Hardware Acceleration of Persistent Homology Computation

Fan Wang, Chunhua Deng, Bo Yuan, Chao Chen

Abstract: As a powerful tool for topological data analysis, persistent homology captures topological structures of data in a robust manner. Its pertinent information is summarized in a persistence diagram, which records topological structures, as well as their saliency. Recent years have witnessed an increased interest of persistent homology in various domains. In biomedical image analysis, persistent homology has been applied to brain images, neuron images, cardiac images and cancer pathology images. Meanwhile, the computation of persistent homology could be time-consuming due to column operations over a large matrix, called the boundary matrix. This paper seeks to accelerate persistent homology computation with a hardware implementation of the column operations of the boundary matrix. By designing a dedicated hardware to process fast matrix reduction, the proposed hardware accelerator could potentially achieve up to 20k–30k times speed-up.