Multi-view Spectral Clustering with Incomplete Graphs

Traditional multi-view learning usually assumes each instance appears in all views. However, in real-world applications, it is not an uncommon case that a number of instances suffer from some view samples missing. How to effectively cluster this kind of partial multi-view data has attracted much attention. In this paper, we propose an incomplete multi-view clustering method, namely Multi-view Spectral Clustering with Incomplete Graphs (MSCIG), which connects processes of spectral embedding and similarity matrix completion to achieve better clustering performance. Specifically, MSCIG recovers missing entries of each similarity matrix based on multiplications of a common representation matrix and corresponding view-specific representation matrix, and in turn learns these representation matrices based on the complete similarity matrices. Besides, MSCIG adopts the p-th root integration strategy to incorporate losses of multiple views, which characterizes the contributions of different views. Moreover, we develop an iterative algorithm with proved convergence to solve the resultant problem of MSCIG, which updates the common representation matrix, view-specific representation matrices, similarity matrices, and view weights alternatively. We conduct extensive experiments on 9 benchmark datasets to compare the proposed algorithm with existing state-of-the-art incomplete multi-view clustering methods. Experimental results validate the effectiveness of the proposed algorithm.