A Privacy-Enhanced Multi-Stage Dimensionality Reduction Vertical Federated Clustering Framework

Federated Clustering (FL clustering) aims to discover latent knowledge in multi-source distributed data through clustering algorithms while preserving data privacy. Federated learning is categorized into horizontal and vertical federated learning based on data partitioning scenarios. Horizontal federated learning is applicable to scenarios with overlapping feature spaces but different sample IDs across parties. Vertical federated learning facilitates cross-institutional feature complementarity, which is particularly suited for scenarios with highly overlapping sample IDs yet significantly divergent features. As a classic clustering algorithm, k-means has seen extensive improvements and applications in horizontal federated learning. However, its application in vertical federated learning remains insufficiently explored, with room for enhancement in privacy protection and communication efficiency. Simultaneously, client feature imbalance may lead to biased clustering results. To improve communication efficiency, this paper introduces Product Quantization (PQ) to compress high-dimensional data into low-dimensional codes by generating local codebooks. Leveraging the inherent k-means algorithm within PQ, local training preserves data structures while overcoming privacy risks associated with traditional PQ methods that require server-side data reconstruction (which may leak data distributions). To enhance privacy without compromising performance, Multidimensional Scaling (MDS) maps codebook cluster centers into distance-preserving indices. Only these indices are uploaded to the server, eliminating the need for data reconstruction. The server executes k-means on the indices to minimize intra-group similarity and maximize inter-group divergence. This scheme retains original codebooks locally for strict privacy protection.The nested application of PQ and MDS significantly reduces communication volume and frequency while effectively alleviating clustering bias caused by client feature dimension imbalance. Validation on the MNIST dataset confirms that the approach maintains k-means clustering performance while meeting federated learning requirements for privacy and efficiency.