•Propose the K-DBSCAN clustering method, which can get K clusters of arbitrary shapes.•The novel harmony search is presented to optimize the clustering parameters.•Apply the novel harmony search to DBSCAN to realize the K-DBSCAN clustering. At present, the DBSCAN clustering algorithm has been commonly used principally due to its ability in discovering clusters with arbitrary shapes. When the cluster number K is predefined, though the partitional clustering methods can perform efficiently, they cannot process the non-convex clustering and easily fall into local optimum. Thereby the concept of K-DBSCAN clustering is proposed in this paper. But the basic DBSCAN has a crucial defect, that is, difficult to predict the suitable clustering parameters. Here, the well-known harmony search (HS) optimization algorithm is considered to deal with this problem. By modifying the original HS, the novel harmony search (novel-HS) is put forward, which can improve the accuracy of results as well as enhance the robustness of optimization. In K-DBSCAN, the novel-HS is used to optimize the clustering parameters of DBSCAN to obtain better clustering effect with the number of K classifications. Experimental results show that the designed clustering method has superior performance to others and can be successfully considered as a new clustering scheme for further research.