The Equivalence of Multi-view Clustering via Latent Co-association Matrix

Studying the relationship between multi-view clustering and ensemble clustering is of great practical and theoretical significance in achieving the equivalence of multi-view clustering. The problem of ensemble clustering is usually tackled by generating multiple base clusterings and then combining them to achieve the clustering result. Most existing ensemble clustering methods either linearly combine connective matrices to construct the co-association matrix or refine the co-association matrix with the built coherent-link matrix. However, directly casting ensemble clustering as a multi-view clustering problem becomes challenging. In this paper, we show that the equivalence of multi-view clustering and ensemble clustering can be established based on the formulation of objective function. To be specific, we have multiple co-association matrices by defining $\delta$-sensitive feature descriptor and introduce a latent co-association matrix shared by different co-association matrices. The $\delta$-sensitive feature descriptor can refine the original co-association matrix in a general manner and alleviate the impacts brought by poor base clusterings. We then define the $\delta$-sensitive margin and prove that $\delta$-sensitive feature descriptor generates the largest $\delta$-sensitive margin, which helps lead to a discriminative co-association representation. These multiple co-association representations are collected into a tensor and the low-rank constraint is used to better explore the global relationship among entries in the tensor. Then the relationship between multi-view clustering and ensemble clustering is built in this way. Extensive experiments on several data sets validate the above analysis in terms of different metrics.