{"ID":2834871,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.00849","arxiv_id":"2512.00849","title":"Topological Federated Clustering via Gravitational Potential Fields under Local Differential Privacy","abstract":"Clustering non-independent and identically distributed (non-IID) data under local differential privacy (LDP) in federated settings presents a critical challenge: preserving privacy while maintaining accuracy without iterative communication. Existing one-shot methods rely on unstable pairwise centroid distances or neighborhood rankings, degrading severely under strong LDP noise and data heterogeneity. We present Gravitational Federated Clustering (GFC), a novel approach to privacy-preserving federated clustering that overcomes the limitations of distance-based methods under varying LDP. Addressing the critical challenge of clustering non-IID data with diverse privacy guarantees, GFC transforms privatized client centroids into a global gravitational potential field where true cluster centers emerge as topologically persistent singularities. Our framework introduces two key innovations: (1) a client-side compactness-aware perturbation mechanism that encodes local cluster geometry as \"mass\" values, and (2) a server-side topological aggregation phase that extracts stable centroids through persistent homology analysis of the potential field's superlevel sets. Theoretically, we establish a closed-form bound between the privacy budget $ε$ and centroid estimation error, proving the potential field's Lipschitz smoothing properties exponentially suppress noise in high-density regions. Empirically, GFC outperforms state-of-the-art methods on ten benchmarks, especially under strong LDP constraints ($ε\u003c 1$), while maintaining comparable performance at lower privacy budgets. By reformulating federated clustering as a topological persistence problem in a synthetic physics-inspired space, GFC achieves unprecedented privacy-accuracy trade-offs without iterative communication, providing a new perspective for privacy-preserving distributed learning.","short_abstract":"Clustering non-independent and identically distributed (non-IID) data under local differential privacy (LDP) in federated settings presents a critical challenge: preserving privacy while maintaining accuracy without iterative communication. Existing one-shot methods rely on unstable pairwise centroid distances or neigh...","url_abs":"https://arxiv.org/abs/2512.00849","url_pdf":"https://arxiv.org/pdf/2512.00849v1","authors":"[\"Yunbo Long\",\"Jiaquan Zhang\",\"Xi Chen\",\"Alexandra Brintrup\"]","published":"2025-11-30T11:41:16Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}