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Federated t-SNE and UMAP for Distributed Data Visualization

AAAI 2025 · Federated learning and privacy › Differential privacy · approach: Private data analysis frameworks · 5 citations (OpenAlex)

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Proposes Fed-tSNE/Fed-UMAP (and + variants with noise, plus federated spectral clustering) that learn a global set of landmark points via MMD-based federated distribution learning and Nyström-approximate the global distance matrix without sharing raw data.

Problem

Running t-SNE and UMAP (and spectral clustering) on high-dimensional data distributed across clients requires pairwise distances across all points, which requires sharing raw data and leaks privacy.

Approach

Federated distribution learning (FedDL) learns intermediate landmark points Y by minimizing the average MMD between each client's data and Y; the server then estimates the global distance/kernel matrix via Nyström approximation from client-side cross-distance matrices, enabling t-SNE, UMAP, and spectral clustering. Privacy-enhanced variants add Gaussian noise to data, variables, or gradients.

Key results

• On MNIST IID, Fed-tSNE 1-NN classification accuracy is 0.9400 vs 0.9618 for standard t-SNE, and Fed-UMAP 0.9066 vs 0.9322 for UMAP.
• Fed-SpeClust on COIL-20 yields NMI 0.8425 vs 0.8885 for standard spectral clustering (IID).
• Privacy-enhanced Fed-tSNE+ on non-IID MNIST shows lower NPA (e.g. 1-NN 0.1928 vs 0.2729 for Fed-tSNE), indicating a privacy-accuracy trade-off.

Measured effects reported in the paper

Surprising findings

• Fed-tSNE performs slightly better on IID than non-IID splits, and the paper notes the non-IID setting with one class per client is hardest.
• Fed-tSNE+ noise reduces neighbor preservation considerably on non-IID data (e.g. Fashion-MNIST NPA 1-NN 0.0071 vs 0.0356 for standard t-SNE is not the comparison; within-method drops are large).

Limitations

• Accuracy drops relative to non-federated t-SNE/UMAP/spectral clustering, with privacy-enhanced variants losing more.
• Privacy guarantees depend on noise levels and assumptions (bounded data norms), and the trade-off between accuracy and privacy is governed by sigma.
• Experiments use only four datasets with a simple client-partition setup (IID vs single-class non-IID).

Experimental setup

Datasets: MNIST Fashion-MNIST COIL-20 Mice-Protein

Benchmarks: MNIST Fashion-MNIST COIL-20 Mice-Protein

Metrics: CA k-NN accuracy NPA k-NN NMI Silhouette coefficient ARI

Baselines: t-SNE UMAP dSNE SpeClust

Builds on: t-SNE UMAP Nyström method FedAvg

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