Affiliations: [a] Business School, Shandong Normal University, Jinan, Shandong 250014, China
Correspondence:
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Corresponding author: Xin Wang, Business School, Shandong Normal University, Jinan, Shandong 250014, China. E-mail: sdxyliu@163.com.
Abstract: This paper combines the graph theory and P system to solve the clustering problem. In order to effectively identify clusters with arbitrary shapes and uneven densities, we combine MkNN clustering algorithm and graph theory to propose a mutual k-nearest neighbors graph (MkNNG) clustering algorithm. In order to further improve the efficiency of MkNNG algorithm, based on the non-determinism and great parallelism of P system, a cell-like P system with multi-promoters and multi-inhibitors named mutual k-nearest neighbors graph P system (MkNNG-P) is designed. And then based on MkNNG-P system, a novel clustering algorithm named MkNNG-P clustering algorithm is proposed, which uses the membrane objects and rules to solve the clustering problem. MkNNG-P algorithm first calculates the dissimilarity between any two nodes in n-1 membranes in parallel. After then it uses one membrane to get k-nearest neighbors of n nodes. Finally, one membrane is used to find mutual k-nearest neighbors and construct MkNNG to discover the natural clusters in the data set. Experiments show that MkNNG-P algorithm has the advantages of both MkNNG and P system. It not only can obtain good clustering quality for data of different sizes and shapes without presetting clustering numbers, but also has extremely high computing speed.
Keywords: Membrane computing, P system, graph theory, MkNN clustering algorithm
