Topological Data Analysis of Collective Behavior

Speaker: Dhananjay Bhaskar

Date: Wed, Sep 29, 2021

Location: PIMS, University of British Columbia, Online, Zoom

Conference: Mathematical Biology Seminar

Subject: Mathematics, Mathematical Biology

Class: Scientific


Active matter systems, ranging from liquid crystals to populations of cells and animals, exhibit complex collective behavior characterized by pattern formation and dynamic phase transitions. However, quantitative classification is challenging for heterogeneous populations of varying size, and typically requires manual supervision. In this talk, I will demonstrate that a combination of topological data analysis (TDA) and machine learning can uniquely identify the spatial arrangement of agents by keeping track of clusters, loops, and voids at multiple scales. To validate the approach, I will present 3 case studies: (1) data-driven modeling and analysis of epithelial-mesenchymal transition (EMT) in mammary epithelia, (2) unsupervised classification of cell sorting, and self-assembly patterns in co-cultures, and (3) parameter recovery from animal swarming trajectories.