Kernel method is a proven technique in multi-view learning. It implicitly defines a Hilbert space where samples can be linearly separated. Most kernel-based multi-view learning algorithms compute a kernel function aggregating and compressing the views into a single kernel. However, existing approaches compute the kernels independently for each view. This ignores complementary information across views and thus may result in a bad kernel choice. In contrast, we propose the Contrastive Multi-view Kernel — a novel kernel function based on the emerging contrastive learning framework. The Contrastive Multi-view Kernel implicitly embeds the views into a joint semantic space where all of them resemble each other while promoting to learn diverse views. We validate the method's effectiveness in a large empirical study. It is worth noting that the proposed kernel functions share the types and parameters with traditional ones, making them fully compatible with existing kernel theory and application. On this basis, we also propose a contrastive multi-view clustering framework and instantiate it with multiple kernel $k$ -means, achieving a promising performance. To the best of our knowledge, this is the first attempt to explore kernel generation in multi-view setting and the first approach to use contrastive learning for a multi-view kernel learning.

Taking the assumption that data samples are able to be reconstructed with the dictionary formed by themselves, recent multiview subspace clustering (MSC) algorithms aim to find a consensus reconstruction matrix via exploring complementary information across multiple views. Most of them directly operate on the original data observations without preprocessing, while others operate on the corresponding kernel matrices. However, they both ignore that the collected features may be designed arbitrarily and hard guaranteed to be independent and nonoverlapping. As a result, original data observations and kernel matrices would contain a large number of redundant details. To address this issue, we propose an MSC algorithm that groups samples and removes data redundancy concurrently. In specific, eigendecomposition is employed to obtain the robust data representation of low redundancy for later clustering. By utilizing the two processes into a unified model, clustering results will guide eigendecomposition to generate more discriminative data representation, which, as feedback, helps obtain better clustering results. In addition, an alternate and convergent algorithm is designed to solve the optimization problem. Extensive experiments are conducted on eight benchmarks, and the proposed algorithm outperforms comparative ones in recent literature by a large margin, verifying its superiority. At the same time, its effectiveness, computational efficiency, and robustness to noise are validated experimentally.

Multi-View clustering has attracted broad attention due to its capacity to utilize consistent and complementary information among views. Although tremendous progress has been made recently, most existing methods undergo high complexity, preventing them from being applied to large-scale tasks. Multi-View clustering via matrix factorization is a representative to address this issue. However, most of them map the data matrices into a fixed dimension, limiting the model’s expressiveness. Moreover, a range of methods suffers from a two-step process, i.e., multimodal learning and the subsequent $k$ -means, inevitably causing a suboptimal clustering result. In light of this, we propose a one-step multi-view clustering with diverse representation (OMVCDR) method, which incorporates multi-view learning and $k$ -means into a unified framework. Specifically, we first project original data matrices into various latent spaces to attain comprehensive information and auto-weight them in a self-supervised manner. Then, we directly use the information matrices under diverse dimensions to obtain consensus discrete clustering labels. The unified work of representation learning and clustering boosts the quality of the final results. Furthermore, we develop an efficient optimization algorithm with proven convergence to solve the resultant problem. Comprehensive experiments on various datasets demonstrate the promising clustering performance of our proposed method. The code is publicly available at https://github.com/wanxinhang/OMVCDR.

Multi-view clustering has gained broad attention owing to its capacity to exploit complementary information across multiple data views. Although existing methods demonstrate delightful clustering performance, most of them are of high time complexity and cannot handle large-scale data. Matrix factorization-based models are a representative of solving this problem. However, they assume that the views share a dimension-fixed consensus coefficient matrix and view-specific base matrices, limiting their representability. Moreover, a series of large-scale algorithms that bear one or more hyperparameters are impractical in real-world applications. To address the two issues, we propose an auto-weighted multi-view clustering (AWMVC) algorithm. Specifically, AWMVC first learns coefficient matrices from corresponding base matrices of different dimensions, then fuses them to obtain an optimal consensus matrix. By mapping original features into distinctive low-dimensional spaces, we can attain more comprehensive knowledge, thus obtaining better clustering results. Moreover, we design a six-step alternative optimization algorithm proven to be convergent theoretically. Also, AWMVC shows excellent performance on various benchmark datasets compared with existing ones. The code of AWMVC is publicly available at https://github.com/wanxinhang/AAAI-2023-AWMVC.

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 .

Multi-view clustering has been received considerable attention due to the widespread collection of multi-view data from diverse domains and sources. However, storing multi-view data across multiple devices in many real scenarios poses significant challenges for efficient data analysis. Federated Learning framework enables collaborative machine learning on distributed devices while preserving privacy constraints. Even though there have been intensive algorithms on multi-view fuzzy clustering, federated multi-view fuzzy clustering has not been adequately investigated so far. In this study, we first develop the federated learning mode into multi-view fuzzy clustering and realize the federated optimization procedure, called Federated Multiview Fuzzy C-Means clustering (FedMVFCM). Then, we design an original strategy of consensus prototype learning during federated multi-view fuzzy clustering. It is termed as Federated Multi-view Fuzzy c-means consensus Prototypes Clustering (FedMVFPC). We also further develop the federated alternative optimization algorithm with proven convergence. This study also introduces the notion of clustering prototype communication within the federated learning framework, and integrates the clustering prototypes of different views into a unified optimization formulation. The experimental studies on various benchmark datasets demonstrate that the proposed FedMVFPC method improves the federated clustering performance and efficiency. It achieves comparable or better clustering performance against the existing state-of-the-art multi-view clustering algorithms