Multi-view spectral clustering has become appealing due to its good performance in capturing the correlations among all views. However, on one hand, many existing methods usually require a quadratic or cubic complexity for graph construction or eigenvalue decomposition of Laplacian matrix; on the other hand, they are inefficient and unbearable burden to be applied to large scale data sets, which can be easily obtained in the era of big data. Moreover, the existing methods cannot encode the complementary information between adjacency matrices, i.e. , similarity graphs of views and the low-rank spatial structure of adjacency matrix of each view. To address these limitations, we develop a novel multi-view spectral clustering model. Our model well encodes the complementary information by Schatten $p$ -norm regularization on the third tensor whose lateral slices are composed of the adjacency matrices of the corresponding views. To further improve the computational efficiency, we leverage anchor graphs of views instead of full adjacency matrices of the corresponding views, and then present a fast model that encodes the complementary information embedded in anchor graphs of views by Schatten $p$ -norm regularization on the tensor bipartite graph. Finally, an efficient alternating algorithm is derived to optimize our model. The constructed sequence was proved to converge to the stationary KKT point. Extensive experimental results indicate that our method has good performance.

Multi-modal clustering (MMC) aims to explore complementary information from diverse modalities for clustering performance facilitating. This article studies challenging problems in MMC methods based on deep neural networks. On one hand, most existing methods lack a unified objective to simultaneously learn the inter- and intra-modality consistency, resulting in a limited representation learning capacity. On the other hand, most existing processes are modeled for a finite sample set and cannot handle out-of-sample data. To handle the above two challenges, we propose a novel Graph Embedding Contrastive Multi-modal Clustering network (GECMC), which treats the representation learning and multi-modal clustering as two sides of one coin rather than two separate problems. In brief, we specifically design a contrastive loss by benefiting from pseudo-labels to explore consistency across modalities. Thus, GECMC shows an effective way to maximize the similarities of intra-cluster representations while minimizing the similarities of inter-cluster representations at both inter- and intra-modality levels. So, the clustering and representation learning interact and jointly evolve in a co-training framework. After that, we build a clustering layer parameterized with cluster centroids, showing that GECMC can learn the clustering labels with given samples and handle out-of-sample data. GECMC yields superior results than 14 competitive methods on four challenging datasets. Codes and datasets are available: https://github.com/xdweixia/GECMC.

Attributed graph clustering, which learns node representation from node attribute and topological graph for clustering, is a fundamental and challenging task for multimedia network-structured data analysis. Recently, graph contrastive learning (GCL)-based methods have obtained impressive clustering performance on this task. Nevertheless, there still remain some limitations to be solved: 1) most existing methods fail to consider the self-consistency between latent representations and cluster structures; and 2) most methods require a post-processing operation to get clustering labels. Such a two-step learning scheme results in models that cannot handle newly generated data, i.e. , out-of-sample (OOS) nodes. To address these issues in a unified framework, a S elf-consistent C ontrastive A ttributed G raph C lustering (SCAGC) network with pseudo-label prompt is proposed in this article. In SCAGC, by clustering labels prompt information, a self-consistent contrastive loss, which aims to maximize the consistencies of intra-cluster representations while minimizing the consistencies of inter-cluster representations, is designed for representation learning. Meanwhile, a clustering module is built to directly output clustering labels by contrasting the representation of different clusters. Thus, for the OOS nodes, SCAGC can directly calculate their clustering labels. Extensive experimental results on seven benchmark datasets have shown that SCAGC consistently outperforms 16 competitive clustering methods. The source code could be accessed at https://github.com/xdweixia/SCAGC .