of Science:

• Computational chemistry and topology
• Data analysis and representation
• Bioinformatics

Background:

• Persistent homology analyzes data topology at multiple scales.
• Current methods struggle to integrate nongeometric molecular data (element types, charges) with geometric information.
• Existing approaches like element-specific homology partially address this but lack a unified framework.

Purpose of the Study:

• To develop a mathematical framework for systematically embedding both geometric and nongeometric (heterogeneous) molecular information into unified topological representations.
• To propose a persistent cohomology-based approach for enriched data representation.
• To validate the framework's effectiveness on diverse datasets, particularly for molecular property prediction.

Main Methods:

• Developed a persistent cohomology-based framework to represent multicomponent heterogeneous information.
• Defined nongeometric information globally or locally on simplicial complexes.
• Extracted enriched barcodes from datasets to capture heterogeneous features.

Main Results:

• The proposed framework successfully represents complex, multicomponent molecular data.
• Enriched barcodes effectively capture both geometric and nongeometric information.
• The method demonstrates superior or comparable performance to state-of-the-art approaches in protein-ligand binding affinity prediction on large datasets.

Conclusions:

• The persistent cohomology framework provides a unified and powerful method for representing heterogeneous molecular data.
• This approach enhances the characterization of molecular structures beyond purely geometric topological invariants.
• The method offers a promising, deep learning-free alternative for molecular property prediction tasks.