Topological Federated Clustering via Gravitational Potential Fields Under Local Differential Privacy
Yunbo Long, Jiaquan Zhang, Xi Chen, Alexandra Brintrup
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
BibTeX
@inproceedings{aaai2026_topologicalfeder,
title = {Topological Federated Clustering via Gravitational Potential Fields Under Local Differential Privacy},
author = {Yunbo Long and Jiaquan Zhang and Xi Chen and Alexandra Brintrup},
booktitle = {AAAI 2026},
year = {2026}
}