Prototype Selection Using Topological Data Analysis

TL;DR

This paper introduces TPS, a topological data analysis-based method for selecting representative data prototypes, which improves classification performance and reduces data size across various datasets.

Contribution

The paper presents TPS, a novel topological data analysis framework for prototype selection, enhancing interpretability and efficiency in classification tasks.

Findings

TPS significantly improves classification accuracy.

TPS reduces dataset size while maintaining performance.

Effective across simulated and real datasets.

Abstract

Recently, there has been an explosion in statistical learning literature to represent data using topological principles to capture structure and relationships. We propose a topological data analysis (TDA)-based framework, named Topological Prototype Selector (TPS), for selecting representative subsets (prototypes) from large datasets. We demonstrate the effectiveness of TPS on simulated data under different data intrinsic characteristics, and compare TPS against other currently used prototype selection methods in real data settings. In all simulated and real data settings, TPS significantly preserves or improves classification performance while substantially reducing data size. These contributions advance both algorithmic and geometric aspects of prototype learning and offer practical tools for parallelized, interpretable, and efficient classification.