Metric Embedding Initialization-Based Differentially Private and Explainable Graph Clustering (2509.06214v1)

Abstract: Graph clustering under the framework of differential privacy, which aims to process graph-structured data while protecting individual privacy, has been receiving increasing attention. Despite significant achievements in current research, challenges such as high noise, low efficiency and poor interpretability continue to severely constrain the development of this field. In this paper, we construct a differentially private and interpretable graph clustering approach based on metric embedding initialization. Specifically, we construct an SDP optimization, extract the key set and provide a well-initialized clustering configuration using an HST-based initialization method. Subsequently, we apply an established k-median clustering strategy to derive the cluster results and offer comparative explanations for the query set through differences from the cluster centers. Extensive experiments on public datasets demonstrate that our proposed framework outperforms existing methods in various clustering metrics while strictly ensuring privacy.