Novel Fuzzy Clustering Algorithm Based on Fireflies

Abstract

Aiming at the existence of fuzzy C-means algorithm was sensitive to the initial clustering center and its shortcoming of easily plunged into local optimum ,this paper proposed a novel fuzzy clustering algorithm based on fireflies .The algorithm employed the chaos initialization individuals as the initial population .Then it utilized the improved fireflies as the accurately clustering center and received a new clustering center as the initial clustering center of fuzzy C-means .Thus it can overcome the fuzzy C-means’ sensitivity to the initial clustering center and solve the deficiency of easily falling into local optimum. Simulation experiment results based on UCI standard data sets show that the algorithm can avoid falling into local optimum and precocious, it also gets better performance and results compared with other algorithms. Introduction Clustering is a process of dividing collection of physical or abstract objects into a certain amount of classes or clusters.It makes the clusters in the similar degree is high, low degree of similarity between clusters. Clustering analysis has been widely used in many fields, such as data mining, biology, statistics, image processing, pattern recognition and business intelligence, etc [1]. Fuzzy C–means algorithm has the characteristics of simple calculation and speediness, it has been widely applied. However, there are still existing problems like falling into local optimal easily and the algorithm is sensitive to the initial clustering center, etc. Therefore, in order to overcome these shortcomings of the fuzzy C-means algorithm, many scholars combine with the fuzzy C-means algorithm and particle swarm optimization (pso) [2], artificial bee colony algorithm [3], genetic algorithm, ant colony algorithm and artificial fish algorithm [4]. In 2008,Yang Xinshe proposed firefly algorithm[5,6]. The firefly algorithm is a novel and intelligent optimization algorithm, which mimic natural biological fireflies glow and the biological characteristics of mutual attraction. The algorithm has a good search and optimization performance. It dropped some biological significances of the firefly, only using their luminescence properties to search its sight partners, through comparing the fluorescence intensity and the degree of attraction to determine a certain directionand, realizing the optimized position in the process of iteration. Algorithm has been applied to many areas such as image processing [7], pipeline scheduling [8], path planning. Firefly algorithm has strong global search ability and convergence speed, less algorithm parameters, and it is suitable for parallel processing. This paper combined firefly algorithm with good local searching ability of the fuzzy C-means, took the advantages of both algorithms in order to get better results. Therefore, this paper proposed a novel fuzzy clustering algorithm based on fireflies, using logistic map produced by chaos variable initialization population, and modifying parameters of fireflies’ location updating formula, utilizing the characteristics of the chaos optimization algorithm in order to overcome premature convergence. In addition, it can improve the population diversity and searching ergodicity by chaos theory. What’s more, it avoids trapping into local optimum and improving the ability of global optimization. International Conference on Applied Science and Engineering Innovation (ASEI 2015) © 2015. The authors Published by Atlantis Press 112 Propaedeutics Fuzzy C-means algorithm.To a limited data set on given feature space { } n x x x X ,..., , 2 1 = , X is divided into c ( n c ≤ ≤ 2 )class, Assuming a class of c for clustering center { } c v v v V ,..., , 2 1 = , ij u is sample of the membership degree matrix, ] 1 , 0 [ ∈ ij u , n i ,..., 2 , 1 = , c j ,..., 2 , 1 = ; m is the fuzzy weighted index, this paper sets ] 3 , 1 [ ∈ m ,the objective function of FCM algorithm can be formulated as: