Abstract
Membrane computing is widely used in many areas, however, there are several limitations in its structures and rules. Although many researchers are engaged in the study of P systems, seldom focus on improving membrane structures. The purpose of this paper is to propose a new kind of communication P system on lattice (LTC-P systems). We describe membrane structures on lattice with communication rules. The computational completeness of the new P system is proved by simulation of register machine. The new P system is used in solving clustering problems. It is combined with the thought of density-based, partition-based and hierarchical clustering algorithm. Clustering is implemented by supremum and infimum rules. The result is obtained through output membrane. All the processes are conducted in membranes. Cluster result via a \(20\) points data set verifies that the proposed new P systems cluster data set accurately and reduce time complexity. Wine data set are also used in testing the influence of parameters. More suitable \(\varepsilon \) and \({ MinPts}\) are found to gain less missing data which are seen as noise. Comparative results in various aspects indicate LTC-P system based clustering algorithm consumes less time than traditional algorithms significantly. It also uses less rules and gives more simple membrane structures than conventional cell-like P system. The new P system provides an alternative for traditional membrane computing.
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Acknowledgments
Research is supported by the Natural Science Foundation of China (No. 61170038), the Natural Science Foundation of Shandong Province (No. ZR2011FM001), the Shandong Soft Science Major Project (No. 2010RKMA2005), Humanities and Social Sciences project Supported by Chinese Ministry of Education (12YJA630152), Science-Technology Program of the Higher Education Institutions of Shandong Province, China (J12LN22), Science-Technology Program of the Higher Education Institutions of Shandong Province, China (J12LN65). The authors would like to thank anonymous referees for their helpful comments and valuable suggestions which improved the content and composition substantially.
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Communicated by T.-P. Hong.
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Xue, J., Liu, X. Lattice based communication P systems with applications in cluster analysis. Soft Comput 18, 1425–1440 (2014). https://doi.org/10.1007/s00500-013-1155-y
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DOI: https://doi.org/10.1007/s00500-013-1155-y