One-step multi-view spectral clustering by learning common and specific nonnegative embeddings

Multi-view spectral clustering is a hot research area which has attracted increasing attention. Most existing multi-view spectral clustering methods utilize a two-step strategy. The first step obtains a common embedding by fusing spectral embeddings of different views, and the second step conducts hard clustering, such as K-means or spectral rotation, on the common embedding. Because the goal of the first step is not obtaining optimal clustering result, and the requirement to post-processing makes the final clustering result uncertain. In this paper, we propose a novel one-step multi-view spectral clustering method, in which the spectral embedding and nonnegative embedding are unified into one framework. Therefore, our method can avoid the uncertainty brought by post-processing and obtain optimal clustering result. Moreover, the nonnegative embedding is divided into two parts. The common nonnegative embedding indicates the shared cluster structure, and the specific nonnegative embedding indicates the exclusive cluster structure of each view. Hence, our method can well tackle with noises and outliers of different views. Furthermore, an alternating iterative algorithm is used to solve the joint optimization problem. Extensive experimental results on four real-world datasets have demonstrated the effectiveness of the proposed method.