# K-Means Clustering Algorithm Based on Chaotic Adaptive Artificial Bee Colony
## 1 Introduction  
Clustering procedure [1; 2; 3] is a process that divides a set of objects into clusters according to the predefined criteria such that objects in the same cluster are more parallel to each other than other objects in different clusters. Clustering is often used in solving a part of complicated tasks in pattern recognition [4], image analysis [5], and other fields on data processing [6]. An excellent clustering algorithm still has a higher interference capability and lower time complexity than traditional algorithm when processing large amounts of data. The clustering algorithms can be subdivided into two categories: hierarchical clustering and partitional clustering. The hierarchical clustering algorithm divides the pattern into fewer structures continuously, and it is usually described by the tree structure. Partition clustering is the division of a set of objects into K non-intersecting subsets with high internal similarity. The center-based clustering algorithms are the most popular partitional clustering methods. K-means is simple and efficient, in which case it becomes one of the most popular center-based cluster methods [3]. However, relying on the initialization of K states and convergence towards the local minimum are significant shortcomings of K-means classification. In order to overcome these problems, many other methodologies have been applied to algorithm. A clustering algorithm which based on genetic algorithm was proposed by [PERSON] and [PERSON], and its effectiveness is proved on real-life datasets. Simulated Annealing (SA) approach is proposed to solve the clustering puzzle by [PERSON] and [PERSON] (1991). Beyond that, many heuristic algorithms like Particle Swarm Optimization (PSO) [7], Differential Evolution (DE), and ABC, have also been successively adapted in the clustering algorithm optimization improvements. ABC is a swarm intelligence algorithm that is derived from the honeybee colony's gathering behavior. After Turkish scholars [PERSON] raised this problem in 2005 [8; 9], it was widely applied to solve function optimization problems, for the advantages of less parameters, simpler structure, and being easier to implement [10]. Compared with PSO and Genetic Algorithm (GA), ABC's advantage is proved further in Section 4. Similar to other swarm intelligence algorithms, the performance of optimized ABC mainly depends on its search strategy. Due to the randomness of the search mechanism, the algorithm is easy to get stuck at local optimal value and has slow convergence speed. ABC has been optimized gradually after the proposal, and it has been extended to various fields. Inspired by PS0 algorithm, the global optimal solution is used to guide the search formula (GABC) in [11]. Inspired by the DE algorithm, another new improved algorithm MABC was proposed. In [10], comparing with the original ABC algorithm, the MABC modifies the employed bee stage and onlooker bee stage, which improves the efficiency. The proposed algorithm is then applied to solve a loudspeaker design problem using FEM. The CGABC based on the crossover is proposed in [12]. The Crossover operator of genetic algorithm is introduced into the Global optimized Artificial Bee Colony algorithm. Crossover is the transfer of good genes from the parent of a population to its offspring. The brand new ABC_elite is proposed in [13]. To better balance the tradeoff between exploration and exploitation, it proposes a depth-first search (DFS) framework. The article introduces two novel solution search equations which incorporates the information of elite solutions and can be applied to the employed bee phase. Furthermore, many studies increase search efficiency by changing the greedy search mechanism. [PERSON] [14] changes the search path of scout bee. Two new mechanisms for the movements of scout bees are proposed. In the first method, the scout bee follows a non-linear interpolated path while in the second one, scout bee follows Gaussian movement.