Global Optimal Path-Based Clustering Algorithm

Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based clustering (GOPC) algorithm in this paper. The GOPC algorithm is based on two facts: (1) medoids have the minimum degree in their clusters; (2) the minimax distance between two objects in one cluster is smaller than the minimax distance between objects in different clusters. Extensive experiments are conducted on synthetic and real-world datasets to evaluate the performance of the GOPC algorithm. The results on synthetic datasets show that the GOPC algorithm can recognize all kinds of clusters regardless of their shapes, sizes, or densities. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of the GOPC algorithm. In addition, the GOPC algorithm needs only one parameter, i.e., the number of clusters, which can be estimated by the decision graph. The advantages mentioned above make GOPC a good candidate as a general clustering algorithm. Codes are available at https://github.com/Qidong-Liu/Clustering.