Clustering explanation based on multi-hyperrectangle

Clustering plays a crucial role in data mining and pattern recognition, but the interpretation of clustering results is often challenging. Existing interpretation methods usually lack an intuitive and accurate description of irregular shapes and high dimensional datas. This paper proposes a novel clustering explanation method based on a Multi-HyperRectangle(MHR), for extracting post hoc explanations of clustering results. MHR first generates initial hyperrectangles to cover each cluster, and then these hyper-rectangles are gradually merged until the optimal shape is obtained to fit the cluster. The advantage of this method is that it recognizes the shape of irregular clusters and finds the optimal number of hyper-rectangles based on the hierarchical tree structure, which discovers structural relationships between rectangles. Furthermore, we propose a refinement method to improve the tightness of the hyperrectangles, resulting in more precise and comprehensible explanations. Experimental results demonstrate that MHR significantly outperforms existing methods in both the tightness and accuracy of cluster interpretation, highlighting its effectiveness and innovation in addressing the challenges of clustering interpretation.