Clustering by Hill-Climbing: Consistency Results

TL;DR

This paper analyzes hill-climbing clustering methods, both in continuous and discrete spaces, and proves their consistency, providing theoretical validation for these classical algorithms.

Contribution

It establishes the consistency of various hill-climbing clustering approaches, including both continuous and medoid-based variants, which was previously unproven.

Findings

Proved consistency of continuous-space hill-climbing clustering.

Proved consistency of discrete-space (medoid) hill-climbing clustering.

Provides theoretical foundation for classical clustering algorithms.

Abstract

We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.