Adaptive template systems: Data-driven feature selection for learning with persistence diagrams

TL;DR

This paper introduces adaptive, data-driven feature extraction methods for persistence diagrams, improving machine learning classification performance across various applications by localizing features effectively.

Contribution

It proposes and evaluates three adaptive algorithms—CDER, GMM, HDBSCAN—for feature localization in persistence diagrams, with CDER showing superior robustness.

Findings

Adaptive template systems outperform traditional methods in classification tasks.

CDER provides the most reliable and robust feature extraction.

Methods are validated on manifold, human shapes, and protein classification datasets.

Abstract

Feature extraction from persistence diagrams, as a tool to enrich machine learning techniques, has received increasing attention in recent years. In this paper we explore an adaptive methodology to localize features in persistent diagrams, which are then used in learning tasks. Specifically, we investigate three algorithms, CDER, GMM and HDBSCAN, to obtain adaptive template functions/features. Said features are evaluated in three classification experiments with persistence diagrams. Namely, manifold, human shapes and protein classification. The main conclusion of our analysis is that adaptive template systems, as a feature extraction technique, yield competitive and often superior results in the studied examples. Moreover, from the adaptive algorithms here studied, CDER consistently provides the most reliable and robust adaptive featurization.