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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]

Partitional clustering is a type of clustering that can organize the data into non-overlapping groups or clusters. This technique has diverse applications across the different various domains like image processing, pattern recognition, data mining, rule-based systems, customer segmentation, image segmentation, and anomaly detection, etc. Hence, this survey aims to identify the key concepts and approaches in partitional clustering. Further, it also highlights its widespread applicability including major advantages and challenges. Partitional clustering faces challenges like selecting the optimal number of clusters, local optima, sensitivity to initial centroids, etc. Therefore, this survey describes the clustering problems as partitional clustering, dynamic clustering, automatic clustering, and fuzzy clustering. The objective of this survey is to identify the meta-heuristic algorithms for the aforementioned clustering. Further, the meta-heuristic algorithms are also categorised into simple meta-heuristic algorithms, improved meta-heuristic algorithms, and hybrid meta-heuristic algorithms. Hence, this work also focuses on the adoption of new meta-heuristic algorithms, improving existing methods and novel techniques that enhance clustering performance and robustness, making partitional clustering a critical tool for data analysis and machine learning. This survey also highlights the different objective functions and benchmark datasets adopted for measuring the effectiveness of clustering algorithms. Before the literature survey, several research questions are formulated to ensure the effectiveness and efficiency of the survey such as what are the various meta-heuristic techniques available for clustering problems? How to handle automatic data clustering? What are the main reasons for hybridizing clustering algorithms? The survey identifies shortcomings associated with existing algorithms and clustering problems and highlights the active area of research in the clustering field to overcome these limitations and improve performance. [ABSTRACT FROM AUTHOR]

Image segmentation through fuzzy clustering has been widely used in diverse areas. However, most of those clustering algorithms require that some of their parameter values be determined manually. The number of clusters, C, is one of the most important parameters because it impacts the number of regions to segment and directly affects the performance of the clustering algorithms. Some state-of-the-art general clustering algorithms methods automatically determine C. However, not all of them can be employed for image segmentation. Therefore, this paper describes the method automatic estimation of number of clusters by image complexity (AENCIC). AENCIC is a method that automatically estimates the best C needed by state-of-the-art clustering algorithms to segment an image, considering the image complexity perceived by humans. AENCIC was designed to work with fuzzy clustering algorithms employed to segment real-world images because this kind of segmentation is an ill-defined problem causing a high variation of C per image to attain a good segmentation. Results using the database BSDS500 demonstrate that using AENCIC to estimate C improves the performance of state-of-the-art fuzzy clustering image segmentation algorithms up to 94% of their ideal maximum performance, allowing those algorithms to work without human intervention. [ABSTRACT FROM AUTHOR]

In recent years, Quantum Inspired Metaheuristic algorithms have emerged to be promising due to their efficiency, robustness and faster computational capability. In this paper, a novel Quantum Inspired Differential Evolution (QIDE) algorithm has been presented for automatic clustering of unlabeled datasets. In case of automatic clustering, the datasets have been clustered into optimal number of groups on the run without any apriori knowledge of the datasets. In this work, the proposed algorithm has been compared with other two quantum inspired algorithms, viz., Fast Quantum Inspired Evolutionary Clustering Algorithm (FQEA) and Quantum Evolutionary Algorithm for Data Clustering (QEAC), a Classical Differential Evolution (CDE) algorithm with different mutation probabilities and an Improved Differential Evolution (IDE) algorithm. The experiments have been conducted on six real life publicly available datasets to identify the optimal number of clusters. By introducing some concepts of quantum gates, the proposed algorithm not only achieves good convergence speed but also provides better results than other competitive algorithms. In addition, Sobol's sensitivity analysis has been conducted for tuning the parameters of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Nature acts as a source of concepts, mechanisms, and principles for designing artificial computing systems to deal with complex computational problems. Most heuristic and metaheuristic algorithms are taken from the behavior of biological systems or physical systems in nature. Clustering is the process of grouping a set of data and putting it in a class of similar examples. Since the clustering problem is an NP-hard problem, using metaheuristics can be an appropriate tool to deal with these issues. Indeed, clustering is a special case of an optimization problem. In classic clustering, knowing the number of clusters is required before clustering. This paper presents an algorithm that requires no prior knowledge to classify the data. In this paper, we proposed a swarm-based Emperor Penguins Colony (EPC) algorithm to solve both classic and automatic clustering problems. The proposed approach is compared with six state-of-the-art, popular, and improved nature-inspired algorithms, a partitioning-based heuristic algorithm, and a hierarchical clustering method on ten real-world datasets. The results show that classic and automatic clustering using the EPC algorithm has better performance in comparison with other competing algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to data clustering by introducing the Chaotic Quasi-Opposition-Based Learning Marine Predators Algorithm (CQOBLMPA). The primary objective is to enhance the efficiency and accuracy of automatic data clustering by integrating chaotic local search and quasi-opposition-based learning (QOBL) into the Marine Predators Algorithm (MPA). The proposed CQOBLMPA method addresses the slow convergence issue of MPA and improves its ability to avoid local optima. Our contributions include: firstly, an enhanced exploration phase through QOBL to accelerate convergence; secondly, the refinement of the search process using chaotic local search techniques; and thirdly, the development of an automatic clustering framework that does not require prior knowledge of the number of clusters. The effectiveness of CQOBLMPA is demonstrated through extensive tests on 23 global benchmark functions and the CEC2022 benchmarks, showing significant improvements over the original MPA and other metaheuristics. Additionally, the proposed method is validated on eleven real-world and four artificial datasets, achieving superior clustering performance as measured by the Davies–Bouldin index (DB-index) and the Compact-Separated index (CS-index). The results confirm the robustness and efficiency of CQOBLMPA, highlighting its potential for solving complex clustering problems in various domains, with notable performance in the CEC2022 benchmark tests. [ABSTRACT FROM AUTHOR]

Clustering for probability density functions (CDF) can be categorized as non-fuzzy and fuzzy approaches. Regarding the second approach, the iterative refinement technique has been used for searching the optimal partition. This method could be easily trapped at a local optimum. In order to find the global optimum, a meta-heuristic optimization (MO) algorithm must be incorporated into the fuzzy CDF problem. However, no research utilizing MO to solve the fuzzy CDF problem has been proposed so far due to the lack of a reasonable encoding for converting a fuzzy clustering solution to a chromosome. To address this shortcoming, a new definition called Gaussian prototype is defined first. This type of prototype is capable of accurately representing the cluster without being overly complex. As a result, prototypes' information can be easily integrated into the chromosome via a novel prototype-based encoding method. Second, a new objective function is introduced to evaluate a fuzzy CDF solution. Finally, Differential Evolution (DE) is used to determine the optimal solution for fuzzy clustering. The proposed method, namely DE-AFCF, is the first to propose a globally automatic fuzzy CDF algorithm, which not only can automatically determine the number of clusters k but also can search for the optimal fuzzy partition matrix by taking into account both clustering compactness and separation. The DE-AFCF is also applied in some image clustering problems, such as processed image detection, and traffic image recognition. [ABSTRACT FROM AUTHOR]

In data, analysis clustering plays a major role. In the past decade varieties of clustering algorithms are proposed and produced better results. But many of them required prior information on the number of clusters and failed to produce optimum results when such information is not available. In real-life problems, it is difficult to predict the number of clusters due to the complexity of data in shape and dimensionality. Therefore predicting the number of clusters is a difficult task and this draws the attention of many researchers. In this work, we proposed DKCSMO, dynamic kernel clustering with a spider monkey optimization algorithm. In this work for better clustering results, the local leader phase of the spider monkey optimization algorithm is improved with the neighborhood search strategy. Further to improve the quality of results, we modified CS-Index with Gaussian kernel distribution. The proposed algorithm is compared with five well-known meta-heuristic algorithms and seven previously published automatic clustering algorithms. Experimental results show that the proposed algorithm produced better results in terms of the predicted clusters, DB, SIL, and ARI measures. [ABSTRACT FROM AUTHOR]

This work explores the effectiveness and robustness of quantum computing by conjoining the principles of quantum computing with the conventional computational paradigm for the automatic clustering of colour images. In order to develop such a computationally efficient algorithm, two population-based meta-heuristic algorithms, viz., Particle Swarm Optimization (PSO) algorithm and Enhanced Particle Swarm Optimization (EPSO) algorithm have been consolidated with the quantum computing framework to yield the Quantum Inspired Particle Swarm Optimization (QIPSO) algorithm and the Quantum Inspired Enhanced Particle Swarm Optimization (QIEPSO) algorithm, respectively. This paper also presents a comparison between the proposed quantum inspired algorithms with their corresponding classical counterparts and also with three other evolutionary algorithms, viz., Artificial Bee Colony (ABC), Differential Evolution (DE) and Covariance Matrix Adaption Evolution Strategies (CMA-ES). In this paper, twenty different sized colour images have been used for conducting the experiments. Among these twenty images, ten are Berkeley images and ten are real life colour images. Three cluster validity indices, viz., PBM, CS-Measure (CSM) and Dunn index (DI) have been used as objective functions for measuring the effectiveness of clustering. In addition, in order to improve the performance of the proposed algorithms, some participating parameters have been adjusted using the Sobol's sensitivity analysis test. Four segmentation evaluation metrics have been used for quantitative evaluation of the proposed algorithms. The effectiveness and efficiency of the proposed quantum inspired algorithms have been established over their conventional counterparts and the three other competitive algorithms with regards to optimal computational time, convergence rate and robustness. [ABSTRACT FROM AUTHOR]

For solving the clustering for probability density functions (CDF) problem with a given number of clusters, the metaheuristic optimization (MO) algorithms have been widely studied because of their advantages in searching for the global optimum. However, the existing approaches cannot be directly extended to the automatic CDF problem for determining the number of clusters k. Besides, balance-driven clustering, an essential research direction recently developed in the problem of discrete-element clustering, has not been considered in the field of CDF. This paper pioneers a technique to apply an MO algorithm for resolving the balance-driven automatic CDF. The proposed method not only can automatically determine the number of clusters but also can approximate the global optimal solution in which both the clustering compactness and the clusters' size similarity are considered. The experiments on one-dimensional and multidimensional probability density functions demonstrate that the new method possesses higher quality clustering solutions than the other conventional techniques. The proposed method is also applied in analyzing the difficulty levels of entrance exam questions. [ABSTRACT FROM AUTHOR]

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 ). 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. [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]

Cluster analysis is an essential tool in data mining. Several clustering algorithms have been proposed and implemented, most of which are able to find good quality clustering results. However, the majority of the traditional clustering algorithms, such as the K-means, K-medoids, and Chameleon, still depend on being provided a priori with the number of clusters and may struggle to deal with problems where the number of clusters is unknown. This lack of vital information may impose some additional computational burdens or requirements on the relevant clustering algorithms. In real-world data clustering analysis problems, the number of clusters in data objects cannot easily be preidentified and so determining the optimal amount of clusters for a dataset of high density and dimensionality is quite a difficult task. Therefore, sophisticated automatic clustering techniques are indispensable because of their flexibility and effectiveness. This paper presents a systematic taxonomical overview and bibliometric analysis of the trends and progress in nature-inspired metaheuristic clustering approaches from the early attempts in the 1990s until today's novel solutions. Finally, key issues with the formulation of metaheuristic algorithms as a clustering problem and major application areas are also covered in this paper. [ABSTRACT FROM AUTHOR]

This study proposes an improved differential evolution (DE) algorithm to solve an automatic clustering problem. Automatic clustering is a clustering technique in data mining which can automatically define the best number of clusters, as well as construct those clusters. In order to overcome the weakness of the DE algorithm for automatic clustering, some improvement scenarios are proposed. They include the best solution effect, saturated solution, acceleration and handling downhill scenarios. The best solution effect and acceleration factor are proposed to boost the convergence of the DE algorithm. The saturated solution helps the algorithm maintain the diversity of the population. The handling downhill scenario allows chromosomes to move to a worse solution, since it might later lead to a better solution. The proposed algorithm is evaluated using four well-known datasets. The computational results indicate that the proposed improvements can enhance the DE algorithm's performance. In addition, the proposed method is also applied to cluster customers for a ladies' office wear clothing franchise. The results can be used to plan a marketing strategy for the case company. [ABSTRACT FROM AUTHOR]

Air-writing is an attractive method of interaction between human and machine due to lack of any interface device on the user side. After removing existing limitations and solving the current challenges, it can be used in many applications in the future. In this paper, using the Kinect depth and color images, an air-writing system is proposed to identify single characters such as digits or letters and connected characters such as numbers or words. In this system, automatic clustering, slope variations detection, and a novel analytical classification are proposed as new approaches to eliminate noise in the trajectory from the depth image and hand segmentation, to extract the feature vector, and to identify the character from the feature vector, respectively. Experimental results show that the proposed system can successfully identify single characters and connected characters with the average recognition rate of 97%. It provides a better result than other similar approaches proposed in the literature. In the proposed system, the character recognition time is quite low, about 3 ms, because of using a novel analytical classifier. Evaluation of 4 classifiers shows that the proposed classifier has a higher speed and precision than the SVM, HMM, and K-nearest neighbors classifiers. [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]

Route calculation is a problem in real life of every day. Multilevel road network is an effective way to speed up the optimal route calculation on large size road networks by separating the original road network into subnetworks and pre-computing new sections on the higher level network. The efficiency of the route calculation depend on how to separating the original road networks. In order to optimize the structure of multilevel networks, an evolutionary-based automatic clustering method, which can automatically search for a proper number as the number of clusters, is proposed to sperate the road network in this paper. Geographic based crossover and differential evolution based mutation are used to enhance the searching ability of the proposed method. Two objectives are considered during the evolutionary process. A practical evaluation is designed to select a proper solution from the Pareto solution set. The proposed algorithm is systematically studied in various sizes of road networks. Experimental results show that the multilevel networks constructed by the proposed approach are effective and efficient for route calculation. [ABSTRACT FROM AUTHOR]

A new method for automatic event-cause classification in power distribution networks for the detection and clustering of previously unknown classes of transient voltage waveforms is presented. The approach performs the detection of novelties-events that are not present during modeling of the classifier-in addition to the classification of known events, using a formulation based on support vector data description. Additionally, an unsupervised clustering method for novelties is proposed, in order to collect relevant information about their features and allow identification of new classes of events, which constitutes the main contribution of this work. Two different automatic clustering methods are compared: X-Means clustering and Rival Penalized Expectation Maximization. Experiments using both simulated and real data for the entire classification process, which includes multi-class classification with novelty detection and identification of new classes, are presented. The results obtained demonstrate that the proposed method fully agrees with current trends in smart distribution networks, in which automatic identification, characterization, and mitigation of events are critical for network operation and maintenance. [ABSTRACT FROM AUTHOR]

In this paper, a synergy of two mutation based immune multi-objective automatic fuzzy clustering algorithm (STMIMAFC) is proposed for the task of automatically evolving the number of clusters as well as a proper partitioning of data set. In the proposed algorithm, firstly, two new mutation operators, which are designed for the different structures of chromosomes respectively, are cooperated with each other to generate the new individuals. Secondly, we propose an exponential function based compactness validity index. The proposed method has been extensively compared with a synergy of genetic algorithm and multi-objective differential evolution, multi-objective modified differential evolution based fuzzy clustering, multi-objective clustering with automatic $$k$$ -determination over a test suit of several real life data sets and synthetic data sets. Experimental results indicate the superiority of the STMIMAFC over other three compared clustering algorithms on clustering accuracy and running time. [ABSTRACT FROM AUTHOR]

Understanding the spatial-temporal distribution of vector mosquitoes is essential in designing an efficient mosquito control strategy to reduce the risk of the mosquito-borne disease. In this paper, we apply a non-parametric clustering method, CLUES, to the surveillance data of West Nile virus vector mosquitoes collected by light traps in Peel Region, Ontario, during the mosquito seasons in 2004-2010. In order to obtain robust and reliable results, a statistical smoothing procedure LOWESS is applied to the original time series data. It was found that the mosquito trap sites can be clustered into three groups. The weather impact on the mosquito abundance of each clustered group are similar, while the interannual variability and the highest abundance and peak time in each mosquito season are different. The impact of weather factors on this clustering is investigated. [ABSTRACT FROM AUTHOR]

The clustering problem has an important application in software engineering, which usually deals with large software systems with complex structures. To facilitate the work of software maintainers, components of the system are divided into groups in such a way that the groups formed contain highly-interdependent modules and the independent modules are placed in different groups. The measure used to analyze the quality of the system partition is called Modularization Quality (MQ). Designers represent the software system as a graph where modules are represented by nodes and relationships between modules are represented by edges. This graph is referred in the literature as Module Dependency Graph (MDG). The Software Clustering Problem (SCP) consists in finding the partition of the MDG that maximizes the MQ. In this paper we present three new mathematical programming formulations for the SCP. Firstly, we formulate the SCP as a sum of linear fractional functions problem and then we apply two different linearization procedures to reformulate the problem as Mixed-Integer Linear Programming (MILP) problems. We discuss a preprocessing technique that reduces the size of the original problem and develop valid inequalities that have been shown to be very effective in tightening the formulations. We present numerical results that compare the formulations proposed and compare our results with the solutions obtained by the exhaustive algorithm supported by the freely available Bunch clustering tool, for benchmark problems. [ABSTRACT FROM AUTHOR]