Federated learning, as a privacy-preserving distributed machine learning paradigm, enables collaborative model training without sharing raw data. However, it faces dual challenges of communication efficiency and model performance under Non-IID (Non-Independent and Identically Distributed) data scenarios. Existing approaches primarily reduce communication overhead by decreasing rounds or compressing per-round data volume, yet exhibit significant limitations: Firstly, strategies like FedAvg with local multi-step updates often lead to unstable convergence when handling highly heterogeneous data; Secondly, gradient quantization and sparsification techniques ignore inter-client gradient correlations during independent compression, causing information loss and accuracy degradation. To address these issues, we propose an efficient communication scheme tailored for data heterogeneity. First, we perform dynamic cluster analysis on client gradients via MiniBatchKMeans, leveraging low-rank characteristics within clusters to extract shared basis vectors through Singular Value Decomposition (SVD) for gradient compression. Second, a heterogeneity-aware group weighting mechanism is designed to optimize global aggregation by jointly considering intra-group data volume and distribution divergence. Finally, a periodic basis vector update strategy is introduced to maintain gradient representation capability. Extensive experiments demonstrate that our method significantly reduces communication overhead under Non-IID settings compared to existing approaches. For example, compared to the popular collaborative gradient compression method SVDFed, our method achieves average communication overhead reductions of 33.33%, 44.54%, and 44.38% across three different datasets.