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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cardona, M., Colomer, M.A., Pérez-Jiménez, M.J.: Hierarchical clustering with membrane computing. Computing and Informatics 27(3), 497–513 (2008)
Zhang, H.Y.: The research on clustering algorithm based on DNA computing. Ph.D. dissertation, Dept. Management Science and Engineering, Shandong Normal Univ., Jinan, China (2011) (in Chinese)
Zhang, G.X., Pan, L.Q.: A survey of membrane computing as a new branch of natural computing. Chinese Journal of Computers 33(2), 208–214 (2010) (in Chinese)
Huang, L.: Research on Membrane Computing Optimization Methods. Ph.D. dissertation, Dept. Control Science and Engineering, Zhejiang Univ., Hangzhou, China (2007) (in Chinese)
Paun, G., Rozenberg, G., Salomaa, A.: Membrane Computing, pp. 282–301. Oxford University Press, New York (2010)
Marc, G.A., Daniel, M., Alfonso, R.P., Petr, S.: A P system and a constructive membrane-inspired DNA algorithm for solving the Maximum Clique Problem. BioSystems 90(3), 687–697 (2007)
Zhang, H.Y., Liu, X.Y.: A CLIQUE algorithm using DNA computing techniques based on closed-circle DNA sequences. Biosystems 105(1), 73–82 (2011)
Zhang, X.Y., Zeng, X.X., Pang, L.Q., Luo, B.: A Spiking Neural P System for Performing Multiplication of Two Arbitrary Natural Numbers. Chinese Journal of Computers 32(12), 2362–2372 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhao, Y., Liu, X., Qu, J. (2013). Research on the Application of the P System with Active Membranes in Clustering. In: Zu, Q., Hu, B., Elçi, A. (eds) Pervasive Computing and the Networked World. ICPCA/SWS 2012. Lecture Notes in Computer Science, vol 7719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37015-1_78
Download citation
DOI: https://doi.org/10.1007/978-3-642-37015-1_78
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37014-4
Online ISBN: 978-3-642-37015-1
eBook Packages: Computer ScienceComputer Science (R0)