用群体稳定性指数优化非独立同分布联邦学习，提升模型准确率与公平性。

Federated learning (FL) supports privacy-preserving, decentralized machine learning (ML) model training by keeping data on client devices. However, non-independent and identically distributed (non-IID) data across clients biases updates and degrades performance. To alleviate these issues, we propose Clust-PSI-PFL, a clustering-based personalized FL framework that uses the Population Stability Index (PSI) to quantify the level of non-IID data. We compute a weighted PSI metric, $WPSI^L$, which we show to be more informative than common non-IID metrics (Hellinger, Jensen-Shannon, and Earth Mover's distance). Using PSI features, we form distributionally homogeneous groups of clients via K-means++; the number of optimal clusters is chosen by a systematic silhouette-based procedure, typically yielding few clusters with modest overhead. Across six datasets (tabular, image, and text modalities), two partition protocols (Dirichlet with parameter $α$ and Similarity with parameter S), and multiple client sizes, Clust-PSI-PFL delivers up to 18% higher global accuracy than state-of-the-art baselines and markedly improves client fairness by a relative improvement of 37% under severe non-IID data. These results establish PSI-guided clustering as a principled, lightweight mechanism for robust PFL under label skew.