Multiview subspace clustering (MVSC) has attracted an increasing amount of attention in recent years. Most existing MVSC methods first collect complementary information from different views and consequently derive a consensus reconstruction coefficient matrix to indicate the subspace structure of a multi-view data set. In this paper, we initially assume the existence of a consensus reconstruction coefficient matrix and then use it to build a consensus graph filter. In each view, the filter is employed for smoothing the data and designing a regularizer for the reconstruction coefficient matrix. Finally, the obtained reconstruction coefficient matrices from different views are used to create constraints for the consensus reconstruction coefficient matrix. Therefore, in the proposed method, the consensus reconstruction coefficient matrix, the consensus graph filter, and the reconstruction coefficient matrices from different views are interdependent. We provide an optimization algorithm to obtain their optimal values. Extensive experiments on diverse multi-view data sets demonstrate that our approach outperforms some state-of-the-art methods.
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