Stochastic Numerical P Systems With Application in Data Clustering Problems

Abstract

This paper proposes an extension of numerical P (NP) systems, called stochastic numerical P (StNP) systems. In StNP systems, a novel stochastic production function-repartition protocol is developed to evolve the variables. Compared with usual production function-repartition protocol in NP systems, there are two differences in stochastic production function-repartition protocol: (i) some stochastic/randomized factors are introduced in production function and/or repartition protocol; (ii) data updating way is relaxed and can be flexibly used. An StNP system has a nested structure and contains some variables and a group of programs. The programs consist of stochastic production function-repartition protocols and/or usual production function-repartition protocols. Therefore, StNP systems are a class of distributed parallel computing models with stochastic and dynamic characteristics. Data clustering problems are used as an application to demonstrate the availability and effectiveness of StNP systems. Based on StNP systems, a novel partition clustering algorithm is presented. Experimental results demonstrate advantage of StNP systems for data clustering problems.

Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes

“…For the theoretical research of membrane computing, three types of P systems have been extended to obtain several universal computational models [ 3 , 4 , 5 , 6 , 7 ], and the computational complexity of extended P systems has been explored [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. For the application research of membrane computing, existing studies have realized the integration of membrane computing with algorithms for applications in robot control [ 21 , 22 ], data modeling, and optimization [ 23 , 24 , 25 , 26 ], algorithms for solving NP problems [ 27 , 28 , 29 ], clustering algorithms [ 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ], and image processing [ 38 , 39 , 40 ].…”

A Grid-Density Based Algorithm by Weighted Spiking Neural P Systems with Anti-Spikes and Astrocytes in Spatial Cluster Analysis

“…SN P systems, which are inspired by neural cells [3], have a series of spikes and information processing rules, called firing and forgetting rules [4]. Inspired by different biological phenomena and mathematical motivations, several families of SN P systems have been constructed, such as SN P systems with anti-spikes [5], SN P systems with weight [6], SN P systems with astrocyte [7], stochastic numerical P systems [8], SN P systems with threshold [9], numerical spiking neural P systems [10], double layers self-organized spiking neural P systems [11], SN P systems with rules on synapses [12], SN P systems with structural plasticity [13]. For applications, SN P systems are used to design logic gates, logic circuits [7] and operating systems [14], perform basic arithmetic operations [15], solve combinatorial optimization problems [16], and realize fingerprint recognition [11].…”