An improved form of the ant lion optimization algorithm for image clustering problems

Turkish Journal of Electrical Engineering & Computer Sciences http://journals.tubitak.gov.tr/elektrik/ Research Article Turk J Elec Eng & Comp Sci (2019) 27: 1445 – 1460 © TÜBİTAK doi:10.3906/elk-1703-240 An improved form of the ant lion optimization algorithm for image clustering problems Metin TOZ∗ Department of Computer Engineering, Faculty of Technology, Düzce University, Düzce, Turkey Received: 20.03.2017 • Accepted/Published Online: 22.01.2019 • Final Version: 22.03.2019 Abstract: This paper proposes an improved form of the ant lion optimization algorithm (IALO) to solve image clustering problem. The improvement of the algorithm was made using a new boundary decreasing procedure. Moreover, a recently proposed objective function for image clustering in the literature was also improved to obtain well-separated clusters while minimizing the intracluster distances. In order to accurately demonstrate the performances of the proposed methods, firstly, twenty-three benchmark functions were solved with IALO and the results were compared with the ALO and a chaos-based ALO algorithm from the literature. Secondly, four benchmark images were clustered by IALO and the obtained results were compared with the results of particle swarm optimization, artificial bee colony, genetic, and Kmeans algorithms. Lastly, IALO, ALO, and the chaos-based ALO algorithm were compared in terms of image clustering by using the proposed objective function for three benchmark images. The comparison was made for the objective function values, the separateness and compactness properties of the clusters and also for two clustering indexes Davies– Bouldin and Xie–Beni. The results showed that the proposed boundary decreasing procedure increased the performance of the IALO algorithm, and also the IALO algorithm with the proposed objective function obtained very competitive results in terms of image clustering. Key words: Image clustering, improved ant lion optimization, Davies–Bouldin, Xie–Beni 1. Introduction Clustering is an unsupervised data grouping technique that has been widely applied in many fields such as machine learning, pattern recognition, data mining, and image processing [1]. It aims to reveal the hidden structures in an unlabeled dataset and thus to provide the possibility of making a preliminary assessment about the organization of the dataset [2]. By utilizing a clustering algorithm, a dataset can be divided into several disjoint groups of data points according to some similarity measures. The algorithm tries to maximize the similarity within each group while minimizing the similarity between the groups. The clustering algorithms can be classified into two basic categories, hierarchical and partitional clustering [3]. The data points are being grouped into a tree-like structure with the hierarchical clustering while the dataset is divided into several clusters that provide some predefined criteria by using the partitional clustering [3]. In the literature, there are a number of subtypes of these two clustering approaches; agglomerative and divisive clustering are two hierarchical clustering techniques, the agglomerative clustering starts by assigning each data member to a distinct cluster and continues by combining the successive clusters while divisive clustering begins with one cluster and continues by dividing this cluster into different numbers of clusters [1]. Both of these techniques ∗ Correspondence: 1445 This work is licensed under a Creative Commons Attribution 4.0 International License. TOZ/Turk J Elec Eng & Comp Sci continue until a predefined stopping criterion is met. A partitional approach starts with a predefined number of clusters and tries to divide the dataset into that number of disjoint clusters by evaluating the data points according to some optimization criteria [4]. K-means clustering algorithm that was proposed by McQueen [5] and its fuzzy-based version, the fuzzy C-means (FCM) proposed by Dunn [6] and improved by Bezdek [7], are the two most widely known partitional algorithms. These two algorithms have very simple formulations to be applied to most kinds of the clustering applications and also very computational efficient. However, they have some disadvantages such as being trapped in the local minima and being very sensitive to the selection of the initial cluster centers [4]. The partitional clustering can also be regarded as an optimization process because of optimizing a certain criterion such as minimizing the distance between the cluster centers[8]. Therefore, in order to tackle the drawbacks of K-means and FCM algorithms, many researchers proposed to use evolutionary and/or metaheuristic optimization algorithms. Some of the studies about hybridization FCM or K-means with the optimization algorithms can be given as follows; Nikham and Amiri [9] proposed a hybrid clustering algorithm based on a fuzzy adaptive form of particle swarm optimization (PSO), ant colony optimization (ACO), and K-means algorithms and presented that their algorithm showed better results than some other metaheuristic algorithms such as PSO, genetic algorithms (GA), and ACO. Krishnasamy et al. [3] combined K-means and cohort intelligence algorithm and proposed a new hybrid data clustering algorithm named K-MCI. In [10], Biniaz and Abbasi combined FCM with an unsupervised ACO algorithm in medical image segmentation applications. Kumar and Sahoo [11] proposed a two-step artificial bee colony (ABC) algorithm, where they produced the initial population by using K-means, and they also proposed an improved solution search equation based on PSO social behavior. The authors showed that their algorithm outperforms the classical form of ABC in solving the clustering problem. Wang et al. [12] composed the supervised learning normal mixture model and the FCM. They conducted some experiments on real datasets and concluded that the supervised learning normal mixture model can improve the performance of FCM. Toz and Toz [13] proposed a hybrid clustering algorithm based on differential search optimization algorithm and FCM in order to use in image clustering applications. Different from the hybrid algorithms, metaheuristic and evolutionary optimization algorithms have also been successfully used to solve clustering problems. In [14], the authors proposed to use GA as a clustering technique and showed the superiority of GA-clustering algorithm over K-means by using some artificial and real-life datasets. Shelokar et al. [15] proposed to use ACO for clustering purposes and concluded that the ACO is superior to simulated annealing, GA, and tabu search techniques. Omran et al. [16] developed a PSO-based approach to solve image clustering problem and showed that their method is better than K-means, FCM, K-Harmonic means, and GA. An improved form of gravitational search algorithm by a special encoding scheme, called grouping encoding has been used in [17] in order to solve data clustering (...truncated)