Research on the Application of the P System with Active Membranes in Clustering

Abstract

In this paper a clustering algorithm based on a P System with active membranes is proposed which provides new ideas and methods for cluster analysis. The membrane system has great parallelism. It could reduce the computational time complexity. Firstly a clustering problem is transformed into a graph theory problem by transforming the objects into graph nodes and dissimilarities into edges with weights of complete undirected graph, and then a P system with all the rules to solve the problem is constructed. The specific P system with external output is designed for the dissimilarity matrix associated with n objects. First all combinations of all nodes are listed to show all possibilities of the paths (the solution space) by using division rules of P system. Then a shortest path with the minimum sum of weights is selected. At last the path is divided into k parts from the edges with the k-1 biggest weights according to the preset number of clusters k. That is to say, all nodes are divided into k clusters. The calculation of the P system can get all the clustering results. Through example test, the proposed algorithm is appropriate for cluster analysis. This is a new attempt in applications of membrane system.

Project supported by the Natural Science Foundation of China(No.61170038), Natural Science Foundation of Shandong Province, China (No.ZR2011FM001), Humanities and Social Sciences Project of Ministry of Education, China (No.12YJA630152), Social Science Fund of Shandong Province, China (No.11CGLJ22), Science-Technology Program of the Higher Education Institutions of Shandong Province, China (No.J12LN22), Science-Technology Program of the Higher Education Institutions of Shandong Province, China (No. J12LN65), Science-Technology Program of the Higher Education Institutions of Shandong Province, China(No.J12LN22), Research Award Foundation for Outstanding Young Scientists of Shandong Province, China (No.BS2012DX041).