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OmniFC: Rethinking Federated Clustering via Lossless and Secure Distance Reconstruction

NeurIPS 2025 · Federated learning and privacy › Personalized and heterogeneous FL · approach: Federated semi-supervised and graph learning · 1 citations (OpenAlex)

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Proposes OmniFC, a one-shot, model-agnostic federated clustering framework that uses Lagrange coded computing to let clients share encoded data so the server can exactly reconstruct the global pairwise distance matrix and run any distance-based centralized clustering method.

Problem

Federated clustering must discover global cluster structure without sharing raw data, but existing methods rely on model-specific local proxies (centroids, basis matrices, kernel factors) that are fragile under Non-IID data and leak privacy or inherit centralized inductive biases.

Approach

Clients encode their samples with Lagrange polynomial interpolation (with t noise terms) and share encoded data with peers; each client computes pairwise squared distances on encoded data and sends them to the server, which interpolates and sums segment distances to recover the exact global distance matrix. The matrix then feeds any centralized clustering method, decoupling FC from model-specific

Key results

• On the Kappa tables, OmniFC-SC matches centralized SC (e.g., 0.89 on 10x_73k and 0.95 on Iris) across all Non-IID levels, while FedSC drops to 0.31 on Iris at p=1.00.
• OmniFC is the best method in 27 of 35 SC-based settings in the Kappa table count row, versus 8 for FedSC.
• Distance reconstruction RMSE is 0.0002 on MNIST across sample sizes from 1000 to 10000.

Measured effects reported in the paper

Surprising findings

• Kappa-based OmniFC-KM occasionally exceeds its centralized KM counterpart (e.g., 0.56 vs 0.85 is lower on 10x_73k, but 0.95 vs 0.95 on Iris and 0.51 vs 0.50 on Fashion-MNIST), suggesting the distance matrix can act as a surrogate for raw features.
• Under the NMI evaluation, several baselines or OmniFC variants are sometimes better than centralized counterparts, so the authors caution that NMI is less reliable than Kappa.

Limitations

• Exact reconstruction requires m >= 2l + 2t - 1, which constrains the number of clients relative to segment and noise hyperparameters.
• Full n x n pairwise distance matrices are needed, so experiments subsample datasets above 5000 samples to 1000, limiting scalability.
• Server-side decoding cost grows with l, and the paper gives no theoretical analysis of the overall complexity trade-off.

Experimental setup

Datasets: Iris MNIST Fashion-MNIST COIL-20 COIL-100 Pendigits 10x_73k

Benchmarks: Iris MNIST Fashion-MNIST COIL-20 COIL-100 Pendigits 10x_73k

Metrics: Kappa NMI RMSE

Baselines: k-FED MUFC FFCM FedSC FedMAvg SecFC

Builds on: Lagrange coded computing k-means spectral clustering SecFC

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