Partitional Clustering Problem Research Articles

Data clustering using leaders and followers optimization and differential evolution

Data clustering is an important research topic in data mining. Although cluster analysis based on optimization algorithms has attracted great attention, optimization-based techniques face difficulties due to the non-linear objective function and complicated search space. Leaders and followers optimization (LaF) introduced in the 2015 IEEE Congress on Evolutionary Computation, and differential evolution algorithm (DE) are two efficient evolutionary computation methods, and they own some special advantages. The key power of LaF is the exploration in multi-modal search spaces, but it has a poor performance in the exploitation. On the other hand, DE based on the DE/best/1 mutation operator significantly promotes the exploitation process. In this study, the strong properties of LaF and DE are combined to balance exploration and exploitation in the search space to discover the cluster centroids. Besides, the proposed clustering method, i.e., LaF-DE, does not need parameter settings, unlike the existing optimization-based partitional clustering methods. Hence, this study proposes a straightforward, parameter-free, and efficient novel hybrid algorithm for the optimization-based partitional data clustering problem. Many experiments on the functions from CEC2017 test suite show that LaF-DE has better optimization performance and higher stability than the state-of-the-art metaheuristic algorithms. LaF-DE has been compared with well-known clustering techniques on the UCI and Shape datasets. The experimental results and statistical tests indicate that LaF-DE outperforms the well-known partitional clustering methods on 8 of 12 datasets in terms of internal performance metrics. Besides, LaF-DE performs better than density peaks clustering on 9 of 12 datasets in terms of external performance metrics.

An Approach Based on Tunicate Swarm Algorithm to Solve Partitional Clustering Problem

The tunicate swarm algorithm (TSA) is a newly proposed population-based swarm optimizer for solving global optimization problems. TSA uses best solution in the population in order improve the intensification and diversification of the tunicates. Thus, the possibility of finding a better position for search agents has increased. The aim of the clustering algorithms is to distributed the data instances into some groups according to similar and dissimilar features of instances. Therefore, with a proper clustering algorithm the dataset will be separated to some groups with minimum similarities. In this work, firstly, an approach based on TSA algorithm has proposed for solving partitional clustering problem. Then, the TSA algorithm is implemented on ten different clustering problems taken from UCI Machine Learning Repository, and the clustering performance of the TSA is compared with the performances of the three well known clustering algorithms such as fuzzy c-means, k-means and k-medoids. The experimental results and comparisons show that the TSA based approach is highly competitive and robust optimizer for solving the partitional clustering problems.

Variants of bat algorithm for solving partitional clustering problems

Clustering is an exploratory data analysis technique that organize the data objects into clusters with optimal distance efficacy. In this work, a bat algorithm is considered to obtain optimal set of clusters. The bat algorithm is based on the echolocation feature of micro bats. Moreover, some improvements are proposed to overcome the shortcoming associated with bat algorithm like local optima, slow convergence, initial seed points and trade-off between local and global search mechanisms etc. An enhanced cooperative co-evolution method is proposed for addressing the initial seed points selection issue. The local optima issue is handled through neighbourhood search-based mechanism. The trade-off issue among local and global searches of bat algorithm is addressed through a modified elitist strategy. On the basis of aforementioned improvements, three variants (BA-C, BA-CN and BA-CNE) of bat algorithm is developed and efficacy of these variants is tested over twelve benchmark clustering datasets suing intra-cluster distance, accuracy and rand index parameters. Simulation results showed that BA-CNE variant achieves more effective clustering results as compared to BA-C, BA-CN and BA. The simulation results of BA-CNE are also compared with several existing clustering algorithms and two statistical tests are also applied to investigate the statistical difference among BA-CNE and other clustering algorithms. The simulation and statistical results confirmed that BA-CNE is an effective and robust algorithm for handling partitional clustering problems.

Grey Wolf Optimizer (GWO) Algorithm to Solve the Partitional Clustering Problem

The clustering which is an unsupervised classification method is very important for data processing applications. The main purpose of the clustering is to separate the data samples into different groups by using the similarity (or dissimilarity) between data samples. There are many conventional and heuristic algorithms which are used for the clustering problem. Nevertheless, in last years, it is seen that many new techniques are proposed and improved to solve the clustering problem. In this paper, grey wolf optimization (GWO) algorithm which is modelled according to the social behaviour of grey wolves is applied to partition the data samples by searching the optimal center of the clusters. The clustering performance of the GWO is compared with the performances of the three clustering algorithms: k-means, k-medoids and fuzzy c-means algorithms. The experiments show that the GWO algorithm has generally better results than the other clustering algorithms and can be alternatively applied on the clustering problem.

A new meta-heuristic algorithm based on chemical reactions for partitional clustering problems

In the field of engineering, heuristic algorithms are widely adopted to solve variety of optimization problems. These algorithms have proven its efficacy over classical algorithms. It is seen that chemical reactions consist of an efficient computational procedure to design a new product. The formation of new product contains numbers of objects, states, events and well defined procedural steps. A meta-heuristic algorithm inspired through chemical reaction is developed, called artificial chemical reaction optimization (ACRO) algorithm. In this work, an ACRO algorithm is adopted to solve partitional clustering problems. But, this algorithm suffers with slow convergence rate and sometimes stuck in local optima. To handle these aforementioned problems, two operators are inculcated in ACRO algorithm. The performance of proposed algorithm is tested over well-known clustering datasets. The simulation results confirm that proposed ACRO algorithm is an effective and competitive algorithm to solve partitional clustering problems.

A survey on partitional clustering using single-objective metaheuristic approach

Clustering is one of the important functions of data mining, which is used to analyse a large amount of data. It groups these set of data according to some similarity property such that data within the cluster are similar to each other and data between the clusters are dissimilar to each other. To obtain an optimal clustering result with the help of an optimisation algorithm is an emerging trend in data mining. The partitional clustering is one of the popularly used types of clustering algorithm. These algorithms often land in local optimum and number of clusters needs to be predefined. To encounter the above problem, optimisation algorithms such as metaheuristic algorithms are used as a suitable problem-solving paradigm. This paper presents an overview of single-objective metaheuristic algorithms used for partitional clustering problem and their applications. This paper even presents the research issues which can be dealt with in future.

Continuous greedy randomized adaptive search procedure for data clustering

Cluster analysis is an unsupervised machine learning task that aims at finding the most similar groups of objects, given a prespecified similarity measure. When modeled as an optimization problem, clustering problems generally are NP-hard. Therefore, the use of metaheuristic approaches appears to be a promising alternative. In this paper, a continuous greedy randomized adaptive search procedure (C-GRASP) approach is proposed to solve a partitional clustering problem that aims at minimizing the intra-cluster distances. Computational experiments carried out on existing databases showed that the results obtained by the proposed algorithm was, on average, superior to those found by other well-known metaheuristics, as well as to those achieved by state-of-the-art algorithms from the literature.

Feature-weighted clustering with inner product induced norm based dissimilarity measures: an optimization perspective

The performance of a clustering algorithm can be improved by assigning appropriate weights to different features of the data. Such feature weighting is likely to reduce the effect of noise and irrelevant features while enhancing the effect of the discriminative features simultaneously. For the clustering purpose, feature-weighted dissimilarity measures are so far limited to Euclidean, Mahalanobis, and exponential distances. In this article, we introduce a novel feature weighting scheme for the general class of inner product induced norm (IPIN) based weighted dissimilarity measures. This class has a wide range and includes the three above-mentioned distances as special cases. We develop the general algorithms to solve the hard (k-means) and fuzzy (fuzzy c-means) partitional clustering problems and undertake in-depth analyses of the convergence of the algorithms as well. In addition, we address issues like feasibility and uniqueness of the solutions of these problems in sufficient details. The novelty of the article lies in the introduction of a general feature weighting scheme for the generalized class of IPIN-based dissimilarity measures and a complete convergence analysis for the automated feature-weighted clustering algorithms using such measures.

Optimizing cluster structures with inner product induced norm based dissimilarity measures: Theoretical development and convergence analysis

Dissimilarity measures play a key role in exploring the inherent cluster structure of the data for any partitional clustering algorithm. Commonly used dissimilarity functions for clustering purpose are so far confined to the Euclidean, exponential and Mahalanobish distances. In this article we develop generalized algorithms to solve the partitional clustering problems formulated with a general class of Inner Product Induced Norm (IPIN) based dissimilarity measures. We provide an in-depth mathematical analysis of the underlying optimization framework and analytically address the issue of existence of a solution and its uniqueness. In absence of a closed form solution, we develop a fast stochastic gradient descent algorithm and the Minimization by Incremental Surrogate Optimization (MISO) algorithm (in case of constrained optimization) with exponential convergence rate to obtain the solution. We carry out a convergence analysis of the fuzzy and k-means clustering algorithms with the IPIN based dissimilarity measures and also establish how these algorithms guarantee convergence to a stationary point. In addition, we investigate the nature of the stationary point. Novelty of the paper lies in the introduction of a generalized class of divergence measures, development of fuzzy and k-means clustering algorithms with the general class of divergence measures and a thorough convergence analysis of the developed algorithms.

Hybridization of magnetic charge system search and particle swarm optimization for efficient data clustering using neighborhood search strategy

Clustering is a popular data analysis technique, which is applied for partitioning of datasets. The aim of clustering is to arrange the data items into clusters based on the values of their attributes. Magnetic charge system search (MCSS) algorithm is a new meta-heuristic optimization algorithm inspired by the electromagnetic theory. It has been proved better than other meta-heuristics. This paper presents a new hybrid meta-heuristic algorithm by combining both MCSS and particle swarm optimization (PSO) algorithms, which is called MCSS---PSO, for partitional clustering problem. Moreover, a neighborhood search strategy is also incorporated in this algorithm to generate more promising solutions. The performance of the proposed MCSS---PSO algorithm is tested on several benchmark datasets and its performance is compared with already existing clustering algorithms such as K-means, PSO, genetic algorithm, ant colony optimization, charge system search, chaotic charge system search algorithm, and some PSO variants. From the experimental results, it can be seen that performance of the proposed algorithm is better than the other algorithms being compared and it can be effectively used for partitional clustering problem.

A fast particle swarm optimization for clustering

This paper presents a high-performance method to reduce the time complexity of particle swarm optimization (PSO) and its variants in solving the partitional clustering problem. The proposed method works by adding two additional operators to the PSO-based algorithms. The pattern reduction operator is aimed to reduce the computation time, by compressing at each iteration patterns that are unlikely to change the clusters to which they belong thereafter while the multistart operator is aimed to improve the quality of the clustering result, by enforcing the diversity of the population to prevent the proposed method from getting stuck in local optima. To evaluate the performance of the proposed method, we compare it with several state-of-the-art PSO-based methods in solving data clustering, image clustering, and codebook generation problems. Our simulation results indicate that not only can the proposed method significantly reduce the computation time of PSO-based algorithms, but it can also provide a clustering result that matches or outperforms the result PSO-based algorithms by themselves can provide.

Cooperative bare-bone particle swarm optimization for data clustering

Cooperative coevolution (CC) was used to improve the performance of evolutionary algorithms (EAs) on complex optimization problems in a divide-and-conquer way. In this paper, we show that the CC framework can be very helpful to improve the performance of particle swarm optimization (PSO) on clustering high-dimensional datasets. Based on CC framework, the original partitional clustering problem is first decomposed to several subproblems, each of which is then evolved by an optimizer independently. We employ a very simple but efficient optimization algorithm, namely bare-bone particle swarm optimization (BPSO), as the optimizer to solve each subproblem cooperatively. In addition, we design a new centroid-based encoding schema for each particle and apply the Chernoff bounds to decide a proper population size. The experimental results on synthetic and real-life datasets illustrate the effectiveness and efficiency of the BPSO and CC framework. The comparisons show the proposed algorithm significantly outperforms five EA-based clustering algorithms, i.e., PSO, SRPSO, ACO, ABC and DE, and K-means on most of the datasets.

Dynamic clustering using combinatorial particle swarm optimization

Combinatorial Particle Swarm Optimization (CPSO) is a relatively recent technique for solving combinatorial optimization problems. CPSO has been used in different applications, e.g., partitional clustering and project scheduling problems, and it has shown a very good performance. In partitional clustering problem, CPSO needs to determine the number of clusters in advance. However, in many clustering problems, the correct number of clusters is unknown, and it is usually impossible to estimate. In this paper, an improved version, called CPSOII, is proposed as a dynamic clustering algorithm, which automatically finds the best number of clusters and simultaneously categorizes data objects. CPSOII uses a renumbering procedure as a preprocessing step and several extended PSO operators to increase population diversity and remove redundant particles. Using the renumbering procedure increases the diversity of population, speed of convergence and quality of solutions. For performance evaluation, we have examined CPSOII using both artificial and real data. Experimental results show that CPSOII is very effective, robust and can solve clustering problems successfully with both known and unknown number of clusters. Comparing the obtained results from CPSOII with CPSO and other clustering techniques such as KCPSO, CGA and K-means reveals that CPSOII yields promising results. For example, it improves 9.26 % of the value of DBI criterion for Hepato data set.

Clustering by data competition

Clustering analysis is an unsupervised method to find out hidden structures in datasets. Most partitional clustering algorithms are sensitive to the selection of initial exemplars, the outliers and noise. In this paper, a novel technique called data competition algorithm is proposed to solve the problems. First the concept of aggregation field model is defined to describe the partitional clustering problem. Next, the exemplars are identified according to the data competition. Then, the members will be assigned to the suitable clusters. Data competition algorithm is able to avoid poor solutions caused by unlucky initializations, outliers and noise, and can be used to detect the coexpression gene, cluster the image, diagnose the disease, distinguish the variety, etc. The provided experimental results validate the feasibility and effectiveness of the proposed schemes and show that the proposed approach of data competition algorithm is simple, stable and efficient. The experimental results also show that the proposed approach of data competition clustering outperforms three of the most well known clustering algorithms K-means clustering, affinity propagation clustering, hierarchical clustering.

An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis

Clustering is a popular data analysis and data mining technique. A popular technique for clustering is based on k-means such that the data is partitioned into K clusters. However, the k-means algorithm highly depends on the initial state and converges to local optimum solution. This paper presents a new hybrid evolutionary algorithm to solve nonlinear partitional clustering problem. The proposed hybrid evolutionary algorithm is the combination of FAPSO (fuzzy adaptive particle swarm optimization), ACO (ant colony optimization) and k-means algorithms, called FAPSO-ACO–K, which can find better cluster partition. The performance of the proposed algorithm is evaluated through several benchmark data sets. The simulation results show that the performance of the proposed algorithm is better than other algorithms such as PSO, ACO, simulated annealing (SA), combination of PSO and SA (PSO–SA), combination of ACO and SA (ACO–SA), combination of PSO and ACO (PSO–ACO), genetic algorithm (GA), Tabu search (TS), honey bee mating optimization (HBMO) and k-means for partitional clustering problem.

Stochastic optimal competitive Hopfield network for partitional clustering

This paper presents a stochastic optimal competitive Hopfield network to solve NP-hard partitional clustering problem. Cluster analysis has played a central role in different fields and is often adopted as an approach for preliminary and descriptive data analysis and classification. The objective of the partitional clustering problem is to partition a data set into a specified number of clusters according to certain criteria, e.g. a square error function, and therefore can be treated as an optimization problem. The proposed stochastic optimal competitive Hopfield network introduces a hill-climbing dynamics which helps the network escape from local minima, and therefore can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the stochastic optimal competitive Hopfield network outperforms previous approaches, such as optimal competitive Hopfield model, k-means, genetic algorithm, particle swarm optimization, differential evolution and combinatorial particle swarm optimization for partitional clustering problem.

Combinatorial particle swarm optimization (CPSO) for partitional clustering problem

This paper presents a new clustering approach based on the combinatorial particle swarm optimization (CPSO) algorithm. Each particle is represented as a string of length n (where n is the number of data points) the ith element of the string denotes the group number assigned to object i. An integer vector corresponds to a candidate solution to the clustering problem. A swarm of particles are initiated and fly through the solution space for targeting the optimal solution. To verify the efficiency of the proposed CPSO algorithm, comparisons with a genetic algorithm are performed. Computational results show that the proposed CPSO algorithm is very competitive and outperforms the genetic algorithm.