Principal Geodesic Analysis of Merge Trees (and Persistence Diagrams). (arXiv:2207.10960v2 [cs.GR] UPDATED)

This paper presents a computational framework for the Principal Geodesic
Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated
Principal Component Analysis (PCA) framework [87] to the Wasserstein metric
space of merge trees [92]. We formulate MT-PGA computation as a constrained
optimization problem, aiming at adjusting a basis of orthogonal geodesic axes,
while minimizing a fitting energy. We introduce an efficient, iterative
algorithm which exploits shared-memory parallelism, as well as an analytic
expression of the fitting energy gradient, …

analysis arxiv merge persistence trees