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Creating Coherence in Federated Non-Negative Matrix Factorization

AAAI 2025 · Federated learning and privacy › Communication-efficient FL · approach: Local drift correction · 0 citations (OpenAlex)

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Proposes FNMF, a federated non-negative matrix factorization method that uses alignment-aware drift (permutation-aware matching distance), proximal client updates, and barycenter aggregation at the server.

Problem

Federated NMF clients learn permutation-equivalent but misaligned components, so standard federated drift and averaging produce incoherent global coefficient matrices and degraded reconstructions.

Approach

Replace the standard drift with a matching distance that optimally aligns components (LAP, incomplete LAP, or Sinkhorn soft alignment), use a proximal operator built on this distance for client updates, and aggregate client coefficient matrices via matrix barycenters computed with a fixed-point heuristic.

Key results

• On nine real-world datasets with 50 clients, FNMF variants achieve the lowest RMSD on most datasets, e.g., MNIST 6.48 (FNMF-LAP-rho) vs 12.52 for FedProx and Fashion MNIST 6.73 vs 11.88 for FedAvg.
• On TCGA, FedProx (48.94) outperforms FNMF (84.35 for LAP), showing a limitation of the proposed method on that dataset.
• Barycenter computation is shown NP-hard via reduction to k-means, and the fixed-point heuristic matches the ideal barycenter under idealized conditions.

Measured effects reported in the paper

Surprising findings

• FedProx outperforms FNMF on TCGA by a large margin, and FedAvg/FedProx are better on HPA Brain than FNMF variants.
• Plain k-means heuristics for barycenters yield lower-quality solutions than the proposed alignment-based fixed-point method.

Limitations

• Barycenter computation is NP-hard, so the method relies on heuristics without optimality guarantees.
• Underperforms FedProx on TCGA and FedAvg on HPA Brain in some settings.
• Experiments are on NMF with synthetic and public datasets; no evaluation on large-scale or heterogeneous real federated deployments.

Experimental setup

Datasets: ArXiv abstracts tf-idf CIFAR-10 Fashion MNIST Goodreads HPA Brain Movielens 25M MNIST Netflix Prize TCGA

Benchmarks: ArXiv CIFAR-10 Fashion MNIST Goodreads HPA Brain Movielens 25M MNIST Netflix TCGA

Metrics: RMSD total reconstruction distance orthogonality gap runtime loss vs synchronization

Baselines: FedAvg FedProx iPALM MUR k-means (Lloyd) fuzzy c-means

Builds on: FedProx FedAvg iPALM Wasserstein barycenters Sinkhorn algorithm

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