Clean and robust affinity matrix learning for multi-view clustering

Recently, the popularity of multi-view clustering (MVC) has increased, and many MVC methods have been developed. However, the affinity matrix that is learned by the MVC method is only block diagonal if noise and outliers are not included in the data.; however, data always contain noise and outliers. As a result, the affinity matrix is unreliable for subspace clustering because it is neither clean nor robust enough, which affects clustering performance. To compensate for these shortcomings, in this paper, we propose a novel clean and robust affinity matrix (CRAA) learning method for MVC. Specifically, firstly, the global structure of data is obtained by constructing the representation space shared by all views. Next, by borrowing the idea of robust principal component analysis (RPCA), the affinity matrix is divided into two parts, i.e., a cleaner and more robust affinity matrix and a noisy matrix. Then, the two-step procedure is integrated into a unified optimization framework and a cleaner and robust affinity matrix is learned. Finally, based on the augmented Lagrangian multiplier (ALM) method, an efficient optimization procedure for obtaining the CRAA is also developed. In fact, the main idea for obtaining a cleaner and more robust affinity matrix can also be generalized to other MVC methods. The experimental results on eight benchmark datasets show that the clustering performance of the CRAA is better than that of some of the state-of-the-art clustering methods in terms of NMI, ACC, F-score, Recall and ARI metrics.