On the Optimal Number of Grids for Differentially Private Non-Interactive K-Means Clustering
Authors: Pranjal Naman, Yogesh Simmhan
Differentially private K-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.
Journal/Conference
SPCOM 2026
Graph Neural Networks (GNNs) have experienced rapid advancements in recent years due to their ability to learn meaningful representations from graph data structures. Federated Learning (FL) has emerged as a viable machine learning approach for training a shared model on decentralized data, addressing privacy concerns while leveraging parallelism. Existing methods that address the unique requirements of federated GNN training using remote embeddings to enhance convergence accuracy are limited by their diminished performance due to large communication costs with a shared embedding server. In this paper, we present OpES, an optimized federated GNN training framework that uses remote neighbourhood pruning, and overlaps pushing of embeddings to the server with local training to reduce the network costs and training time. The modest drop in per-round accuracy due to pre-emptive push of embeddings is out-stripped by the reduction in per-round training time for large and dense graphs like Reddit and Products, converging up to ≈2× faster than the state-of-the-art technique using an embedding server and giving up to 20% better accuracy than vanilla federated GNN learning.
We also theoretically show that minimizing the activation norm reduces the top eigenvalue of the layer-wise Hessian of the client’s loss, which in turn decreases the overall Hessian’s top eigenvalue, ensuring convergence to a flat minimum. We apply our proposed flatness-constrained optimization to the existing FL techniques and obtain significant improvements, thereby establishing new state-of-the-art.