Convex Clustering Redefined: Robust Learning with the Median of Means Estimator

TL;DR

This paper introduces a robust convex clustering method that combines the Median of Means estimator to improve outlier resistance and efficiency, eliminating the need to predefine the number of clusters.

Contribution

It develops a novel convex clustering framework integrated with MoM, enhancing robustness and scalability without requiring prior knowledge of cluster count.

Findings

Outperforms existing clustering methods on synthetic datasets.

Demonstrates robustness to noise and outliers in real-world data.

Achieves weak consistency under certain theoretical conditions.

Abstract

Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all of them require the number of clusters k to be supplied as input, and many are notably sensitive to initialization. Convex clustering provides a more stable alternative by formulating the clustering task as a convex optimization problem, ensuring a unique global solution. However, it faces challenges in handling high-dimensional data, especially in the presence of noise and outliers. Additionally, strong fusion regularization, controlled by the tuning parameter, can hinder effective cluster formation within a convex clustering framework. To overcome these challenges, we introduce a robust approach that integrates convex clustering with the Median of Means (MoM) estimator, thus developing an outlier-resistant and efficient clustering framework that does not necessitate prior knowledge of the number of clusters. By leveraging the robustness of MoM alongside the stability of convex clustering, our method enhances both performance and efficiency, especially on large-scale datasets. Theoretical analysis demonstrates weak consistency under specific conditions, while experiments on synthetic and real-world datasets validate the method's superior performance compared to existing approaches.