Discrete Dynamics in Nature and Society

Volume 2015 (2015), Article ID 194792, 12 pages

http://dx.doi.org/10.1155/2015/194792

## An Improved Animal Migration Optimization Algorithm for Clustering Analysis

^{1}College of Information Science and Engineering, Guangxi University for Nationalities, Nanning 530006, China^{2}Guangxi High School Key Laboratory of Complex System and Intelligent Computing, Nanning 530006, China

Received 14 June 2014; Revised 17 December 2014; Accepted 17 December 2014

Academic Editor: Josef Diblík

Copyright © 2015 Mingzhi Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Animal migration optimization (AMO) is one of the most recently introduced algorithms based on the behavior of animal swarm migration. This paper presents an improved AMO algorithm (IAMO), which significantly improves the original AMO in solving complex optimization problems. Clustering is a popular data analysis and data mining technique and it is used in many fields. The well-known method in solving clustering problems is -means clustering algorithm; however, it highly depends on the initial solution and is easy to fall into local optimum. To improve the defects of the -means method, this paper used IAMO for the clustering problem and experiment on synthetic and real life data sets. The simulation results show that the algorithm has a better performance than that of the -means, PSO, CPSO, ABC, CABC, and AMO algorithm for solving the clustering problem.

#### 1. Introduction

Data clustering is the process of grouping data into a number of clusters. The goal of data clustering is to make the data in the same cluster share a high degree of similarity while being very dissimilar to data from other clusters. It is a main task of exploratory data mining and a common technique for statistical data analysis used in many fields, including machine learning, pattern recognition, image analysis, information retrieval, and bioinformatics. Cluster analysis was originated in anthropology by Driver and Kroeber in 1932 and introduced to psychology by Zubin in 1938 and Tryon in 1939 and famously used by Cattell beginning in 1943 [1] for trait theory classification in personality psychology. Many clustering methods have been proposed; they are divided into two main categories: hierarchical and partitional. The -means clustering method [2] is one of the most commonly used partitional methods. However, the results of -means solving the clustering problem highly depend on the initial solution and it is easy to fall into local optimal solutions. Zhang et al. have proposed an improved -means clustering algorithm called -harmonic means [3]. But the accuracy of the results obtained by the method is not high enough.

In recent years, many studies have been inspired by animal behavior phenomena for developing optimization techniques, such as firefly algorithm (FA) [4], cuckoo search (CS) [5], bat algorithm (BA) [6], artificial bee colony (ABC) [7], and particle swarm optimization (PSO) [8]. Because of its advantages of global, parallel efficiency, robustness, and universality, these bioinspired algorithms have been widely used in constrained optimization and engineering optimization [9, 10], scientific computing, automatic control, and clustering problem [11–21]. Niknam et al. have proposed an efficient hybrid evolutionary algorithm based on combining ACO and SA for clustering problem [15, 16] in 2008. In 1991, Colorni et al. have presented ant colony optimization (ACO) algorithm based on the behavior of ants seeking a path between their colony and a source of food [22]. Then Shelokar et al. and Kao and Cheng have solved the clustering problem using the ACO algorithm [17, 18] in 2004 and 2006. Eberhart and Kennedy have proposed particle swarm optimizer (PSO) algorithm which simulates the movement of organisms in a bird flock or fish school [8] in 1995 and the algorithm also has been adopted to solve this problem by Omran et al. and van der Merwe and Engelbrecht [19, 23] in 2005 and 2003. Kao et al. have presented a hybrid approach according to combination of the -means algorithm, Nelder-Mead simplex search, and PSO for clustering analysis [14] in 2008. Niknam et al. have presented a hybrid evolutionary algorithm based on PSO and SA (simulated annealing algorithm, 1989 [24]) to solve the clustering problem [13] in 2009. Zou et al. have proposed a cooperative artificial bee colony algorithm to solve the clustering problem and experiment on synthetic and real life data sets to evaluate the performance [11] in 2010. Niknam and Amiri have proposed an efficient hybrid approach based on PSO, ACO, and -means called PSO-ACO-K approach for clustering analysis [12] in 2010. The artificial bee colony (ABC) algorithm is described by Karaboga [25] in 2005 and it has been adopted to solve clustering problem by Karaboga and Ozturk [20] in 2011. Voges and Pope have used an evolutionary-based rough clustering algorithm for the clustering problem [21] in 2012. Chen et al. have used monkey search algorithm for clustering analysis [26] in 2014.

Animal migration algorithm (AMO) is a new bioinspired intelligent optimization algorithm by simulating animal migration behavior proposed by Li et al. [27] in 2013. AMO simulates the widespread migration phenomenon in the animal kingdom, through the change of position, replacement of individual, and finding the optimal solution gradually. AMO has obtained good experimental results on many optimization problems. This paper presents an algorithm to improve the performance of AMO. We proposed a new migration method to modify the performance of AMO, the migration process based on shrinking animals living area operator; this method guarantees AMO rapid convergence to global optimum. By means of selecting the better solution space around the current solution, it improves search ability and accelerates convergence velocity, and it has more chance to find the global optima.

The structure of the paper is as follows. In Section 2, the traditional method -means for clustering is presented. In Section 3, the original AMO algorithm is introduced. Section 4 describes our proposed novel approach of migration process. Section 5 elaborates the improved AMO and some biological foundations of animal behaviors are explained. Section 6 illustrates experiments and discusses the results. Section 7 studies the extent of different size of shrinkage coefficient impact of the proposed algorithm. At the end of the paper, we conclude it with future directions and developments with the improved AMO.

#### 2. The -Means Clustering Algorithm

The target of data clustering is grouping data into a number of clusters; -means is one of the simplest unsupervised learning algorithms that solve the clustering problem. It is proposed by MacQueen in 1967 [28]. The procedure follows a simple and easy way to classify a given data set through a certain number of clusters (assume clusters) fixed a priori; each data vector is a -dimensional vector, satisfying the following conditions [29, 30]:(1);(2);(3).The -means clustering algorithm is as follows.(1)Set the number of clusters and the data set .(2)Randomly choose points as the cluster centroids from .(3)Assign each object to the group that has the closest centroid. The principle of division is as follows: if , and . The data will be divided into classified collection .(4)When all objects have been assigned, recalculate the positions of the centroids : where is the number of the points in the classified collection .(5)Repeat Steps and until the centroids no longer move.

The main idea is to define centroids, one for each cluster. These centroids should be placed in a cunning way because of different location causing different result. So the better choice is to place them as much as possible far away from each other. In this study, we will use Euclidian metric as a distance metric. The expression is given as follows: Finally, this algorithm aims at minimizing an objective function, in this case a squared error function. The objective function is as follows:

#### 3. Animal Migration Optimization (AMO)

Animal migration algorithm can be divided into animal migration process and animal updating process. In the migration process, the algorithm simulates how the groups of animals move from current position to a new position. During the population updating process, the algorithm simulates how animals are updated by the probabilistic method.

##### 3.1. Animal Migration Process

During the animal migration process, an animal should obey three rules: avoid collisions with your neighbors; move in the same direction as your neighbors; and remain close to your neighbors. In order to define concept of the local neighborhood of an individual, we use a topological ring, as has been illustrated in Figure 1. For the sake of simplicity, we set the length of the neighborhood to be five for each dimension of the individual. Note that, in our algorithm, the neighborhood topology is static and is defined on the set of indices of vectors. If the index of animal is , then its neighborhood consists of animal having indices , if the index of animal is 1, the neighborhood consists of animal having indices , and so forth. Once the neighborhood topology has been constructed, we select one neighbor randomly and update the position of the individual according to this neighbor, as can be seen in the following formula: where is the current position of the neighborhood, is produced by using a random number generator controlled by a Gaussian distribution, is the current position of th individual, and is the new position of th individual.