Deterministic Feature Selection for $k$-means Clustering

TL;DR

This paper introduces a deterministic feature selection algorithm for k-means clustering that offers provable theoretical guarantees, addressing the limitations of existing randomized methods.

Contribution

The paper presents the first deterministic algorithm for feature selection in k-means with proven theoretical performance guarantees.

Findings

The algorithm guarantees successful feature selection with high probability.

It improves reliability over randomized methods.

The approach is based on deterministic identity decomposition.

Abstract

We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these algorithms are randomized and fail with, say, a constant probability. We address this issue by presenting a deterministic feature selection algorithm for k-means with theoretical guarantees. At the heart of our algorithm lies a deterministic method for decompositions of the identity.