# \(K\)-Means Cloning: Adaptive Spherical \(K\)-Means Clustering
###### Abstract
Therefore, they tried to find the number of clusters and cluster centers simultaneously. In order to adapt the number of clusters, a similarity degree between the clusters is computed and the clusters with the highest similarity are merged. The authors of [39] developed a new method for automatically determination of the number of clusters based on some existing image and signal processing algorithms. Their algorithm generates an image representation of the data dissimilarity matrix and converts it to a Laplacian matrix. Then, visual assessment of cluster tendency techniques is applied in the latter matrix after normalizing its rows. Metaheuristics are powerful and practical tools that have been applied to many different problems [40; 41]. Many clustering methods have been designed as metaheuristic-based methods [42; 43; 44]. Such methods try to find global optimal configurations of data clusters within reasonable processing times. Different types of metaheuristics have been used to solve different data clustering problems such as genetic algorithms [45; 46; 47; 48; 49; 50; 51], simulated annealing [52; 53; 18], tabu search [54; 55], particle swarm optimization [54; 56; 57; 58; 59], ant colony optimization [60; 61; 62; 63], harmony search algorithm [64; 65], and firefly algorithm [66; 67]. Most of the above-mentioned papers mainly use statistical tests, probabilistic models, incremental estimation process, or visualization schemes. These procedures are usually deteriorated when applied to complex or big data sets. Therefore, we propose \(K\)-Means Cloning (KMC) algorithm as a dynamic clustering approach that generates continuously evolving clusters as new samples are added to the input dataset; the case which makes it very adequate to real-time fed data streams and for large datasets whose unpredictable number of clusters. This paper describes KMC and its application to the automatic clustering of large unlabeled data sets. In contrast to most of the existing clustering techniques, the proposed algorithm requires no prior knowledge of the data to be classified. Rather, it determines the optimal number of partitionsof the data with consistency of the results in every runs. KMC generates dynamic \"colonies\" of \(K\)-means clusters. As data samples are added to the dataset the initial number of clusters as well as the clusters structures are modified for the sake of achieving optimality constraints. The structure of the iteratively-generated clusters is changed using intensification and diversification of the \(K\)-means cluster. Superiority of the new method is demonstrated by comparing it with some state-of-the-arts clustering techniques. The rest of this paper is organized as follows. In Section 2, the outlines of the proposed \(K\)-means cloning are described. Necessary overview of the used simulated annealing approach as well as the problem modeling are explained. Section 3 shows how the procedure ingredients are used to build up the entire KMC algorithm. Experimental setup is detailed in Section 4. A comprehensive discussion of the obtained evaluation results is presented in Section 5. Finally, the paper is concluded in Section 6.