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. © 2013 Springer-Verlag.