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In complex data with high dimensions, the dimension reduction methods are used to increase accuracy and speed in the classification algorithms. Feature clustering methods have had a good performance in the selection of important features of data due to using clustering methods. The process of selecting important features of data is a challenge in feature clustering methods which has led to the creation of different algorithms with different performances. The combination of the clustering methods and metaheuristic algorithms, especially the kind of population-based algorithms, have had good results in most cases. In this paper, a new feature clustering method is proposed which is used as a dimension reduction in the classification of brain tumors in 900 magnetic resonance images (MRI). The classification algorithm includes three main steps: in the first step, the Google-Net and ResNet-18 methods have been used for feature extraction of MRI images. Due to the creation of many features using the Google-Net and ResNet-18 methods, a new proposed feature clustering is introduced to reduce the feature dimensions in the second step. In designing the feature clustering algorithm, a new metaheuristic algorithm is introduced which is called the crocodiles hunting strategy optimization algorithm (CHS) that simulates crocodiles’ behavior in hunting. Also, the feature clustering algorithm introduced the new chromosome encoding for feature clustering which is called feature clustering based on the crocodiles hunting strategy optimization algorithm (FC-CHS). Finally, in the third step, the support vector machine (SVM) algorithm is used for classification. According to the results of classification on the MRI images, the proposed algorithm has achieved high accuracy in Google-Net and ResNet features based on confusion matrices. For comparing the performance of the FC-CHS, this algorithm is compared with five well-known dimension reduction algorithms. Also, real data are used to further investigate the performance of the FC-CHS algorithm. The results show that the combination of the FC-CHS and SVM algorithms have been reached high accuracy in Iris, and Wine data, and in other real data, the proposed algorithm is outperformed compared to other dimension reduction methods in most cases.

Cluster Validity Indices (CVI) evaluate the efficiency of a clustering algorithm and Data Envelopment Analysis (DEA) evaluate the efficiency of Decision-Making Units (DMUs) using a number of inputs data and outputs data. Combination of the CVI and DEA inspired the development of a new automatic clustering algorithm called Automatic Clustering Based on Data Envelopment Analysis (ACDEA). ACDEA is able to determine the optimal number of clusters in four main steps. In the first step, a new clustering algorithm called CSA-Kmeans is introduced. In this algorithm, clustering is performed by the Crow Search Algorithm (CSA), in which the K-means algorithm generates the initial centers of the clusters. In the second step, the clustering of data is performed from k min cluster to k max cluster, using CSA-Kmeans. At each iteration of clustering, using correct data labels, Within-Group Scatter (WGS) index, Between-Group Scatter (BGS) index, Dunn Index (DI), the Calinski-Harabasz (CH) index, and the Silhouette index (SI) are extracted and stored, which ultimately these indices make a matrix that the columns of this matrix indicate the values of validity indices and the rows or DMUs represent the number of clustering times from k min cluster to k max cluster. In the third step, the efficiency of the DMUs is calculated using the DEA method based on the second stage matrix, and given that the DI, CH, and SI estimate the relationship within group scatter and between group scatter, WGS and BGS are used as input variables and the indices of DI, CH and SI are used as output variables to DEA. Finally, in step four, AP method is used to calculate the efficiency of DMUs, so that an efficiency value is obtained for each DMU that maximum efficiency represents the optimal number of clusters. In this study, three categories of data are used to measure the efficiency of the ACDEA algorithm. Also, the efficiency of ACDEA is compared with the DCPSO, GCUK and ACDE algorithms. According to the results, there is a positive significant relationship between input CVI and output CVI in data envelopment analysis, and the optimal number of clusters is achieved for many cases.