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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]

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]

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]

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]

Rice aroma profiles, consisting of different sorts of volatile organic compounds, go through complex alterations during storage period that affect its end-use quality. The aroma active compounds of rice are the key elements to determine its quality characteristics and freshness. This study evaluates the efficiency of electronic nose combined with modern biologically inspired unsupervised algorithms as a fast, real-time, and non-invasive technology for modelling rice aroma change during storage. The developed unsupervised algorithms could present successful results in clustering of the aroma change, and also could provide supplementary facilities for assessment of ageing in aromatic and non-aromatic rice samples. Self-organizing map neural network resulted in reliable grouping of the samples. The provided unified distance matrices were applied to interpret the pace of the aroma change. Fuzzy c-means was hybridized with differential evolution, and the fuzzifier parameter was applied for controlling of the samples' memberships to the storage clusters. The developed fuzzy clustering proposed more reasonable solutions when there were overlappings among the clusters. The automatic clustering developed by artificial bee colony algorithm proposed original grouping of the aromatic samples. For the non-aromatic rice, the structures obtained by the automatic approach agreed satisfactorily with the aroma change during ageing. The automatic clustering eliminated the need for the number of clusters as well as the descriptive labelled samples, and presented smarter performance. The electronic nose system combined with the developed unsupervised algorithms could be utilized as a reliable and rapid tool for analysis of rice aroma change. [Display omitted] • MOS based e-nose was applied for unsupervised modelling of rice aroma change. • Self-organizing map and the resulting U-matrix was applied for crisp clustering. • Differential evolution was hybridized with fuzzy c-means for fuzzy clustering. • Artificial bee colony was developed in automatic clustering framework. • E-nose combined with bio-inspired methods is fast and reliable in analyzing rice aroma. [ABSTRACT FROM AUTHOR]

Clustering of biological datasets proved to reveal a lot of significant insights into the medical and biological research. It is an important step towards drug design, vaccine discovery, disease diagnosis, and more. The current trend in biological and medical research is to combine more than one dataset, referred to as multi-omics, related to a specific problem, then perform the clustering or the analysis. The insights we gain for a particular biological problem or disease are double using multi-omics rather than using one dataset. It is like investigating a problem from many dimensions rather than using one dimension. On the other hand, the difficulty of clustering is increased. Another tricky problem in data clustering is determining the best number of clusters used by a clustering algorithm. Due to the big success of metaheuristics in solving the automatic clustering problems, we propose in this paper a new hybrid method that utilizes two powerful metaheuristics algorithms, the Binary Differential Evolution and Marine Predators Algorithm, to perform automatic clustering on multi-omics datasets. Our proposal's performance is investigated upon eight multi-omics datasets from TCGA, and it is compared with four recent and powerful metaheuristics. The used performance metrics are clustering quality and execution time. The experimental results show that the proposed algorithm not only outperformed its competitors in terms of clustering quality, it also only needed a third of the execution time that of its fastest competitor. Moreover, the statistical analysis shows that the obtained results are statistically significant. Accordingly, the proposed method can be considered as an efficient clustering method for multi-omics 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]

In the process of clustering, for the reason that the randomness of the class-center selection may lead to the phenomenon that the selected class-center deviates from the data set, or the class-center is too centralized, the proposed algorithm selected the class-center for two times: it screened out the class-centers which have too small density or have small distances between pairs of class-centers, and the algorithm did not allow them to participate in clustering. Then the algorithm continued to cluster the remaining class-centers. In order to make the algorithm get the optimal class-center quickly, it proposed an improved clustering criterion function to penalize the number of clusters dynamically. In order to evaluate the performance of the proposed algorithm on clustering problems, it carried out experiments on two types of data sets. Compared with the other three existing automatic clustering algorithms, simulation experiments show that the proposed algorithm can obtain better clustering results, which validates the effectiveness of the proposed strategies. [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]

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 this paper, a novel hybrid model for forecasting low dimensional numerical data is proposed which is named as ClusFuDE . The proposed method uses an improved automatic clustering approach for clustering the historical numerical data. Further fuzzy logical relationships are used to forecast the approximate values which are then defuzzified to calculate the exact forecasted values of the data. The fuzzy logical relationships are useful in modelling the fuzzy relations and help in forecasting the fuzzy time series data in a very simplified manner. The forecasted sub-optimal candidate solutions are optimized using Differential Evolution. The Differential Evolution method uses a dynamic differential crossover rate ( C r i ) for the i th solution, for identifying and discarding suboptimal candidate solutions in early stages of the iterative run. This makes the method more suitable for iterative modification of candidate solutions by using differential mutation and crossover, and suitable for global search. The proposed method is applied for forecasting, the year wise enrollments of the University of Alabama, Lahi (crop) production, monthly amount of outpatients visit in a hospital, inventory demand and population of India from years 1930–2000 and the results are consistent. We have compared our method with the recent forecasting methods available in literature and the proposed method outperforms all the existing methods in the literature. The accuracy of the proposed method is computed by calculating the Mean square error (MSE) and Mean Absolute percentage error (MAPE). The proposed method provides the lowest MSE and MAPE when compared to all other methods available in the literature. [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]

Today's real-world data mostly involves incomplete, inconsistent, and/or irrelevant information that causes many drawbacks to transform it into an understandable format. In order to deal with such issues, data preprocessing is a proven discipline in data mining. One of the typical tasks in data preprocessing, feature selection aims to reduce the dimensionality in the data and thereby contributes to further processing. Feature selection is widely used to enhance the performance of a supervised learning algorithm (e.g., classification) but is rarely used in unsupervised tasks (e.g., clustering). This paper introduces a new multi-objective differential evolution approach in order to find relatively homogeneous clusters without the prior knowledge of cluster number using a smaller number of features from all available features in the data. To analyze the goodness of the introduced approach, several experiments are conducted on a various number of real-world and synthetic benchmarks using a variety of clustering approaches. From the analyzes through several different criteria, it is suggested that our method can significantly improve the clustering performance while reducing the dimensionality at the same time. [ABSTRACT FROM AUTHOR]