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.

Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction coefficient matrix or feature extraction methods for finding latent features of original data samples. In this paper, inspired by graph convolutional networks, we use the graph convolution technique to develop a feature extraction method and a coefficient matrix constraint simultaneously. And the graph-convolutional operator is updated iteratively and adaptively in our proposed algorithm. Hence, we call the proposed method adaptive graph convolutional subspace clustering (AGCSC). We claim that by using AGCSC, the aggregated feature representation of original data samples is suitable for subspace clustering, and the coefficient matrix could reveal the subspace structure of the original data set more faithfully. Finally, plenty of subspace clustering experiments prove our conclusions and show that AGCSC outperforms some related methods as well as some deep models.

The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block diagonal with each block indicating a subspace; 2) each block is fully connected. Though there are various spectral-type subspace clustering algorithms have been proposed, some defects still exist in the reconstruction coefficient matrices constructed by these algorithms. We find that a normalized membership matrix naturally satisfies the above two conditions. Therefore, in this paper, we devise an idempotent representation (IDR) algorithm to pursue reconstruction coefficient matrices approximating normalized membership matrices. IDR designs a new idempotent constraint for reconstruction coefficient matrices. And by combining the doubly stochastic constraints, the coefficient matrices which are closed to normalized membership matrices could be directly achieved. We present the optimization algorithm for solving IDR problem and analyze its computation burden as well as convergence. The comparisons between IDR and related algorithms show the superiority of IDR. Plentiful experiments conducted on both synthetic and real world datasets prove that IDR is an effective and efficient subspace clustering algorithm.