Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and model-agnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix—a fundamental representation of sample relationships—without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods. Code will be released.

Community structures are critical towards understanding not only the network topology but also how the network functions. However, how to evaluate the quality of detected community structures is still challenging and remains unsolved. The most widely used metric, normalized mutual information (NMI), was proven to have finite size effect, and its improved form relative normalized mutual information (rNMI) has reverse finite size effect. Corrected normalized mutual information (cNMI) was thus proposed and has neither finite size effect nor reverse finite size effect. However, in this paper, we show that cNMI violates the so-called proportionality assumption. In addition, NMI-type metrics have the problem of ignoring importance of small communities. Finally, they cannot be used to evaluate a single community of interest. In this paper, we map the computed community labels to the ground-truth ones through integer linear programming, and then use kappa index and F-score to evaluate the detected community structures. Experimental results demonstrate the advantages of our method.

DNA methylation is a critical epigenetic modification that plays an important role in cancers. The available algorithms fail to fully characterize epigenetic modules. To address this issue, we first characterize the epigenetic module as a group of well-connected genes in the protein interaction network and are also co-methylated based on gene methylation profiles. Then, the epigenetic module discovery problem is transformed into an optimization problem. Then, a regularized nonnegative matrix factorization algorithm for methylation modules (RNMF-MM) is presented, where the co-methylation constraint is treated as a regularizer. Using the artificial networks with known module structure, we demonstrate that the proposed algorithm outperforms state-of-the-art approaches in terms of accuracy. On the basis of breast cancer methylation data and protein interaction network, the RNMF-MM algorithm discovers methylation modules that are significantly more enriched by the known pathways than those obtained by other algorithms. These modules serve as biomarkers for predicting cancer stages and estimating survival time of patients. The proposed model and algorithm provide an effective way for the integrative analysis of protein interaction network and methylation data.