RETRACTED CHAPTER: U-Control Chart Based Differential Evolution Clustering for Determining the Number of Cluster in k-Means

Abstract

The automatic clustering differential evolution (ACDE) is one of the clustering methods that are able to determine the cluster number automatically. However, ACDE still makes use of the manual strategy to determine k activation threshold thereby affecting its performance. In this study, the ACDE problem will be ameliorated using the u-control chart (UCC) then the cluster number generated from ACDE will be fed to k-means. The performance of the proposed method was tested using six public datasets from the UCI repository about academic efficiency (AE) and evaluated with Davies Bouldin Index (DBI) and Cosine Similarity (CS) measure. The results show that the proposed method yields excellent performance compared to prior researches.

K-Means-Based Nature-Inspired Metaheuristic Algorithms for Automatic Data Clustering Problems: Recent Advances and Future Directions

“…Wang [129] proposed a weighted K-means algorithm based on DE with an initial clustering center and strong global search capability. Silva et al [130] used a u-control chart (UCC) to automatically determine the k activation threshold for ACDE with the cluster number generated serving as the specified k value for the K-means algorithm, thus improving the performance of the clustering algorithm. Sheng et al [131] presented a combination of differential evolution algorithms with adaptive niching and K-means termed DE-NS-AKO for partitional clustering.…”

“…The idea of using a manual strategy to find k activation threshold by DE to automatically determine the number of clusters was adopted by Silva et al [130]. At the same time, Cai et al [125] used the idea of random generation of k values, where k is an arbitrarily generated integer number [36,97].…”

“…Sood and Bansal [86] achieved better and efficient cluster analysis while integrating K-medoids with the bat algorithm. According to Silva et al [130] and Kuo, Suryani, and Yasid [126], the integration of K-means with DE yielded an excellent cluster result. Cai et al [125] reported a balance between exploration and exploitation in the search algorithm and improving the quality of the final cluster result.…”

“…Mohammadrezapour, Kisi and Pourahmad [46] Optimizing a uniform distribution over a specified range of values Barekatain, Dehghani & Pourzaferani [44] Segmented into nonequivalent cells and selection of nodes whose residual energy is more than the cell's average 9 Sinha & Jana [33] The use of Mahalanobis distance and MapReduce framework Kapil, Chawla & Ansari [3] Executing GA operators on data objects as candidates for cluster centroids to find the fittest instance Rahman and Islam [32] Selecting a fixed number of chromosomes (half selected deterministically and the other half randomly) as the initial population for the GA process to obtain the fittest instances Islam et al [34] Allocating a range of values for k (between 2 and 10) and selecting the best value that produced the optimal solution Mustafi and Sahoo [36] Combining GA framework with differential evolution Xiao et al [31] Employing GA-based method that adopts Q-bit representation for dataset pattern with a single run of the conventional K-means on each chromosome Omran, Salman and Engelbrecht [58] Using PSO to find the best set of cluster centroids among the existing data objects Kao and Lee [61] Using discrete PSO in optimizing the number of clusters Sood and Bansal [86] Using Bat algorithm to optimize the initial representative objects for each cluster Silva et al [130] Using a manual strategy to find k activation threshold by DE Cai et al [125] Random generation of k value as k = rndint [2] where NP is the population size and rndint is a random integer number Kuo, Suryani and Yasid [126] DE approach in obtaining the number of clusters Cobos et al [143] Optimizing Bayesian information criterion (BIC) or the Davies-Bouldin index (BDI) Yang and Sutrisno [198] Specifying the initial number of clusters as half of ecosize generated as sub-ecosystems which CSOS then optimizes 3.4. RQ4.…”

A Case Study on Data Mining Application in a Virtual Power Plant: Cluster Analysis of Power Quality Measurements

“…However, the main disadvantage is that for the nonhierarchical approach, there is a need to define the final number of clusters for which data may be divided. There are different approaches to realize this optimal number of cluster selection, e.g., an entropybased initialization method [66], gap statistic [67], u-control chart [68], or k-fold crossvalidation test [69]. In this research, the k-fold cross-validation test was selected.…”