Distributed Computation of Persistent Cohomology

TL;DR

This paper introduces a novel distributed algorithm for computing persistent cohomology in topological data analysis, effectively handling global connectivity challenges and improving scalability over existing methods.

Contribution

It presents a new distributed algorithm combining domain and range partitioning to compute persistent cohomology more efficiently.

Findings

Significant improvement in strong scaling compared to DIPHA.

Effective reduction and sparsification of the coboundary matrix locally.

Successful distributed computation of persistent cohomology.

Abstract

Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to compute in parallel because it relies on global connectivity of the data. We propose a new algorithm to compute persistent cohomology in the distributed setting. It combines domain and range partitioning. The former is used to reduce and sparsify the coboundary matrix locally. After this initial local reduction, we redistribute the matrix across processors for the global reduction. We experimentally compare our cohomology algorithm with DIPHA, the only publicly available code for distributed computation of persistent (co)homology; our algorithm demonstrates a significant improvement in strong scaling.