Julien Tierny - Principal Geodesic Analysis of Merge Trees and Persistence Diagrams

Explore a computational framework for Principal Geodesic Analysis of merge trees (MT-PGA) in this 55-minute talk by Julien Tierny. Learn about this novel adaptation of Principal Component Analysis (PCA) to the Wasserstein metric space of merge trees. Discover how MT-PGA computation is formulated as a constrained optimization problem, aiming to adjust orthogonal geodesic axes while minimizing fitting energy. Understand the efficient, iterative algorithm that utilizes shared-memory parallelism and an analytic expression of the fitting energy gradient for fast computations. See how this approach extends to extremum persistence diagrams and its applications in data reduction and dimensionality reduction. Examine the utility of MT-PGA through extensive experiments on public ensembles, demonstrating its efficiency in compressing merge trees and generating two-dimensional layouts for visual inspections of feature variability. Gain insights into the quantitative experiments that assess the framework's relevance and learn about the available C++ implementation for reproducing results.