Centroid cross-efficiency approach for clustering

Recognizing the critical importance of explainable clustering results for decision-making and the influence of sample importance on the clustering result, this study proposes a clustering method based on the centroid data envelopment analysis (DEA) cross-efficiency approach. Specifically, this study first introduces the centroid DEA cross-efficiency approach. The approach is constructed based on the unique set of centroid weights of the convex polytope formed by all optimal weight vectors for each DMU. Then, a gravity model is constructed based on the centroid DEA cross-efficiency approach. The gravity model simultaneously accounts for the sample importance and the distance between samples. Based on the gravity between samples, this study develops the gravity clustering method. This clustering method enhances interpretability and provides decision support by identifying the importance degree of the features for samples across different clusters through centroid weights. To validate the effectiveness, an empirical example is conducted, and the result shows that the proposed clustering method outperforms existing DEA-based clustering approaches. Furthermore, a clustering study is conducted on the healthcare levels of various provinces in China, and policy recommendations are provided for the medical development of provinces within different clusters.