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Traditional K-means clustering assumes, to some extent, a uniform distribution of data around predefined centroids, which limits its effectiveness for many realistic datasets. In this paper, a new clustering technique, simulated-annealing-based ellipsoidal clustering (SAELLC), is proposed to automatically partition data into an optimal number of ellipsoidal clusters, a capability absent in traditional methods. SAELLC transforms each identified cluster into a hyperspherical cluster, where the diameter of the hypersphere equals the minor axis of the original ellipsoid, and the center is encoded to represent the entire cluster. During the assignment of points to clusters, local ellipsoidal properties are independently considered. For objective function evaluation, the method adaptively transforms these ellipsoidal clusters into a variable number of global clusters. Two objective functions are simultaneously optimized: one reflecting partition compactness using the silhouette function (SF) and Euclidean distance, and another addressing cluster connectedness through a nearest-neighbor algorithm. This optimization is achieved using a newly-developed multiobjective simulated annealing approach. SAELLC is designed to automatically determine the optimal number of clusters, achieve precise partitioning, and accommodate a wide range of cluster shapes, including spherical, ellipsoidal, and non-symmetric forms. Extensive experiments conducted on UCI datasets demonstrated SAELLC's superior performance compared to six well-known clustering algorithms. The results highlight its remarkable ability to handle diverse data distributions and automatically identify the optimal number of clusters, making it a robust choice for advanced clustering analysis. [ABSTRACT FROM AUTHOR]

Clustering methods aim to categorize the elements of a dataset into groups according to the similarities and dissimilarities of the elements. This paper proposes the Multi-objective Clustering Algorithm (MCA), which combines clustering methods with the Nondominated Sorting Genetic Algorithm II. In this way, the proposed algorithm can automatically define the optimal number of clusters and partition the elements based on clustering measures. For this, 6 intra-clustering and 7 inter-clustering measures are explored, combining them 2-to-2, to define the most appropriate pair of measures to be used in a bi-objective approach. Out of the 42 possible combinations, 6 of them were considered the most appropriate, since they showed an explicitly conflicting behavior among the measures. The results of these 6 Pareto fronts were combined into two Pareto fronts, according to the measure of intra-clustering that the combination has in common. The elements of these Pareto fronts were analyzed in terms of dominance, so the nondominanted ones were kept, generating a hybrid Pareto front composed of solutions provided by different combinations of measures. The presented approach was validated on three benchmark datasets and also on a real dataset. The results were satisfactory since the proposed algorithm could estimate the optimal number of clusters and suitable dataset partitions. The obtained results were compared with the classical k-means and DBSCAN algorithms, and also two hybrid approaches, the Clustering Differential Evolution, and the Game-Based k-means algorithms. The MCA results demonstrated that they are competitive, mainly for the advancement of providing a set of optimum solutions for the decision-maker. [ABSTRACT FROM AUTHOR]

In cluster analysis, determining the number of clusters is an important issue because there is less information about the most appropriate number of clusters in the real problem. Automatic clustering is a clustering method that automatically finds the most appropriate number of clusters and divides instances into the corresponding clusters. In this paper, a novel automatic clustering algorithm based on the improved marine predator algorithm (IMPA) and K-means algorithm is proposed. The new IMPA utilizes refracted opposition-based learning in population initialization, generates opposite solutions to improve the diversity of the population and produces more accurate solutions. In addition, the sine-cosine algorithm is incorporated to balance global exploration and local development of the algorithm for dynamic updating of the predator and prey population positions. At the same time, the Gaussian-Cauchy mutation is combined to improve the probability of obtaining the globally optimal solution. The proposed IMPA is validated with some benchmark data sets. The calculation results show that IMPA is superior to the original MPA in automatic clustering. In addition, IMPA is also used to solve the problem of fault classification of Xi*an Jiaotong University bearing data. The results show that the IMPA has better and more stable results than other algorithms such as the original MPA, whale optimization algorithm, fuzzy C-means and K-means in automatic clustering.

Wireless communication greatly contributes to the evolution of new technologies, such as the Internet of Things (IoT) and edge computing. The new generation networks, including 5G and 6G, provide several connectivity advantages for multiple applications, such as smart health systems and smart cities. Adopting wireless communication technologies in these applications is still challenging due to factors such as mobility and heterogeneity. Predicting accurate radio environment maps (REMs) is essential to facilitate connectivity and improve resource utilization. The construction of accurate REMs through the prediction of reference signal received power (RSRP) can be useful in densely distributed applications, such as smart cities. However, predicting an accurate RSRP in the applications can be complex due to intervention and mobility aspects. Given the fact that the propagation environments can be different in a specific area of interest, the estimation of a common path loss exponent for the entire area produces errors in the constructed REM. Hence, it is necessary to use automatic clustering to distinguish between different environments by grouping locations that exhibit similar propagation characteristics. This leads to better prediction of the propagation characteristics of other locations within the same cluster. Therefore, in this work, we propose using the Kriging technique, in conjunction with the automatic clustering approach, in order to improve the accuracy of RSRP prediction. In fact, we adopt K-means clustering (KMC) to enhance the path loss exponent estimation. We use a dataset to test the proposed model using a set of comparative studies. The results showed that the proposed approach provides significant RSRP prediction capabilities for constructing REM, with a gain of about 3.3 dB in terms of root mean square error compared to the case without clustering. [ABSTRACT FROM AUTHOR]

Automatic clustering problems require clustering algorithms to automatically estimate the number of clusters in a dataset. However, the classical K-means requires the specification of the required number of clusters a priori. To address this problem, metaheuristic algorithms are hybridized with K-means to extend the capacity of K-means in handling automatic clustering problems. In this study, we proposed an improved version of an existing hybridization of the classical symbiotic organisms search algorithm with the classical K-means algorithm to provide robust and optimum data clustering performance in automatic clustering problems. Moreover, the classical K-means algorithm is sensitive to noisy data and outliers; therefore, we proposed the exclusion of outliers from the centroid update's procedure, using a global threshold of point-to-centroid distance distribution for automatic outlier detection, and subsequent exclusion, in the calculation of new centroids in the K-means phase. Furthermore, a self-adaptive benefit factor with a three-part mutualism phase is incorporated into the symbiotic organism search phase to enhance the performance of the hybrid algorithm. A population size of 40 + 2 g was used for the symbiotic organism search (SOS) algorithm for a well distributed initial solution sample, based on the central limit theorem that the selection of the right sample size produces a sample mean that approximates the true centroid on Gaussian distribution. The effectiveness and robustness of the improved hybrid algorithm were evaluated on 42 datasets. The results were compared with the existing hybrid algorithm, the standard SOS and K-means algorithms, and other hybrid and non-hybrid metaheuristic algorithms. Finally, statistical and convergence analysis tests were conducted to measure the effectiveness of the improved algorithm. The results of the extensive computational experiments showed that the proposed improved hybrid algorithm outperformed the existing SOSK-means algorithm and demonstrated superior performance compared to some of the competing hybrid and non-hybrid metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

As a typical unsupervised learning technique, clustering has been widely applied. However, in many cases, prior information about the number of clusters is unknown, so how to determine it automatically in clustering is getting more attention. In this article, a method named automatic clustering based on dynamic parameters harmony search optimization algorithm, i.e., AC-DPHS, is proposed to solve this problem. By improving the basic harmony search (HS), the dynamic parameters harmony search (DPHS) is devised, which makes the parameters change dynamically without pre-definition. The AC-DPHS takes advantage of the merits of both DPHS and K-means clustering and can determine the optimal number of clusters automatically. A comprehensive experiment is carried out to evaluate the performance of AC-DPHS. The results illustrate that the AC-DPHS generated by using the PBM validity index as its fitness function is relatively superior, and it performs over other approaches developed recently in real-life data clustering as well as grayscale images segmentation. Consequently, the method explained in this article is effectiveness and practical, which can be considered as a new automatic clustering scheme. [ABSTRACT FROM AUTHOR]

Wireless communication greatly contributes to the evolution of new technologies, such as the Internet of Things (IoT) and edge computing. The new generation networks, including 5G and 6G, provide several connectivity advantages for multiple applications, such as smart health systems and smart cities. Adopting wireless communication technologies in these applications is still challenging due to factors such as mobility and heterogeneity. Predicting accurate radio environment maps (REMs) is essential to facilitate connectivity and improve resource utilization. The construction of accurate REMs through the prediction of reference signal received power (RSRP) can be useful in densely distributed applications, such as smart cities. However, predicting an accurate RSRP in the applications can be complex due to intervention and mobility aspects. Given the fact that the propagation environments can be different in a specific area of interest, the estimation of a common path loss exponent for the entire area produces errors in the constructed REM. Hence, it is necessary to use automatic clustering to distinguish between different environments by grouping locations that exhibit similar propagation characteristics. This leads to better prediction of the propagation characteristics of other locations within the same cluster. Therefore, in this work, we propose using the Kriging technique, in conjunction with the automatic clustering approach, in order to improve the accuracy of RSRP prediction. In fact, we adopt K-means clustering (KMC) to enhance the path loss exponent estimation. We use a dataset to test the proposed model using a set of comparative studies. The results showed that the proposed approach provides significant RSRP prediction capabilities for constructing REM, with a gain of about 3.3 dB in terms of root mean square error compared to the case without clustering.

K-means clustering algorithm is a partitional clustering algorithm that has been used widely in many applications for traditional clustering due to its simplicity and low computational complexity. This clustering technique depends on the user specification of the number of clusters generated from the dataset, which affects the clustering results. Moreover, random initialization of cluster centers results in its local minimal convergence. Automatic clustering is a recent approach to clustering where the specification of cluster number is not required. In automatic clustering, natural clusters existing in datasets are identified without any background information of the data objects. Nature-inspired metaheuristic optimization algorithms have been deployed in recent times to overcome the challenges of the traditional clustering algorithm in handling automatic data clustering. Some nature-inspired metaheuristics algorithms have been hybridized with the traditional K-means algorithm to boost its performance and capability to handle automatic data clustering problems. This study aims to identify, retrieve, summarize, and analyze recently proposed studies related to the improvements of the K-means clustering algorithm with nature-inspired optimization techniques. A quest approach for article selection was adopted, which led to the identification and selection of 147 related studies from different reputable academic avenues and databases. More so, the analysis revealed that although the K-means algorithm has been well researched in the literature, its superiority over several well-established state-of-the-art clustering algorithms in terms of speed, accessibility, simplicity of use, and applicability to solve clustering problems with unlabeled and nonlinearly separable datasets has been clearly observed in the study. The current study also evaluated and discussed some of the well-known weaknesses of the K-means clustering algorithm, for which the existing improvement methods were conceptualized. It is noteworthy to mention that the current systematic review and analysis of existing literature on K-means enhancement approaches presents possible perspectives in the clustering analysis research domain and serves as a comprehensive source of information regarding the K-means algorithm and its variants for the research community. [ABSTRACT FROM AUTHOR]

Time series is a set of sequential data point in time order. The sizes and dimensions of the time series datasets are increasing day by day. Clustering is an unsupervised data mining technique that groups objects based on their similarities. It is used to analyze various datasets, such as finance, climate, and bioinformatics datasets. k -means is one of the most used clustering algorithms. However, it is challenging to determine the value of k parameter, which is the number of clusters. One of the most used methods to determine the number of clusters (such as k) is cluster validity indexes. Several internal and external validity indexes are used to find suitable cluster numbers based on characteristics of datasets. In this study, we propose a hybrid validity index to determine the value of k parameter of k -means algorithm. The proposed hybrid validity index comprises four internal validity indexes, such as Dunn, Silhouette, C index, and Davies–Bouldin indexes. The proposed method was applied to nine real-life finance and benchmarks time series datasets. The financial dataset was obtained from Yahoo Finance, consisting of daily closing data of stocks. The other eight benchmark datasets were obtained from UCR time series classification archive. Experimental results showed that the proposed hybrid validity index is promising for finding the suitable number of clusters with respect to the other indexes for clustering time-series datasets. [ABSTRACT FROM AUTHOR]

The Automatic Clustering using Differential Evolution (ACDE) is one of the grouping methods capable of automatically determining the number of the cluster. However, ACDE continues making use of the strategy manual to determine the activation threshold of k, which affects its performance. In this study, the problem of ACDE is enhanced using the U Control Chart (UCC). The performance of the proposed method was tested using five data sets from the National Administrative Department of Statistics (DANE - Departamento Administrativo Nacional de Estadísticas) and the Ministry of Commerce, Industry, and Tourism of Colombia for the innovative capacity of Small and Medium-sized Enterprises (SMEs) and were assessed by the Davies Bouldin Index (DBI) and the Cosine Similarity (CS) measure. The results show that the proposed method yields excellent performance compared to prior researches for most datasets with optimal cluster number yet lowest DBI and CS measure. It can be concluded that the UCC method is able to determine k activation threshold in ACDE that caused effective determination of the cluster number for k-means clustering. [ABSTRACT FROM AUTHOR]

Purpose: The multi-robot task allocation (MRTA) problem is a challenging issue in the robotics area with plentiful practical applications. Expanding the number of tasks and robots increases the size of the state space significantly and influences the performance of the MRTA. As this process requires high computational time, this paper aims to describe a technique that minimizes the size of the explored state space, by partitioning the tasks into clusters. In this paper, the authors address the problem of MRTA by putting forward a new automatic clustering algorithm of the robots' tasks based on a dynamic-distributed double-guided particle swarm optimization, namely, ACD3GPSO. Design/methodology/approach: This approach is made out of two phases: phase I groups the tasks into clusters using the ACD3GPSO algorithm and phase II allocates the robots to the clusters. Four factors are introduced in ACD3GPSO for better results. First, ACD3GPSO uses the k-means algorithm as a means to improve the initial generation of particles. The second factor is the distribution using the multi-agent approach to reduce the run time. The third one is the diversification introduced by two local optimum detectors LODpBest and LODgBest. The last one is based on the concept of templates and guidance probability Pguid. Findings: Computational experiments were carried out to prove the effectiveness of this approach. It is compared against two state-of-the-art solutions of the MRTA and against two evolutionary methods under five different numerical simulations. The simulation results confirm that the proposed method is highly competitive in terms of the clustering time, clustering cost and MRTA time. Practical implications: The proposed algorithm is quite useful for real-world applications, especially the scenarios involving a high number of robots and tasks. Originality/value: In this methodology, owing to the ACD3GPSO algorithm, task allocation's run time has diminished. Therefore, the proposed method can be considered as a vital alternative in the field of MRTA with growing numbers of both robots and tasks. In PSO, stagnation and local optima issues are avoided by adding assorted variety to the population, without losing its fast convergence. [ABSTRACT FROM AUTHOR]

K-means clustering algorithm is a partitional clustering algorithm that has been used widely in many applications for traditional clustering due to its simplicity and low computational complexity. This clustering technique depends on the user specification of the number of clusters generated from the dataset, which affects the clustering results. Moreover, random initialization of cluster centers results in its local minimal convergence. Automatic clustering is a recent approach to clustering where the specification of cluster number is not required. In automatic clustering, natural clusters existing in datasets are identified without any background information of the data objects. Nature-inspired metaheuristic optimization algorithms have been deployed in recent times to overcome the challenges of the traditional clustering algorithm in handling automatic data clustering. Some nature-inspired metaheuristics algorithms have been hybridized with the traditional K-means algorithm to boost its performance and capability to handle automatic data clustering problems. This study aims to identify, retrieve, summarize, and analyze recently proposed studies related to the improvements of the K-means clustering algorithm with nature-inspired optimization techniques. A quest approach for article selection was adopted, which led to the identification and selection of 147 related studies from different reputable academic avenues and databases. More so, the analysis revealed that although the K-means algorithm has been well researched in the literature, its superiority over several well-established state-of-the-art clustering algorithms in terms of speed, accessibility, simplicity of use, and applicability to solve clustering problems with unlabeled and nonlinearly separable datasets has been clearly observed in the study. The current study also evaluated and discussed some of the well-known weaknesses of the K-means clustering algorithm, for which the existing improvement methods were conceptualized. It is noteworthy to mention that the current systematic review and analysis of existing literature on K-means enhancement approaches presents possible perspectives in the clustering analysis research domain and serves as a comprehensive source of information regarding the K-means algorithm and its variants for the research community.

Determining the cluster number in k-means is problematic since it affects the quality of cluster for numerous applications in the data mining. The automatic clustering differential evolution (ACDE) is one of the most used clustering methods that are able to determine the cluster number automatically. However, ACDE still makes use of the manual strategy to determine a value k activation threshold thereby affecting its performance. In this study, the u-control chart (UCC) method use to tackle the ACDE method problem. UCC method used for the initial step to get a value of the variables sought before initialization of the variable vector on ACDE. The UCC is a method from statistical process control (SPC) field which has proved to be effective in solving the problem of management control attributes. The performance of the proposed method was tested using seven public datasets from the UCI repository and Clustering basic benchmark repository and evaluated with Davies Bouldin Index (DBI) and CS measure. The results show that, the proposed method yields excellent performance compared to prior researches for most datasets with optimal cluster number yet lowest DBI and CS measure. It can be concluded that the UCC method is able to determine k activation threshold in ACDE that caused effective determination of the cluster number for k-means clustering. [ABSTRACT FROM AUTHOR]

The Automatic Clustering using Differential Evolution (ACDE) is one of the grouping methods capable of automatically determining the number of the cluster. However, ACDE continues making use of the strategy manual to determine the activation threshold of k, which affects its performance. In this study, the problem of ACDE is enhanced using the U Control Chart (UCC). The performance of the proposed method was tested using five data sets from the National Administrative Department of Statistics (DANE - Departamento Administrativo Nacional de Estadísticas) and the Ministry of Commerce, Industry, and Tourism of Colombia for the innovative capacity of Small and Medium-sized Enterprises (SMEs) and were assessed by the Davies Bouldin Index (DBI) and the Cosine Similarity (CS) measure. The results show that the proposed method yields excellent performance compared to prior researches for most datasets with optimal cluster number yet lowest DBI and CS measure. It can be concluded that the UCC method is able to determine k activation threshold in ACDE that caused effective determination of the cluster number for k-means clustering. [ABSTRACT FROM AUTHOR]

In cluster analysis, determining number of clusters is an important issue because information about the most appropriate number of clusters do not exist in the real-world problems. Automatic clustering is a clustering approach which is able to automatically find the most suitable number of clusters as well as divide the instances into the corresponding clusters. This study proposes a novel automatic clustering algorithm using a hybrid of improved artificial bee colony optimization algorithm and K-means algorithm (iABC). The proposed iABC algorithm improves the onlooker bee exploration scheme by directing their movements to a better location. Instead of using a random neighborhood location, the improved onlooker bee considers the data centroid to find a better initial centroid for the K-means algorithm. To increase efficiency of the improvement, the updating process is only applied on the worst cluster centroid. The proposed iABC algorithm is verified using some benchmark datasets. The computational result indicates that the proposed iABC algorithm outperforms the original ABC algorithm for automatic clustering problem. Furthermore, the proposed iABC algorithm is utilized to solve the customer segmentation problem. The result reveals that the iABC algorithm has better and more stable result than original ABC algorithm. [ABSTRACT FROM AUTHOR]

One of the most well-known binary (discrete) versions of the artificial bee colony algorithm is the similarity measure based discrete artificial bee colony, which was first proposed to deal with the uncapacited facility location (UFLP) problem. The discrete artificial bee colony simply depends on measuring the similarity between the binary vectors through Jaccard coefficient. Although it is accepted as one of the simple, novel and efficient binary variant of the artificial bee colony, the applied mechanism for generating new solutions concerning to the information of similarity between the solutions only consider one similarity case i.e. it does not handle all similarity cases. To cover this issue, new solution generation mechanism of the discrete artificial bee colony is enhanced using all similarity cases through the genetically inspired components. Furthermore, the superiority of the proposed algorithm is demonstrated by comparing it with the basic discrete artificial bee colony, binary particle swarm optimization, genetic algorithm in dynamic (automatic) clustering, in which the number of clusters is determined automatically i.e. it does not need to be specified in contrast to the classical techniques. Not only evolutionary computation based algorithms, but also classical approaches such as fuzzy C-means and K-means are employed to put forward the effectiveness of the proposed approach in clustering. The obtained results indicate that the discrete artificial bee colony with the enhanced solution generator component is able to reach more valuable solutions than the other algorithms in dynamic clustering, which is strongly accepted as one of the most difficult NP-hard problem by researchers. [ABSTRACT FROM AUTHOR]