Persistent Cohomology for Data With Multicomponent Heterogeneous Information
Year: 2020
Type: article
Abstract: Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and reveal certain interaction patterns in terms of topological invariants. However, in addition to the geometric information, there is a wide variety of nongeometric information of molecular structures, such as element types, atomic partial charges, atomic pairwise interactions, and electrostatic potential functions, that is not described by persistent homology. Although element-specific homology and electrostatic persistent homology can encode some nongeometric information into geometry based topological invariants, it is desirable to have a mathematical paradigm to systematically embed both geometric and nongeometric information, i.e., multicomponent heterogeneous information, into unified topological representations. To this end, we propose a persistent cohomology based framework for the enriched representation of data. In our framework, nongeometric information can either be distributed globally or reside locally on the datasets in the geometric sense and can be properly defined on topological spaces, i.e., simplicial complexes. Using the proposed persistent cohomology based framework, enriched barcodes are extracted from datasets to represent heterogeneous information. We consider a variety of datasets to validate the present formulation and illustrate the usefulness of the proposed method based on persistent cohomology. It is found that the proposed framework outperforms or at least matches the state-of-the-art methods in the protein-ligand binding affinity prediction from massive biomolecular datasets without resorting to any deep learning formulation.
DOI: 10.1137/19m1272226
Authors: Zixuan Cang, Guo-Wei Wei
Institution: Michigan State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: III: Medium: Geometric and topological approaches to biomolecular structure and dynamics, Synergistic integration of topology and machine learning for the predictions of protein-ligand binding affinities and mutation impacts, Kinetics-Driven Drug Discovery Using Persistent Homology, Rare-Event Molecular Dynamics and Experimental Data, Geometric and Topological Modeling and Computation of Biomolecular Structure, Function, and Dynamics, III: Medium: De Rham-Hodge theory modeling and learning of biomolecular data
OpenAlex ID: W3026446969