Adaptively Robust and Sparse K-means Clustering

While K-means is known to be a standard clustering algorithm, it 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. We introduce a redundant error component for each observation for robustness, 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 superiority of the proposed method to existing algorithms in identifying clusters without outliers and informative variables simultaneously.