提出联邦多任务聚类框架，实现隐私保护下的个性化聚类与共享结构学习。

Spectral clustering has emerged as one of the most effective clustering algorithms due to its superior performance. However, most existing models are designed for centralized settings, rendering them inapplicable in modern decentralized environments. Moreover, current federated learning approaches often suffer from poor generalization performance due to reliance on unreliable pseudo-labels, and fail to capture the latent correlations amongst heterogeneous clients. To tackle these limitations, this paper proposes a novel framework named Federated Multi-Task Clustering (i.e.,FMTC), which intends to learn personalized clustering models for heterogeneous clients while collaboratively leveraging their shared underlying structure in a privacy-preserving manner. More specifically, the FMTC framework is composed of two main components: client-side personalized clustering module, which learns a parameterized mapping model to support robust out-of-sample inference, bypassing the need for unreliable pseudo-labels; and server-side tensorial correlation module, which explicitly captures the shared knowledge across all clients. This is achieved by organizing all client models into a unified tensor and applying a low-rank regularization to discover their common subspace. To solve this joint optimization problem, we derive an efficient, privacy-preserving distributed algorithm based on the Alternating Direction Method of Multipliers, which decomposes the global problem into parallel local updates on clients and an aggregation step on the server. To the end, several extensive experiments on multiple real-world datasets demonstrate that our proposed FMTC framework significantly outperforms various baseline and state-of-the-art federated clustering algorithms.