Clustering using Max-norm Constrained Optimization

TL;DR

This paper introduces a clustering method based on max-norm constrained optimization, providing improved guarantees for exact cluster recovery over previous nuclear-norm approaches, and evaluates its effectiveness against other methods.

Contribution

The paper proposes using max-norm as a convex surrogate for clustering, offering better theoretical guarantees and empirical performance compared to existing nuclear-norm relaxations.

Findings

Max-norm constrained optimization achieves superior cluster recovery guarantees.

The proposed method outperforms nuclear-norm relaxation in experiments.

Effectiveness of max-norm approach is validated against other clustering techniques.

Abstract

We suggest using the max-norm as a convex surrogate constraint for clustering. We show how this yields a better exact cluster recovery guarantee than previously suggested nuclear-norm relaxation, and study the effectiveness of our method, and other related convex relaxations, compared to other clustering approaches.