SCKM: Symmetric Co-Skew Moment for User Selection in Federated Learning

We introduce the symmetric co-skewness moment (SCKM)-a third-order informational dissimilarity metric that consistently outperforms state-of-the-art client-selection heuristics in federated learning (FL) under heterogeneous data. Unlike similarity-driven schemes, SCKM minimizes redundancy by favoring clients with complementary gradients, delivering faster and more stable convergence even at high heterogeneity levels. Operating on highly compressed 0.5% gradient summaries, our framework provides two operating modes for different deployment scales: (i) SCKM-Select directly ranks and schedules a small candidate pool, whereas (ii) SCKM-Cluster adds a fast, elbow-guided clustering step to scalably choose from thousands of users. We evaluate both variants on a VGG-16 model across multiple non-IID partition schemes and initializations, observing consistent gains over leading cosine-similarity, loss-sketch, and max-diversity baselines-without increasing the communication budget.