Understanding the Power of Persistence Pairing via Permutation Test

Abstract

Recently many efforts have been made to incorporate persistence diagrams, one of the major tools in topological data analysis (TDA), into machine learning pipelines. To better understand the power and limitation of persistence diagrams, we carry out a range of experiments on both graph data and shape data, aiming to decouple and inspect the effects of different factors involved. To this end, we also propose the so-called \emph{permutation test} for persistence diagrams to delineate critical values and pairings of critical values. For graph classification tasks, we note that while persistence pairing yields consistent improvement over various benchmark datasets, it appears that for various filtration functions tested, most discriminative power comes from critical values. For shape segmentation and classification, however, we note that persistence pairing shows significant power on most of the benchmark datasets, and improves over both summaries based on merely critical values, and those based on permutation tests. Our results help provide insights on when persistence diagram based summaries could be more suitable.

arXiv comment20 pages, 6 graphs

References in corpus (6)

• Statistical topological data analysis using persistence landscapes
• PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures
• Learning metrics for persistence-based summaries and applications for graph classification
• Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagrams
• A simple yet effective baseline for non-attributed graph classification
• Diving into the shallows: a computational perspective on large-scale shallow learning

Cited by in corpus (4)

• Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence
• Elder-Rule-Staircodes for Augmented Metric Spaces
• Approximation algorithms for 1-Wasserstein distance between persistence diagrams
• Smart Vectorizations for Single and Multiparameter Persistence