Federated Fuzzy C-means with Schatten- <i>p</i> Norm Minimization

Multi-view clustering has emerged as an important unsupervised method to process unlabelled multi-view data that provides a comprehensive description of an object. Existing multi-view clustering methods focus on centralized settings but ignore the fact that real-world multi-view data may be distributed across different entities. The sensitive information embedded in multi-view data hinders the cooperative training of multi-view clustering, since data of different views cannot be directly shared, leading to a great challenge to cooperatively exploit the consistent and complementary information of different views. To validate the multi-view clustering in distributed scenarios, in this paper, we propose a novel federated multi-view method named Federated Multi-View Fuzzy C-means with Schatten-p Norm Minimization (FMVFCMSP) which is based on fuzzy C-means and tensor Schatten p-norm. Specifically, we utilize the membership degrees to replace conventional hard clustering assignment in K-means, enabling improved uncertainty handling and less information loss. Moreover, we introduce a tensor Schatten p-norm-based regularizer to fully explore the inter-view complementary information and global spatial structure. We also develop a federated optimization algorithm enabling clients to collaboratively learn the clustering results. Extensive experiments on several datasets demonstrate that our proposed method exhibits superior performance in federated multi-view clustering.