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.

The performance of judiciary branches is evaluated based on specific indicators determined by the Statistics and Information Technology Center of Judiciary‎. ‎These indicators‎, ‎which are usually documents recorded in court cases‎, ‎have a specific administrative or judicial score for the branch‎, ‎and by calculating the total scores‎, ‎the performance of the branches is evaluated‎. ‎However‎, ‎with the expansion of these indicators‎, ‎ranking and evaluating branch performance has become more complex‎. ‎In this article‎, ‎Clustering is used as one of the most important data mining tools to evaluate branch performance‎. ‎By identifying similar branches‎, ‎examining branches‎, ‎and facing upcoming challenges more effectively‎, ‎more effective decisions can be made in the judiciary system‎. ‎Here‎, ‎to organize 19 law branches based on 49 different administrative and judicial indicators‎, ‎the K-means Clustering algorithm is applied based on two criteria of Euclidean dissimilarity distance and random forests‎. ‎In addition‎, ‎the Dunn index is used to evaluate Clustering‎. ‎The value of this index is calculated as 0.82 by applying the dissimilarity of random forests‎, ‎indicating the successful performance of the algorithm used in determining similar branches.

Clustering is a widespread data analysis and data mining technique in many fields of study such as engineering, medicine, biology and the like. The aim of Clustering is to collect data points. In this paper, a Cultural algorithm (CA) is presented to optimize partition with N objects into K clusters. The CA is one of the effective methods for searching into the problem space in order to find a near optimal solution. This algorithm has been tested on different scale datasets and has been compared with other well-known algorithms in Clustering, such as K-means, Genetic algorithm (GA), Simulated Annealing (SA), Ant Colony Optimization (ACO) and Particle Swarm Optimization (PSO) algorithm. The results illustrate that the proposed algorithm has a good proficiency in obtaining the desired results.

Distance-based Clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based Clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during Clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the Clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known Clustering methods.

A new Clustering approach has been recently proposed by Guh et al. in [13] that use data envelopment analysis to cluster a data set. This approach uses the piecewise production functions derived from the DEA method to cluster the data with input and output items. But their alternative algorithm has a practical difficulty because of alternative optimal solutions of DEA models. So, in this paper, the algorithm’s problem will be illustrated and a new algorithm will be suggested to conduct a DEA- based Clustering for a group of data, correctly.

Imperialist Competitive algorithm (ICA) is considered as prime meta-heuristic algorithm to find the general optimal solution in optimization problems. This paper presents a use of ICA for automatic Clustering of huge unlabeled data sets. By using proper structure for each of the chromosomes and the ICA، at run time، the suggested method (ACICA) finds the optimum number of clusters while optimal Clustering of the data simultaneously. To increase the accuracy and speed of convergence، the structure of ICA changes. The proposed algorithm requires no background knowledge to classify the data. In addition، the proposed method is more accurate in comparison with other Clustering methods based on evolutionary algorithms. DB and CS cluster validity measurements are used as the objective function. To demonstrate the superiority of the proposed method، the average of fitness function and the number of clusters determined by the proposed method is compared with three automatic Clustering algorithms based on evolutionary algorithms.