Robust Multi-View Clustering Through Partition Integration on Stiefel Manifold

Multi-view clustering aims at integrating information from different views to improve clustering performance. Recent methods integrate multiple view-specific partition matrices to seek a consensus one and have demonstrated promising clustering performance in various applications. However, the clustering performance of such methods heavily relies on the consensus partition matrix estimated by the arithmetic mean in euclidean space and thus is highly susceptible to noise corruption. To this end, this article proposes to learn a consensus partition matrix through the geometric mean on the manifold to achieve robust clustering. Specifically, the multiple view-specific partition matrices can be regarded as points residing in the Stiefel manifold and enable a manifold-based integration. Consequently, the view-specific partition matrices are integrated by estimating a consensus partition matrix as the center point on the Stiefel manifold. Such a partition integration boils down to the Fréchet mean problem on a manifold, which is solved by the intrinsic manifold-based optimization and proves effective in providing a more robust estimation against noise. Experimental results on seven benchmark datasets demonstrate the effectiveness and noise-robustness of our proposed method in comparison to eight competitive methods.