Prototype Selection Using Topological Data Analysis

2025-11-06

AI Summary

This work addresses the low efficiency and poor structural preservation inherent in prototype selection for large-scale datasets. We propose TPS, a topology-aware prototype selection framework grounded in topological data analysis (TDA). TPS leverages persistent homology to characterize the intrinsic geometry and connectivity structure of data, enabling adaptive identification of topologically salient samples as prototypes; it further supports parallel implementation. Compared with conventional methods, TPS achieves substantial data compression—retaining only 5–15% of samples on multiple synthetic and real-world benchmarks—while maintaining or improving classification accuracy by 1.2–3.8 percentage points. The approach also exhibits strong interpretability and robustness. Its core innovation lies in the first systematic integration of TDA’s structural awareness into prototype selection, thereby unifying computational efficiency, structural fidelity, and interpretability.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Data Mining & Knowledge Management: Data Compression
• Computer Vision: Other Foundations of Computer Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Data transparency and provenance
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated 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.

Problem

• Selecting representative subsets from large datasets using topological principles
• Improving classification performance while reducing data size significantly
• Advancing algorithmic and geometric aspects of prototype learning methods

Innovation

• Using topological data analysis for prototype selection
• Proposing Topological Prototype Selector framework
• Preserving classification performance while reducing data size