Search

The Cluster Validity Index is an integral part of clustering algorithms. It evaluates inter-cluster separation and intra-cluster cohesion of candidate clusters to determine the quality of potential solutions. Several cluster validity indices have been suggested for both classical clustering algorithms and automatic metaheuristic-based clustering algorithms. Different cluster validity indices exhibit different characteristics based on the mathematical models they employ in determining the values for the various cluster attributes. Metaheuristic-based automatic clustering algorithms use cluster validity index as a fitness function in its optimization procedure to evaluate the candidate cluster solution's quality. A systematic review of the cluster validity indices used as fitness functions in metaheuristic-based automatic clustering algorithms is presented in this study. Identifying, reporting, and analysing various cluster validity indices is important in classifying the best CVIs for optimum performance of a metaheuristic-based automatic clustering algorithm. This review also includes an experimental study on the performance of some common cluster validity indices on some synthetic datasets with varied characteristics as well as real-life datasets using the SOSK-means automatic clustering algorithm. This review aims to assist researchers in identifying and selecting the most suitable cluster validity indices (CVIs) for their specific application areas.

The Multiple Model Control (MMC) structure comprises three main components: the model bank, controller bank, and supervisor algorithm. Precise design of these components is crucial for achieving high control performance within the MMC framework, albeit this effort is not without its challenges. These challenges involve optimizing the model and controller banks ensuring system stability when dealing with uncertainties in the local models and enabling smooth switching between model-controller pairs. This paper addresses these challenges by presenting a comprehensive approach. Firstly, the optimal model bank is designed using an automatic clustering approach. Then, the design of the adaptive multi-model predictive controller bank and a supervisor algorithm capable of performing soft switching are discussed. The proposed control system exhibits the capability to ensure closed-loop system stability within each individual subspace, as well as during the transitioning between distinct subspaces. This stability is preserved even in the face of inherent uncertainties associated with the local models comprising the model bank. To evaluate and validate the performance of the proposed control system, it is applied to a satellite attitude control system. The results confirm the effectiveness and performance of the control system. The proposed control system holds promise for controlling highly nonlinear, complex, or switched systems, ensuring closed-loop system stability, and achieving high control performance.

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.

The Density Peak Clustering (DPC) algorithm encounters challenges such as difficulty in choosing cluster centers and the chain reaction caused by incorrect assignment of data points when clustering spatial datasets containing clusters with significant density differences or multi-peak clusters. To address these problems, in this paper, starting from enhancing the local density definition, optimizing the selection of cluster centers, and improving the assignment strategy of non-cluster center data points, an Adaptive DPC (NRA-DPC) algorithm is proposed based on the neighbor relationship. The NRA-DPC algorithm utilizes the reverse K-nearest neighbors of data points as the basis for defining the local density of data points and divides the spatial dataset into a core point set and a boundary point set based on the number of elements in the reverse K-nearest neighbor set of data points. The idea of iteration is adopted to select cluster centers from the core point set and assign non-cluster center data points, forming the initial clusters. For each initial cluster formed by the core point set, the corresponding minimum spanning tree (MST) is generated, and based on the average edge length of the MST, the assignment threshold of this cluster is set. The boundary point set completes the corresponding data point assignment task based on this assignment threshold and the mutual K-nearest neighbor relationship. Experimental results indicate that, compared with other typical clustering algorithms, the NRA-DPC algorithm can automatically select cluster centers, reduce the probability of incorrect assignment of non-cluster center data points, and effectively suppress the chain reaction triggered by incorrect assignment of non-cluster center data points, demonstrating more stable clustering performance when dealing with different datasets.

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.

The density peaks clustering (DPC) algorithm plays an important role in data mining by quickly identifying cluster centers using decision graphs to identify arbitrary clusters. However, the decision graph introduces uncertainty in determining the cluster centers, which can result in an incorrect number of clusters. In addition, the cut-off distance parameter relies on prior knowledge, which poses a limitation. To address these issues, we propose an improved automatic density peaks clustering (ADPC) algorithm. First, a novel clustering validity index called density-distance clustering (DDC) is introduced. The DDC index draws inspiration from the density and distance characteristics of cluster centers, which is applicable to DPC and aligns with the general definition of clustering. Based on the DDC index, the ADPC algorithm automatically selects the suitable cut-off distance and acquires the optimal number of clusters without additional parameters. Numerical experimental results validate that the introduced ADPC algorithm successfully automatically determines the optimal number of clusters and cut-off distance, significantly outperforming DPC, AP and DBSCAN algorithms.

In the Multiple Model Control (MMC) strategies, a bank of simple local models is used to describe the behavior of complex systems with vast operation space. In this approach, the system operation space is divided into several subspaces, and in each subspace, a simple local model is assigned to describe the system behavior. This study addresses the two main challenges in this field which involve determining the optimal number of required local models to form the model bank and identifying the optimal distribution of the local models across the system operation space. Providing appropriate answers to these questions directly affects the performance of the MMC system. In this paper, GA-based automatic clustering method is suggested to form an optimal model bank. In this regard, an appropriate mapping is established between the concepts of MMC and automatic clustering, and a novel unsupervised algorithm is designed to determine the optimal model bank. Unlike the existing methods in the literature, the proposed method can form the global optimal model bank without entrapment into local optima regardless of the initial conditions of the used search algorithm. In this paper, the formation of the optimal model bank using the proposed method is investigated by considering the spacecraft attitude dynamics as a complex, MIMO, non-linear case study and its satisfactory and promising performance is demonstrated.

The hydrological model calibration is a challenging task, especially in ungauged catchments. The regionalization calibration methods can be used to estimate the parameters of the model in ungauged sub-catchments. In this article, the model of ungauged sub-catchments is calibrated by a regionalization approach based on automatic clustering. Under the clustering procedure, gauged and ungauged sub-catchments are grouped based on their physical characteristics and similarity. The optimal number of clusters is determined using an automatic differential evolution algorithm-based clustering. Considering obtained five clusters, the value of the silhouette measure is equal to 0.56, which is an acceptable value for goodness of clustering. The calibration process is conducted according to minimizing errors in simulated peak flow and total flow volume. The Storm Water Management Model is applied to calibrate a set of 53 sub-catchments in the Gorganrood river basin. Comparing graphically and statistically simulated and observed runoff values and also calculating the value of the silhouette coefficient demonstrate that the proposed methodology is a promising approach for hydrological model calibration in ungauged catchments. HIGHLIGHTS The model of ungauged sub-catchments is calibrated by a regionalization approach based on automatic clustering.; The optimal number of clusters is determined using an automatic differential evolution algorithm-based clustering.; Comparing graphically and statistically simulated and observed runoff values and also calculating the value of silhouette coefficient proved the superiority of automatic clustering differential evolution in clustering.;

We present CVIK, a Matlab-based toolbox for assisting the process of cluster analysis applications. This toolbox aims to implement 28 cluster validity indices (CVIs) for measuring clustering quality available to data scientists, researchers, and practitioners. CVIK facilitates implementing the entire pipeline of automatic clustering in two approaches: (i) evaluating candidate clustering solutions from classical algorithms, in which the number of clusters increases gradually, and (ii) assessing potential solutions in evolutionary clustering algorithms using single- and multi-objective optimization methods. This toolbox also implements distinct proximity measures to estimate data similarity, and the CVIs are capable of processing both feature data and relational data. The source code and examples can be found in this GitHub repository: https://github.com/adanjoga/cvik-toolbox.

Abstract The density peaks clustering (DPC) algorithm is a classical and widely used clustering method. However, the DPC algorithm requires manual selection of cluster centers, a single way of density calculation, and cannot effectively handle low-density points. To address the above issues, we propose a novel density deviation multi-peaks automatic clustering method (AmDPC) in this paper. Firstly, we propose a new local-density and use the deviation to measure the relationship between data points and the cut-off distance ( $$d_c$$ d c ). Secondly, we divide the density deviation into multiple density levels equally and extract the points with higher distances in each density level. Finally, for the multi-peak points with higher distances at low-density levels, we merge them according to the size difference of the density deviation. We finally achieve the overall automatic clustering by processing the low-density points. To verify the performance of the method, we test the synthetic dataset, the real-world dataset, and the Olivetti Face dataset, respectively. The simulation experimental results indicate that the AmDPC method can handle low-density points more effectively and has certain effectiveness and robustness.

Single-cell RNA sequencing (scRNA-seq) enables quantification of mRNA expression at the level of individual cells. scRNA-seq uncovers the disparity of cellular heterogeneity giving insights about the expression profiles of distinct cells revealing cellular differentiation. The rapid advancements in scRNA-seq technologies enable researchers to exploit questions regarding cancer heterogeneity and tumor microenvironment. The process of analyzing mainly clustering scRNA-seq data is computationally challenging due to its noisy high dimensionality nature. In this paper, a computational clustering approach is proposed to cluster scRNA-seq data based on consensus clustering using swarm intelligent optimization algorithms to accurately recognize cell subtypes. The proposed approach uses variational auto-encoders to handle the curse of dimensionality, as it operates to create a latent biologically relevant feature space representing the original data. The new latent space is then clustered using Particle Swarm Optimization Algorithm, Multi-Verse Optimization Algorithm and Grey Wolf Optimization Algorithm. A consensus solution is found using solutions returned by the swarm intelligent algorithms. The proposed approach automatically derives the number of clusters without any prior knowledge. To evaluate the performance of the proposed approach a total of four datasets have been used then a comparison against the existing methods in literature has been performed. Experimental results show that the proposed approach performs better than widely most used tools, achieving an adjusted rand index of.95,.75,.88,.9 for Biase, Goolam, Melanoma cancer and Lung cancer datasets respectively.

An attributed network contains not only the complex topological structure but also the nodes with rich attribute information.It can be used to more effectively model modern information systems than traditional networks.Community detection of the attributed network has important research value in hierarchical analysis of complex systems,control of information propagation in the network,and prediction of group behavior of network users.In order to make better use of topology information and attribute information for community discovery,an attributed network embedding based on matrix factorization and community detection(CDEMF) are proposed.First,an attributed network embedding method based on matrix factorization is proposed to model the attributed proximity and the similarity of adjacent nodes calculated in term of the local link information of the network,where the low-dimensional embedding vector corresponding to each node can be obtained by a distributed algorithm of matrix decomposition,that is,the network nodes can be mapped into a collection of data points represented by low-dimensional vectors.Then the community detection method based on curvature and modularity is developed to achieve attributed network community division by clustering the data point set,which can automatically determine the number of communities contained in the data point set.CDEMF is compared with the other 8 kinds of well-known approaches on public real network datasets.The experimental results demonstrate the effectiveness and superiority of CDEMF.

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.

With the discovery of new DNAs, a fundamental problem arising is how to categorize those DNA sequences into correct species. Unfortunately, identifying all data groups correctly and assigning a set of DNAs into k clusters where k must be predefined are one of the major drawbacks in clustering analysis, especially when the data have many dimensions and the number of clusters is too large and hard to guess. Furthermore, finding a similarity measure that preserves the functionality and represents both the composition and distribution of the bases in a DNA sequence is one of the main challenges in computational biology. In this paper, a new soft computing metaheuristic framework is introduced for automatic clustering to generate the optimal cluster formation and to determine the best estimate for the number of clusters. Pulse coupled neural network (PCNN) is utilized for the calculation of DNA sequence similarity or dissimilarity. Bat algorithm is hybridized with the well-known genetic algorithm to solve the automatic data clustering problem. Extensive computational experiments are conducted on the expanded human oral microbiome database (eHOMD). A comparative study between the experimental results shows that the proposed hybrid algorithm achieved superior performance over the standard genetic algorithm and bat algorithm. Moreover, the hybrid performance was compared with competing algorithms from the literature review to ascertain its superiority. Mann-Whitney-Wilcoxon rank-sum test is conducted to statistically validate the obtained clusters.

Wind turbines (WTs) are often operated in harsh and remote environments, thus making them more prone to faults and costly repairs. Additionally, the recent surge in wind farm installations have resulted in a dramatic increase in wind turbine data. Intelligent condition monitoring and fault warning systems are crucial to improving the efficiency and operation of wind farms and reducing maintenance costs. Gearbox is the major component that leads to turbine downtime. Its failures are mainly caused by the gearbox bearings. Devising condition monitoring approaches for the gearbox bearings is an effective predictive maintenance measure that can reduce downtime and cut maintenance cost. In this paper, we propose a hybrid intelligent condition monitoring and fault warning system for wind turbine’s gearbox. The proposed framework encompasses the following: a) clustering filter- (based on power, rotor speed, blade pitch angle, and wind speed signals)-using the automatic clustering model and ant bee colony optimization algorithm (ABC), b) prediction of gearbox bearing temperature and lubrication oil temperature signals- using variational mode decomposition (VMD), group method of data handling (GMDH) network, and multi-verse optimization (MVO) algorithm, and c) anomaly detection based on the Mahalanobis distances and wavelet transform denoising approach. The proposed condition monitoring system was evaluated using 10 min average SCADA datasets of two 2 MW on-shore wind turbines located in the south of Sweden. The results showed that this strategy can diagnose potential anomalies prior to failure and inhibit reporting alarms in healthy operations.

In real-world scenarios, identifying the optimal number of clusters in a dataset is a difficult task due to insufficient knowledge. Therefore, the indispensability of sophisticated automatic clustering algorithms for this purpose has been contemplated by some researchers. Several automatic clustering algorithms assisted by quantum-inspired metaheuristics have been developed in recent years. However, the literature lacks definitive documentation of the state-of-the-art quantum-inspired metaheuristic algorithms for automatically clustering datasets. This article presents a brief overview of the automatic clustering process to establish the importance of making the clustering process automatic. The fundamental concepts of the quantum computing paradigm are also presented to highlight the utility of quantum-inspired algorithms. This article thoroughly analyses some algorithms employed to address the automatic clustering of various datasets. The reviewed algorithms were classified according to their main sources of inspiration. In addition, some representative works of each classification were chosen from the existing works. Thirty-six such prominent algorithms were further critically analysed based on their aims, used mechanisms, data specifications, merits and demerits. Comparative results based on the performance and optimal computational time are also presented to critically analyse the reviewed algorithms. As such, this article promises to provide a detailed analysis of the state-of-the-art quantum-inspired metaheuristic algorithms, while highlighting their merits and demerits.

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+2g 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.

In cluster analysis, the goal has always been to extemporize the best possible means of automatically determining the number of clusters. However, because of lack of prior domain knowledge and uncertainty associated with data objects characteristics, it is challenging to choose an appropriate number of clusters, especially when dealing with data objects of high dimensions, varying data sizes, and density. In the last few decades, different researchers have proposed and developed several nature-inspired metaheuristic algorithms to solve data clustering problems. Many studies have shown that the firefly algorithm is a very robust, efficient and effective nature-inspired swarm intelligence global search technique, which has been successfully applied to solve diverse NP-hard optimization problems. However, the diversification search process employed by the firefly algorithm can lead to reduced speed and convergence rate for large-scale optimization problems. Thus this study investigates the application of four hybrid firefly algorithms to the task of automatic clustering of high density and large-scaled unlabelled datasets. In contrast to most of the existing classical heuristic-based data clustering analyses techniques, the proposed hybrid algorithms do not require any prior knowledge of the data objects to be classified. Instead, the hybrid methods automatically determine the optimal number of clusters empirically and during the program execution. Two well-known clustering validity indices, namely the Compact-Separated and Davis-Bouldin indices, are employed to evaluate the superiority of the implemented firefly hybrid algorithms. Furthermore, twelve standard ground truth clustering datasets from the UCI Machine Learning Repository are used to evaluate the robustness and effectiveness of the algorithms against those of the classical swarm optimization algorithms and other related clustering results from the literature. The experimental results show that the new clustering methods depict high superiority in comparison with existing standalone and other hybrid metaheuristic techniques in terms of clustering validity measures.

Background and Objectives: Stock price prediction has become one of the interesting and also challenging topics for researchers in the past few years. Due to the non-linear nature of the time-series data of the stock prices, mathematical modeling approaches usually fail to yield acceptable results. Therefore, machine learning methods can be a promising solution to this problem.Methods: In this paper, a novel machine learning approach, which works in two phases, is introduced to predict the price of a stock in the next day based on the information extracted from the past 26 days. In the first phase of the method, an automatic clustering algorithm clusters the data points into different clusters, and in the second phase a hybrid regression model, which is a combination of particle swarm optimization and support vector regression, is trained for each cluster. In this hybrid method, particle swarm optimization algorithm is used for parameter tuning and feature selection. Results: The accuracy of the proposed method has been measured by 5 companies’ datasets, which are active in the Tehran Stock Exchange market, through 5 different metrics. On average, the proposed method has shown 82.6% accuracy in predicting stock price in 1-day ahead.Conclusion: The achieved results demonstrate the capability of the method in detecting the sudden jumps in the price of a stock.

The external force destruction has become a major threat to the safe and stable operation of overhead transmission lines,bringing difficulties to the defense and early warning work.In order to solve the problem that the traditional clustering center is difficult to accurately determined and susceptible to abnormal points,an automatic clustering method for data analysis work of transmission lines was presented,and external damage data was analyzed from time and space latitude.Firstly,the cluster center was initialized in this method by using Canopy algorithm.Then,the optimized K-means algorithm was used to perform clustering.Finally,the effectiveness of this method was proved by experimental analysis.This method will be applied to the GIS module in the power information system,which can realize the spatio-temporal visualization of the analysis results and provide powerful decision support for finding cause of the external force damage of the transmission line.

The external force destruction has become a major threat to the safe and stable operation of overhead transmission lines,bringing difficulties to the defense and early warning work.In order to solve the problem that the traditional clustering center is difficult to accurately determined and susceptible to abnormal points,an automatic clustering method for data analysis work of transmission lines was presented,and external damage data was analyzed from time and space latitude.Firstly,the cluster center was initialized in this method by using Canopy algorithm.Then,the optimized K-means algorithm was used to perform clustering.Finally,the effectiveness of this method was proved by experimental analysis.This method will be applied to the GIS module in the power information system,which can realize the spatio-temporal visualization of the analysis results and provide powerful decision support for finding cause of the external force damage of the transmission line.

Categorical data clustering has been attracted a lot of attention recently due to its necessary in the real-world applications. Many clustering methods have been proposed for categorical data. However, most of the existing algorithms require the predefined number of clusters which is usually unavailable in real-world problems. Only a few works focused on automatic clustering, but mainly handled for numerical data. This study develops a novel automatic fuzzy clustering using non-dominated sorting particle swarm optimization (AFC-NSPSO) algorithm for categorical data. The proposed AFC-NSPSO algorithm can automatically identify the optimal number of clusters and exploit the clustering result with the corresponding selected number of clusters. In addition, a new technique is investigated to identify the maximum number of clusters in a dataset based on the local density. To select a final solution in the first Pareto front, some internal validation indices are used. The performance of the proposed AFC-NSPSO on the real-world datasets collected from the UCI machine learning repository exhibits effectiveness compared with some other existing automatic categorical clustering algorithms. Besides, this study also applies the proposed algorithm to analyze a real-world case study with an unknown number of clusters.

The firefly algorithm is a nature-inspired metaheuristic optimization algorithm that has become an important tool for solving most of the toughest optimization problems in almost all areas of global optimization and engineering practices. However, as with other metaheuristic algorithms, the performance of the firefly algorithm depends on adequate parameter tuning. In addition, its diversification as a global metaheuristic can lead to reduced speed, as well as an associated decrease in the rate of convergence when applied to solve problems with large number of variables such as data clustering problems. Clustering is an unsupervised data analysis technique used for identifying homogeneous groups of objects based on the values of their attributes. To mitigate the aforementioned drawbacks, an improved firefly algorithm is hybridized with the well-known particle swarm optimization algorithm to solve automatic data clustering problems. To investigate the performance of the proposed hybrid algorithm, it is compared with four popular metaheuristic methods from literature using twelve standard datasets from the UCI Machine Learning Repository and the two moons dataset. The extensive computational experiments and results analysis carried out shows that the proposed algorithm not only achieves superior performance over the standard firefly and particle swarm optimization algorithms, but also exhibits high level of stability and can be efficiently utilized to solve other clustering problems with high dimensionality.

Clustering by fast search and find of density peaks published on journal Science in 2014 is a density-based clustering technique, which is not only unnecessary to determine the number of clusters in advance, but also able to recognize the clusters of arbitrary shapes. Due to a manual selection of clustering centers on a decision graph, samples which belong to one cluster may be assigned to two or more clusters and vice versa. On assumption that boundary points which keep comparable densities with cluster centers should be regarded as inner points, we make a new method which not only can find all possible clusters automatically but also can combine those with similarities simultaneously to obtain the final clusters. Unlike clustering by fast search and find of density peaks, we only focus on densities with discarding the relative metric which measures the minimum distance between a cluster center and a point with a higher density. Qualitative and quantitative experimental results on sufficient datasets demonstrate the effectiveness of our method.

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.

In this study, Neuro Fuzzy network was used to estimate the spatial distribution of Bemisia tabaci in a cucumber field in Behbahan. Pest density assessments were performed based on a 10 m × 10 m grid pattern pattern and a total of 100 sampling units in. In this method latitude and longitude information was used the input data and output of method showed the number of pest. To determine the sensitivity of this method to different levels of the pest after collecting samples, automatic clustering method was used to determine the number of clusters Davies and Bouldin index was used to evaluae criterion. In order to finding the answer, Clustering Search Space Genetic Algorithm was used.Davies and Bouldin index (0.46) showed that the data should be divided into three clusters. Results indicated average, variance, statistical distribution and also coefficient of determination in the observed and the estimated Bemisia tabaci density were not significantly different.Our map showed that patchy pest distribution offers large potential for using site-specific pest control on this field.

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 kmin cluster to kmax 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 kmin cluster to kmax 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.

Our paper focuses on the graphical analysis domain. We propose an automatic image recognition technique. This approach consists of two main pattern recognition steps. First, it performs an image feature extraction operation on an input image set, using statistical dispersion features. Then, an unsupervised classification process is performed on the previously obtained graphical feature vectors. An automatic region-growing based clustering procedure is proposed and utilized in the classification stage.

Remote sensing image clustering is a challenging task considering its intrinsic complexity. Recently, by combining the spectral and spatial information of the remote sensing data, the clustering performance can be dramatically enhanced, termed as Spectral-Spatial Clustering (SSC). However, it has always been difficult to determine the weight parameter for balancing the spectral term and spatial term of the clustering objective function. In this paper, spectral-spatial clustering with a local weight parameter determination method for remote sensing image was proposed, i.e., L-SSC. In L-SSC, considering the large scale of remote sensing images, the weight parameter can be determined locally in a patch image instead of the whole image. Afterwards, the local weight parameter was used in constructing the objective function of L-SSC. Thus, the remote sensing image clustering problem was transformed into an optimization problem. Finally, in order to achieve a better optimization performance, a variant of differential evolution (i.e., jDE) was used as the optimizer due to its powerful optimization capability. Experimental results on three remote sensing images, including a Wuhan TM image, a Fancun Quickbird image, and an Indian Pine AVIRIS image, demonstrated that the proposed L-SSC can acquire higher clustering accuracy in comparison to other spectral-spatial clustering methods.