A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers

Abstract

Traditional clustering algorithms such as k-means and vanilla spectral clustering are known to deteriorate significantly in the presence of outliers. Several previous works in literature have proposed robust variants of these algorithms; however, they do not provide any theoretical guarantees. Extending previous clustering literature on Gaussian mixture models, in their paper “A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers,” Prateek R. Srivastava, Purnamrita Sarkar, and Grani A. Hanasusanto developed a new spectral clustering algorithm and provided error bounds for the algorithm under a general sub-Gaussian mixture model setting with outliers. Surprisingly, their derived error bound matches with the best-known bound for semidefinite programs under the same setting without outliers. Numerical experiments on a variety of simulated and real-world data sets further demonstrate that their algorithm is less sensitive to outliers compared with other state-of-the-art algorithms.