Robust Spectral Clustering via Matrix Aggregation

Spectral clustering has become one of the most popular clustering algorithms in recent years. In real-world clustering problems, the data points for clustering may have considerable noise. To the best of our knowledge, no single clustering algorithm is able to identify all different types of cluster structures. In the existing spectral clustering methods, little effort has been made to explicitly handle both the possibly considerable noise in data points and the robustness of clustering methods, which often degrades the clustering performance. In this paper, motivated by resampling and matrix aggregation, we propose a method for robust spectral clustering. In our method, we first construct multiple transition probability matrices, each is constructed by a subset of randomly selected features. Then, these matrices can be used to recover a shared low-rank similarity matrix, which is the input to the spectral clustering, and several sparse matrices, which represent the noise. The corresponding optimization problem has a low-rank constraint on the transition probability matrix. To solve the corresponding optimization problem, an optimization procedure based on the scheme of Augmented Lagrangian Method of Multipliers is designed. Experimental results on several real-world datasets show that our method has superior performance over several state-of-the-art clustering methods.