Adaptively Robust and Sparse K-means Clustering

TL;DR

This paper introduces ARSK, a novel clustering method that enhances K-means by improving robustness to outliers and selecting informative variables in high-dimensional data, using penalized error components and weights.

Contribution

It proposes a new adaptive robust and sparse K-means algorithm with penalized error components and weights, optimized via Gap statistics, to handle outliers and noisy variables simultaneously.

Findings

ARSK outperforms existing algorithms in simulations.

It effectively identifies clusters without outliers.

It selects informative variables in high-dimensional data.

Abstract

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering (ARSK) to address these practical limitations of the standard K-means algorithm. For robustness, we introduce a redundant error component for each observation, and this additional parameter is penalized using a group sparse penalty. To accommodate the impact of high-dimensional noisy variables, the objective function is modified by incorporating weights and implementing a penalty to control the sparsity of the weight vector. The tuning parameters to control the robustness and sparsity are selected by Gap statistics. Through simulation experiments and real data analysis, we demonstrate the proposed method's superiority to existing algorithms in identifying clusters without outliers and informative variables simultaneously.