Adaptive template systems: Data-driven feature selection for learning with persistence diagrams
This work addresses the need for improved feature selection in topological data analysis for domain-specific applications, representing an incremental advancement.
The paper tackled the problem of feature extraction from persistence diagrams for machine learning by proposing adaptive template systems, which yielded competitive and often superior results in classification experiments on manifolds, human shapes, and proteins, with CDER identified as the most reliable algorithm.
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.