Adaptive Template Systems: Data-Driven Feature Selection for Learning with Persistence Diagrams

Feature extraction from persistence diagrams has received increasing attention in recent years, as a tool to enrich machine learning techniques. 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.