One of the well-known techniques in data mining is clustering. The very popular clustering method is K-means cluster because its algorithm is very easy and simple. However, the K-means cluster has some weaknesses, one of which is that the clustering result is sensitive toward centroid initialization so that the clustering result tends to be locally optimal. This paper explains the modification of the K-means cluster, that is, K-means hybridization with ant colony optimization (K-ACO). Ant Colony Optimization (ACO) is an optimization algorithm based on ant colony behavior. Through K-ACO, the weaknesses of cluster result which tends to be local optimal can be overcome well. The application of the hybrid method of K-ACO with the use of the R program gives better accuracy compared to the K-means cluster. K-means cluster accuracy yielded by Minitab, Matlab, and SAS at iris data is 89%. Meanwhile, K-ACO hybrid clustering with the R program simulated on 38 treatments with 3-time repetitions gives an accuracy result of 93. 10%.

Identifying clusters or clustering is an important aspect of data analysis. It is the task of grouping a set of objects in such a way those objects in the same group/cluster are more similar in some sense or another. It is a main task of exploratory data mining, and a common technique for statistical data analysis This paper proposed an improved version of K-Means algorithm, namely Persistent K-Means, which alters the convergence method of K-Means algorithm to provide more accurate clustering results than the K-means algorithm and its variants by increasing the clusters’ coherence. Persistent K-Means uses an iterative approach to discover the best result for consecutive iterations of KMeans algorithm.

The detection and prevention of crime, in the past few decades, required several years of research and analysis. However, today, thanks to smart systems based on data mining techniques, it is possible to detect and prevent crime in a considerably less time. Classification and clustering-based smart techniques can classify and cluster the crime-related samples. The most important factor in the clustering technique is to find the centrality of the clusters and the distance between the samples of each cluster and the center of the cluster. The problem with clustering techniques, such as k-modes, is the failure to precisely detect the centrality of clusters. Therefore, in this paper, Elephant Herding Optimization (EHO) Algorithm and k-modes are used for clustering and detecting the crime by means of detecting the similarity of crime with each other. The proposed model consists of two basic steps: First, the cluster centrality should be detected for optimized clustering; in this regard, the EHO Algorithm is used. Second, k-modes are used to find the clusters of crimes with close similarity criteria based on distance. The proposed model was evaluated on the Community and Crime dataset consisting of 1994 samples with 128 characteristics. The results showed that purity accuracy of the proposed model is equal to 91. 45% for 400 replicates.

Recently, semi-supervised clustering methods have been considered by many researchers. In this type of clustering, there are some constraints and information about a small portion of data. In constrained k-means method, the user (i.e. an expert) selects the initial seeds. In this paper, a constraint k-means method based on user feedback is proposed. With the help of the user, some initial seeds of boundary data obtained from clustering were selected and then the results of the user feedback were given to the constrained k-means algorithm in order to obtain the most appropriate clustering model for the existing data. The presented method was applied to various standard datasets and the results showed that this method clustered the data with more accuracy than other similar methods.