Discrete Multi-Graph Clustering

Fast Continual Multi-View Clustering With Incomplete Views

Multi-view clustering (MVC) has attracted broad attention due to its capacity to exploit consistent and complementary information across views. This paper focuses on a challenging issue in MVC called the incomplete continual data problem (ICDP). Specifically, most existing algorithms assume that views are available in advance and overlook the scenarios where data observations of views are accumulated over time. Due to privacy considerations or memory limitations, previous views cannot be stored in these situations. Some works have proposed ways to handle this problem, but all of them fail to address incomplete views. Such an incomplete continual data problem (ICDP) in MVC is difficult to solve since incomplete information with continual data increases the difficulty of extracting consistent and complementary knowledge among views. We propose Fast Continual Multi-View Clustering with Incomplete Views (FCMVC-IV) to address this issue. Specifically, the method maintains a scalable consensus coefficient matrix and updates its knowledge with the incoming incomplete view rather than storing and recomputing all the data matrices. Considering that the given views are incomplete, the newly collected view might contain samples that have yet to appear; two indicator matrices and a rotation matrix are developed to match matrices with different dimensions. In addition, we design a three-step iterative algorithm to solve the resultant problem with linear complexity and proven convergence. Comprehensive experiments conducted on various datasets demonstrate the superiority of FCMVC-IV over the competing approaches. The code is publicly available at https://github.com/wanxinhang/FCMVC-IV.

Low-rank discrete multi-view spectral clustering

Spectral clustering has attracted intensive attention in multimedia applications due to its good performance on arbitrary shaped clusters and well-defined mathematical framework. However, most existing multi-view spectral clustering methods still have the following demerits: (1) They ignore useful complementary information embedded in indicator matrices of different views. (2) The conventional post-processing methods based on the relax and discrete strategy inevitably result in the sub-optimal discrete solution. To tackle the aforementioned drawbacks, we propose a low-rank discrete multi-view spectral clustering model. Drawing inspiration from the fact that the difference between indicator matrices of different views provides useful complementary information for clustering, our model exploits the complementary information embedded in indicator matrices with tensor Schatten p-norm constraint. Further, we integrate low-rank tensor learning and discrete label recovering into a uniform framework, which avoids the uncertainty of the relaxed and discrete strategy. Extensive experiments on benchmark datasets have demonstrated the effectiveness and superiority of the proposed method.

High-Order Correlation Preserved Incomplete Multi-View Subspace Clustering

Incomplete multi-view clustering aims to exploit the information of multiple incomplete views to partition data into their clusters. Existing methods only utilize the pair-wise sample correlation and pair-wise view correlation to improve the clustering performance but neglect the high-order correlation of samples and that of views. To address this issue, we propose a high-order correlation preserved incomplete multi-view subspace clustering (HCP-IMSC) method which effectively recovers the missing views of samples and the subspace structure of incomplete multi-view data. Specifically, multiple affinity matrices constructed from the incomplete multi-view data are treated as a third-order low rank tensor with a tensor factorization regularization which preserves the high-order view correlation and sample correlation. Then, a unified affinity matrix can be obtained by fusing the view-specific affinity matrices in a self-weighted manner. A hypergraph is further constructed from the unified affinity matrix to preserve the high-order geometrical structure of the data with incomplete views. Then, the samples with missing views are restricted to be reconstructed by their neighbor samples under the hypergraph-induced hyper-Laplacian regularization. Furthermore, the learning of view-specific affinity matrices as well as the unified one, tensor factorization, and hyper-Laplacian regularization are integrated into a unified optimization framework. An iterative algorithm is designed to solve the resultant model. Experimental results on various benchmark datasets indicate the superiority of the proposed method. The code is implemented by using MATLAB R2018a and MindSpore library: https://github.com/ChangTang/HCP-IMSC.

View-Wise Versus Cluster-Wise Weight: Which Is Better for Multi-View Clustering?

Weighted multi-view clustering (MVC) aims to combine the complementary information of multi-view data (such as image data with different types of features) in a weighted manner to obtain a consistent clustering result. However, when the cluster-wise weights across views are vastly different, most existing weighted MVC methods may fail to fully utilize the complementary information, because they are based on view-wise weight learning and can not learn the fine-grained cluster-wise weights. Additionally, extra parameters are needed for most of them to control the weight distribution sparsity or smoothness, which are hard to tune without prior knowledge. To address these issues, in this paper we propose a novel and effective Cluster-weighted mUlti-view infoRmation bottlEneck (CURE) clustering algorithm, which can automatically learn the cluster-wise weights to discover the discriminative clusters across multiple views and thus can enhance the clustering performance by properly exploiting the cluster-level complementary information. To learn the cluster-wise weights, we design a new weight learning scheme by exploring the relation between the mutual information of the joint distribution of a specific cluster (containing a group of data samples) and the weight of this cluster. Finally, a novel draw-and-merge method is presented to solve the optimization problem. Experimental results on various multi-view datasets show the superiority and effectiveness of our cluster-wise weighted CURE over several state-of-the-art methods.