Multi-view subspace clustering (MSC) is widely studied owing to the ability to capture the diverse and complementary information hidden in multiple views. As a representative model, tensorial MSC can capture global information by leveraging high-order correlations across various perspectives, leading to promising results. However, this approach fails to reveal the local structure in the specific view and ignores the prior information of the self-representation tensor. To address the problems, we propose the novel graph-guided local structure propagation (GGLSP) for tensorial MSC. First, we improve the adaptive graph model to acquire a fused graph similarity matrix for extracting the relationships between samples and propagating the local structure information to the self-representation tensor. Subsequently, we introduce the weighted tensor Schatten p-norm to approximate the tensor rank function by exploiting the contributions of different singular values so that the self-representation tensor can better reveal the global low-rank structure information. Finally, we develop two efficient algorithms to solve the optimization problems. Large numbers of experiments on seven popular datasets confirm the superiority of our proposed GGLSP.

Federated clustering (FC) performs well in independent and identically distributed (IID) scenarios, but it does not perform well in non-IID scenarios. In addition, existing methods lack proof of strict privacy protection. To address the above issues, we propose a new secure federated k-means clustering framework to achieve better clustering results under privacy requirements. Specifically, for the clients, we use cluster centers (representative points) generated by k-means to represent the corresponding clusters. These representative points can effectively preserve the structure of the local data and they are encrypted by differential privacy. For the server, we propose two methods to reprocess the uploaded encrypted representative points to obtain better final cluster centers, one uses k-means, and the other considers the improved density peaks (density cores) as final centers and then sends them back to the clients. Finally, each client assigns local data to their nearest centers. Experimental results show that the proposed methods perform better than several centralized (nonfederated) classical clustering algorithms [k-means, density-based spatial clustering of applications with noise (DBSCAN), and density peak clustering (DPC)] and state-of-the-art (SOTA) centralized clustering algorithms in most cases. In particular, the proposed algorithms perform better than the SOTA FC framework k-FED (ICML2021) and MUFC (ICLR2023).

Federated clustering (FC) is an emerging and important topic in data clustering research. However, for existing works, there are two challenging issues as follows. 1) FC does not perform well on non-IID data. 2) Differential privacy is a common-used way to protect raw data in FC, but there is no solid theoretical basis for selecting privacy budget$\epsilon$in Laplacian noise, and$\epsilon$is randomly set in most algorithms. In this article, we propose a new framework called NN-FC for addressing the above-mentioned issues. Specifically, 1) we provide a rigorous mathematical proof when selecting$\epsilon$, we have shown that when the value of$\epsilon$satisfies certain conditions, the neighbor relationship of data points before and after adding Laplacian noises remains unchanged. 2) According to 1), we propose a new method of obtaining global cluster centers based on distance relationships at the server, and the results of clustering the original data and clustering the privacy data become close. The experimental results show that NN-FC performs better than eight traditional and state-of-the-art (SOTA) centralized (nonfederated) clustering algorithms. In particular, NN-FC performs better than two SOTA FC frameworks k-FED (ICML2021) and MUFC (ICLR2023).