# Clustering Using an Improved Krill Herd Algorithm
## 1 Introduction  
Clustering is an important research direction in data analysis. This method does not make any statistical hypothesis on data and, thus, is called unsupervised learning in pattern recognition and data mining. Clustering is mainly used in text clustering [1], search engine optimization [2], landmark selection [3], face recognition [4], and medicine and biology [5].  
Clustering is one of the most difficult and challenging problems in machine learning. The variety of clustering algorithms is roughly divided into three main types, namely, overlapping (so-called non-exclusive) [6], partitional [7], and hierarchical [8]. Regardless of the type of clustering algorithm applied, the main goal is to maximize homogeneity within each cluster and heterogeneity among different clusters. In other words, objects that belong to the same cluster should be more similar to each other than objects that belong to different clusters.  
Although present algorithms have their own advantages, they are sensitive to the initialization parameters and it is difficult to find their optimal clusters. In recent years, optimization methods inspired by natural phenomena have provided new ways to solve clustering problems. A swarm of individuals are employed to explore the search space and obtain an optimal solution, such as genetic algorithms (GA) [9], particle swarm optimization algorithms (PSO) [10], and ant colony optimization (ACO) [11], among others. Other novel swarm intelligence algorithms have been proposed, such as harmony search (HS) [12], honeybee mating optimization algorithm (HBMO) [13], artificial fish swarm algorithm (AFSA) [14], artificial bee colony (ABC) [15], firefly algorithm (FA) [16], monkey algorithm (MA) [17], bat algorithm (BA) [18], and many others.  
The krill herd algorithm (KHA) [19] is a novel swarm algorithm that is based on the simulation of the herding behavior of krill individuals and the minimum distances of each individual krill fromfood and from the highest density of the herd, which are considered as the objective functions for krill movement. Although proposed recently, KHA has quickly been applied to multiple scenarios. [PERSON] et al. [20] used KHA to optimize a peer-to-peer network. KHA is applied in a smartphone ad hoc network [21]. [PERSON] et al. [22] used KHA for learning an artificial neural network. In [23], KHA demonstrated better performance compared with well-known algorithms, such as PSO and GA. [PERSON] and [PERSON] [19] illustrated that KHA with a crossover operator is superior to other well-known algorithms, including differential evolution (DE) [24], biogeography-based optimization (BBO) [25], and ACO.  
Although KHA outperforms many other swarm intelligent algorithms [19], the algorithm cannot search globally particularly well [26]. In [27], a free search KHA for function optimization was proposed to improve the feasibility and effectiveness of KHA. An improved KHA with a linear decreasing step was proposed by [PERSON] et al. [28]. Furthermore, a new KHA that improved the original genetic operator by modifying the mutation mechanism and adding a new updated scheme will be demonstrated in our paper.  
In this paper, we apply KHA as an optimization means to transform clustering into an optimization problem. In other words, we use individual krill to represent K cluster centers (K is the number of clusters), and KHA is used to search for the optimal clustering center. According to the principle of minimum distance of centers, all of the objects of the dataset are divided into different clusters, which leads to obtaining clustering results.  
The rest of the paper is organized as follows: In Section 2, details of KHA are introduced. Section 3 briefly explains the improved KHA. In Section 4 clustering with the IKHA approach is proposed. Section 5 presents the experimental results of our proposed algorithm. Finally, the summary and future works are provided in Section 6.