A review: accuracy optimization in clustering ensembles using genetic algorithms
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paper_title: Novel clustering approach that employs genetic algorithm with new representation scheme and multiple objectives

paper_content:

In this paper, we propose a new encoding scheme for GA and employ multiple objectives in handling the clustering problem. The proposed encoding scheme uses links so that objects to be clustered form a linear pseudo-graph. As multiple objectives are concerned, we used two objectives: 1) to minimize the Total Within Cluster Variation (TWCV); and 2) minimizing the number of clusters in a partition. Our approach obtains the optimal partitions for all the possible numbers of clusters in the Pareto Optimal set returned by a single GA run. The performance of the proposed approach has been tested using two well-known data sets: Iris and Ruspini. The obtained results demonstrate improvement over classical approaches.
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paper_title: Experimental Comparison of Cluster Ensemble Methods

paper_content:

Cluster ensembles are deemed to be a robust and accurate alternative to single clustering runs. 24 methods for designing cluster ensembles are compared here using 24 data sets, both artificial and real. Adjusted Rand index and classification accuracy are used as accuracy criteria with respect to a known partition assumed to be the "true" one. The data sets are randomly chosen to represent medium-size problems arising within a variety of biomedical domains. Ensemble size of 10 was considered. It was found that there is a significant difference among the compared methods (Friedman's Two Way ANOVA). The best ensembles were based on k-means individual clusterers. Consensus functions interpreting the consensus matrix of the ensemble as data, rather than similarity, were found to be significantly better than the traditional alternatives, including CSPA and HGPA.
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paper_title: Clustering with Niching Genetic K-means Algorithm

paper_content:

GA-based clustering algorithms often employ either simple GA, steady state GA or their variants and fail to consistently and efficiently identify high quality solutions (best known optima) of given clustering problems, which involve large data sets with many local optima. To circumvent this problem, we propose Niching Genetic K-means Algorithm (NGKA) that is based on modified deterministic crowding and embeds the computationally attractive k-means. Our experiments show that NGKA can consistently and efficiently identify high quality solutions. Experiments use both simulated and real data with varying size and varying number of local optima. The significance of NGKA is also shown on the experimental data sets by comparing through simulations with Genetically Guided Algorithm (GGA) and Genetic K-means Algorithm (GKA).
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paper_title: Cluster Ensembles A Knowledge Reuse Framework for Combining Partitionings

paper_content:

It is widely recognized that combining multiple classification or regression models typically provides superior results compared to using a single, well-tuned model. However, there are no well known approaches to combining multiple non-hierarchical clusterings. The idea of combining cluster labelings without accessing the original features leads us to a general knowledge reuse framework that we call cluster ensembles. Our contribution in this paper is to formally define the cluster ensemble problem as an optimization problem and to propose three effective and efficient combiners for solving it based on a hypergraph model. Results on synthetic as well as real data sets are given to show that cluster ensembles can (i) improve quality and robustness, and (ii) enable distributed clustering.
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paper_title: A novel genetic algorithm for automatic clustering

paper_content:

In this paper we have presented a new genetically guided algorithm for solving the clustering problem. The proposed Genetic Clustering Algorithm is basically a two-phase process. At the first phase the original data set is decomposed into a number of fragmented clusters in order to spread the GA search process at the latter phase over the entire space. At the second phase Hierarchical Cluster Merging Algorithm (HCMA) is used. The HCMA is an iterative genetic algorithm based approach that combines some of the fragmented clusters into complete k-cluster. The algorithm contains another component called Adjacent Cluster Checking Algorithm (ACCA). This technique is used for testing adjacency of two segmented clusters so that they can be merged into one cluster. The performance of the algorithm has been demonstrated on several data sets consisting of multiple clusters and it is compared with some well-known clustering methods.
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paper_title: A Survey of Evolutionary Algorithms for Clustering

paper_content:

This paper presents a survey of evolutionary algorithms designed for clustering tasks. It tries to reflect the profile of this area by focusing more on those subjects that have been given more importance in the literature. In this context, most of the paper is devoted to partitional algorithms that look for hard clusterings of data, though overlapping (i.e., soft and fuzzy) approaches are also covered in the paper. The paper is original in what concerns two main aspects. First, it provides an up-to-date overview that is fully devoted to evolutionary algorithms for clustering, is not limited to any particular kind of evolutionary approach, and comprises advanced topics like multiobjective and ensemble-based evolutionary clustering. Second, it provides a taxonomy that highlights some very important aspects in the context of evolutionary data clustering, namely, fixed or variable number of clusters, cluster-oriented or nonoriented operators, context-sensitive or context-insensitive operators, guided or unguided operators, binary, integer, or real encodings, centroid-based, medoid-based, label-based, tree-based, or graph-based representations, among others. A number of references are provided that describe applications of evolutionary algorithms for clustering in different domains, such as image processing, computer security, and bioinformatics. The paper ends by addressing some important issues and open questions that can be subject of future research.
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paper_title: Genetic K-means algorithm

paper_content:

In this paper, we propose a novel hybrid genetic algorithm (GA) that finds a globally optimal partition of a given data into a specified number of clusters. GA's used earlier in clustering employ either an expensive crossover operator to generate valid child chromosomes from parent chromosomes or a costly fitness function or both. To circumvent these expensive operations, we hybridize GA with a classical gradient descent algorithm used in clustering, viz. K-means algorithm. Hence, the name genetic K-means algorithm (GKA). We define K-means operator, one-step of K-means algorithm, and use it in GKA as a search operator instead of crossover. We also define a biased mutation operator specific to clustering called distance-based-mutation. Using finite Markov chain theory, we prove that the GKA converges to the global optimum. It is observed in the simulations that GKA converges to the best known optimum corresponding to the given data in concurrence with the convergence result. It is also observed that GKA searches faster than some of the other evolutionary algorithms used for clustering.
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paper_title: Nearest prototype classification: clustering, genetic algorithms, or random search?

paper_content:

Three questions related to the nearest prototype classifier (NPC) are addressed: when is it better to construct the prototypes instead of selecting them as a subset of the given labeled data; how can we trade classification accuracy for a reduction in the number of prototypes; and how good is pure random search (RS) for selection of prototypes from the data? We compare the resubstitution performance of the NPC on the IRIS data set, where the prototypes are either extracted by replacement (R-prototypes) or by selection (S-prototypes). Results for the R-prototypes are taken from a previous study and are contrasted with S-prototype results obtained by a genetic algorithm (GA) or by RS. The best results reached by both algorithms (GA and RS), followed by resubstitution NPC, are two errors with sets of three S-prototypes. This compares favorably to the best result found with R-prototypes, viz., three errors with five R-prototypes. Based on our results, we recommend GA selection for the NPC. A by-product of this research is a counter example to minimality of a recently published minimal consistent set selection procedure.
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paper_title: Genetic Algorithms and Grouping Problems

paper_content:

From the Publisher: ::: A reader-friendly introduction to the exciting, vast potential of Genetic Algorithms. ::: The book gives readers a general understanding of the concepts underlying the technology, an insight into its perceived benefits and failings, and a clear and practical illustration of how optimization problems can be solved more efficiently using Falkenauer's new class of algorithms.
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paper_title: A New Representation and Operators for Genetic Algorithms Applied to Grouping Problems

paper_content:

An important class of computational problems are grouping problems, where the aim is to group together members of a set (i.e., find a good partition of the set). We show why both the standard and the ordering GAs fare poorly in this domain by pointing out their inherent difficulty to capture the regularities of the functional landscape of the grouping problems. We then propose a new encoding scheme and genetic operators adapted to these problems, yielding the Grouping Genetic Algorithm (GGA). We give an experimental comparison of the GGA with the other GAs applied to grouping problems, and we illustrate the approach with two more examples of important grouping problems successfully treated with the GGA: the problems of Bin Packing and Economies of Scale.
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paper_title: Genetic algorithm with deterministic crossover for vector quantization

paper_content:

Genetic algorithm (GA) provides high quality codebooks for vector quantization (VQ) at the cost of high running time. The crossover method is the most important choice of the algorithm. We introduce a new deterministic crossover method based on the pairwise nearest neighbor method. We show that high quality codebooks can be obtained within a few minutes instead of several hours as required by the previous GA-based methods. The method outperforms all comparative codebook generation methods in quality for the tested training sets.
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paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
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paper_title: Classifier hierarchy learning by means of genetic algorithms

paper_content:

Classifier combination falls in the so called data mining area. Its aim is to combine some paradigms from the supervised classification - sometimes with a previous non-supervised data division phase - in order to improve the individual accuracy of the component classifiers. Formation of classifier hierarchies is an alternative among the several methods of classifier combination. In this paper we present a novel method to find good hierarchies of classifiers for given databases. In this new proposal, a search is performed by means of genetic algorithms, returning the best individual according to the classification accuracy over the dataset, estimated through 10-fold cross-validation. Experiments have been carried out over 14 databases from the UCI repository, showing an improvement in the performance compared to the single classifiers. Moreover, similar or better results than other approaches, such as decision tree bagging and boosting, have been obtained.
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paper_title: Clustering ensembles: models of consensus and weak partitions

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.
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paper_title: Evolutionary Algorithms for Solving Multi-Objective Problems

paper_content:

List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.
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paper_title: Data clustering using evidence accumulation

paper_content:

We explore the idea of evidence accumulation for combining the results of multiple clusterings. Initially, n d-dimensional data is decomposed into a large number of compact clusters; the K-means algorithm performs this decomposition, with several clusterings obtained by N random initializations of the K-means. Taking the co-occurrences of pairs of patterns in the same cluster as votes for their association, the data partitions are mapped into a co-association matrix of patterns. This n/spl times/n matrix represents a new similarity measure between patterns. The final clusters are obtained by applying a MST-based clustering algorithm on this matrix. Results on both synthetic and real data show the ability of the method to identify arbitrary shaped clusters in multidimensional data.
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paper_title: Clustering combination method

paper_content:

Clustering combination uses more than one clustering method with identical pattern features to improve the clustering performance. In general clustering is an optimization procedure based on a specific clustering criterion, so clustering combination can be regarded as a technique that constructs and processes multiple clustering criteria rather than a single criterion. We propose two methods of combining objective function clustering and graph theory clustering. One incorporates multiple criteria into an objective function according to their importance, and solves this problem with constrained nonlinear optimization programming. The other method consists of two sequential procedures: (a) a traditional objective function clustering for generating the initial result, and (b) an autoassociative additive system based on graph theory clustering for modifying the initial result.
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paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
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paper_title: A Survey of Evolutionary Algorithms for Clustering

paper_content:

This paper presents a survey of evolutionary algorithms designed for clustering tasks. It tries to reflect the profile of this area by focusing more on those subjects that have been given more importance in the literature. In this context, most of the paper is devoted to partitional algorithms that look for hard clusterings of data, though overlapping (i.e., soft and fuzzy) approaches are also covered in the paper. The paper is original in what concerns two main aspects. First, it provides an up-to-date overview that is fully devoted to evolutionary algorithms for clustering, is not limited to any particular kind of evolutionary approach, and comprises advanced topics like multiobjective and ensemble-based evolutionary clustering. Second, it provides a taxonomy that highlights some very important aspects in the context of evolutionary data clustering, namely, fixed or variable number of clusters, cluster-oriented or nonoriented operators, context-sensitive or context-insensitive operators, guided or unguided operators, binary, integer, or real encodings, centroid-based, medoid-based, label-based, tree-based, or graph-based representations, among others. A number of references are provided that describe applications of evolutionary algorithms for clustering in different domains, such as image processing, computer security, and bioinformatics. The paper ends by addressing some important issues and open questions that can be subject of future research.
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paper_title: Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions

paper_content:

This paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. We first identify several application scenarios for the resultant 'knowledge reuse' framework that we call cluster ensembles. The cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information. In addition to a direct maximization approach, we propose three effective and efficient techniques for obtaining high-quality combiners (consensus functions). The first combiner induces a similarity measure from the partitionings and then reclusters the objects. The second combiner is based on hypergraph partitioning. The third one collapses groups of clusters into meta-clusters which then compete for each object to determine the combined clustering. Due to the low computational costs of our techniques, it is quite feasible to use a supra-consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation. We evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios: (i) where the original clusters were formed based on non-identical sets of features, (ii) where the original clustering algorithms worked on non-identical sets of objects, and (iii) where a common data-set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution. Promising results are obtained in all three situations for synthetic as well as real data-sets.
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paper_title: Random Projection for High Dimensional Data Clustering: A Cluster Ensemble Approach

paper_content:

We investigate how random projection can best be used for clustering high dimensional data. Random projection has been shown to have promising theoretical properties. In practice, however, we find that it results in highly unstable clustering performance. Our solution is to use random projection in a cluster ensemble approach. Empirical results show that the proposed approach achieves better and more robust clustering performance compared to not only single runs of random projection/clustering but also clustering with PCA, a traditional data reduction method for high dimensional data. To gain insights into the performance improvement obtained by our ensemble method, we analyze and identify the influence of the quality and the diversity of the individual clustering solutions on the final ensemble performance.
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paper_title: A Comparison of Resampling Methods for Clustering Ensembles

paper_content:

Combination of multiple clusterings is an important task in the area of unsupervised learning. Inspired by the success of supervised bagging algorithms, we propose a resampling scheme for integration of multiple independent clusterings. Individual partitions in the ensemble are sequentially generated by clustering specially selected subsamples of the given data set. In this paper, we compare the efficacy of both subsampling (sampling without replacement) and bootstrap (with replacement) techniques in conjunction with several fusion algorithms. The empirical study shows that a meaningful consensus partition for an entire set of data points emerges from multiple clusterings of subsamples of small size. The purpose of this paper is to show that small subsamples generally suffice to represent the structure of the entire data set in the framework of clustering ensembles. Subsamples of small size can reduce computational cost and measurement complexity for many unsupervised data mining tasks with distributed sources of data.
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paper_title: Data clustering: a review

paper_content:

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overviewof pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.
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paper_title: Bagging to improve the accuracy of a clustering procedure

paper_content:

MOTIVATION:The microarray technology is increasingly being applied in biological and medical research to address a wide range of problems such as the classification of tumors. An important statistical question associated with tumor classification is the identification of new tumor classes using gene expression profiles. Essential aspects of this clustering problem include identifying accurate partitions of the tumor samples into clusters and assessing the confidence of cluster assignments for individual samples. RESULTS:Two new resampling methods, inspired from bagging in prediction, are proposed to improve and assess the accuracy of a given clustering procedure. In these ensemble methods, a partitioning clustering procedure is applied to bootstrap learning sets and the resulting multiple partitions are combined by voting or the creation of a new dissimilarity matrix. As in prediction, the motivation behind bagging is to reduce variability in the partitioning results via averaging. The performances of the new and existing methods were compared using simulated data and gene expression data from two recently published cancer microarray studies. The bagged clustering procedures were in general at least as accurate and often substantially more accurate than a single application of the partitioning clustering procedure. A valuable by-product of bagged clustering are the cluster votes which can be used to assess the confidence of cluster assignments for individual observations. SUPPLEMENTARY INFORMATION:For supplementary information on datasets, analyses, and software, consult http://www.stat.berkeley.edu/~sandrine and http://www.bioconductor.org.
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paper_title: Combining multiple weak clusterings

paper_content:

A data set can be clustered in many ways depending on the clustering algorithm employed, parameter settings used and other factors. Can multiple clusterings be combined so that the final partitioning of data provides better clustering? The answer depends on the quality of clusterings to be combined as well as the properties of the fusion method. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. As a result, we show that the consensus function is related to the classical intra-class variance criterion using the generalized mutual information definition. Second, we show the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. We analyze the combination accuracy as a function of parameters controlling the power and resolution of component partitions as well as the learning dynamics vs. the number of clusterings involved. Finally, some empirical studies compare the effectiveness of several consensus functions.
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paper_title: PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization

paper_content:

We describe a new selection technique for evolutionary multiobjective optimization algorithms in which the unit of selection is a hyperbox in objective space. In this technique, instead of assigning a selective fitness to an individual, selective fitness is assigned to the hyperboxes in objective space which are currently occupied by at least one individual in the current approximation to the Pareto frontier. A hyperbox is thereby selected, and the resulting selected individual is randomly chosen from this hyperbox. This method of selection is shown to be more sensitive to ensuring a good spread of development along the Pareto frontier than individual-based selection. The method is implemented in a modern multiobjective evolutionary algorithm, and performance is tested by using Deb's test suite of `T' functions with varying properties. The new selection technique is found to give significantly superior results to the other methods compared, namely PAES, PESA, and SPEA; each is a modern multi-objective optimization algorithm previously found to outperform earlier approaches on various problems.
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paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
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paper_title: Solving Cluster Ensemble Problems by Correlation’s matrix & GA

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. We offer a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clustering. A combined partition is found as a solution to the corresponding maximum likelihood problem using the GA algorithm. The excellent scalability of this algorithm and comprehensible underlying model are particularly important for clustering of large datasets. This study includes two sections, at the first, calculate correlation matrix. this matrix show correlation between samples and we found the best samples that can be in the center of clusters. In the other section a genetic algorithm is employed to produce the most stable partitions from an evolving ensemble (population) of clustering algorithms along with a special objective function. The objective function evaluates multiple partitions according to changes caused by data perturbations and prefers those clustering that are least susceptible to those perturbations.
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paper_title: Clustering ensembles: models of consensus and weak partitions

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph-based, combinatorial, or statistical perspectives. This study extends previous research on clustering ensembles in several respects. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. Second, we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings. A combined partition is found as a solution to the corresponding maximum-likelihood problem using the EM algorithm. Third, we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition. Finally, we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. Combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions. We also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus. Experimental results demonstrate the effectiveness of the proposed methods on several real-world data sets.
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paper_title: Data clustering using evidence accumulation

paper_content:

We explore the idea of evidence accumulation for combining the results of multiple clusterings. Initially, n d-dimensional data is decomposed into a large number of compact clusters; the K-means algorithm performs this decomposition, with several clusterings obtained by N random initializations of the K-means. Taking the co-occurrences of pairs of patterns in the same cluster as votes for their association, the data partitions are mapped into a co-association matrix of patterns. This n/spl times/n matrix represents a new similarity measure between patterns. The final clusters are obtained by applying a MST-based clustering algorithm on this matrix. Results on both synthetic and real data show the ability of the method to identify arbitrary shaped clusters in multidimensional data.
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paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
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paper_title: Cluster Ensembles A Knowledge Reuse Framework for Combining Partitionings

paper_content:

It is widely recognized that combining multiple classification or regression models typically provides superior results compared to using a single, well-tuned model. However, there are no well known approaches to combining multiple non-hierarchical clusterings. The idea of combining cluster labelings without accessing the original features leads us to a general knowledge reuse framework that we call cluster ensembles. Our contribution in this paper is to formally define the cluster ensemble problem as an optimization problem and to propose three effective and efficient combiners for solving it based on a hypergraph model. Results on synthetic as well as real data sets are given to show that cluster ensembles can (i) improve quality and robustness, and (ii) enable distributed clustering.
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paper_title: A Survey of Evolutionary Algorithms for Clustering

paper_content:

This paper presents a survey of evolutionary algorithms designed for clustering tasks. It tries to reflect the profile of this area by focusing more on those subjects that have been given more importance in the literature. In this context, most of the paper is devoted to partitional algorithms that look for hard clusterings of data, though overlapping (i.e., soft and fuzzy) approaches are also covered in the paper. The paper is original in what concerns two main aspects. First, it provides an up-to-date overview that is fully devoted to evolutionary algorithms for clustering, is not limited to any particular kind of evolutionary approach, and comprises advanced topics like multiobjective and ensemble-based evolutionary clustering. Second, it provides a taxonomy that highlights some very important aspects in the context of evolutionary data clustering, namely, fixed or variable number of clusters, cluster-oriented or nonoriented operators, context-sensitive or context-insensitive operators, guided or unguided operators, binary, integer, or real encodings, centroid-based, medoid-based, label-based, tree-based, or graph-based representations, among others. A number of references are provided that describe applications of evolutionary algorithms for clustering in different domains, such as image processing, computer security, and bioinformatics. The paper ends by addressing some important issues and open questions that can be subject of future research.
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paper_title: Solving cluster ensemble problems by bipartite graph partitioning

paper_content:

A critical problem in cluster ensemble research is how to combine multiple clusterings to yield a final superior clustering result. Leveraging advanced graph partitioning techniques, we solve this problem by reducing it to a graph partitioning problem. We introduce a new reduction method that constructs a bipartite graph from a given cluster ensemble. The resulting graph models both instances and clusters of the ensemble simultaneously as vertices in the graph. Our approach retains all of the information provided by a given ensemble, allowing the similarity among instances and the similarity among clusters to be considered collectively in forming the final clustering. Further, the resulting graph partitioning problem can be solved efficiently. We empirically evaluate the proposed approach against two commonly used graph formulations and show that it is more robust and achieves comparable or better performance in comparison to its competitors.
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paper_title: On Spectral Clustering: Analysis and an algorithm

paper_content:

Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.
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paper_title: Combining multiple weak clusterings

paper_content:

A data set can be clustered in many ways depending on the clustering algorithm employed, parameter settings used and other factors. Can multiple clusterings be combined so that the final partitioning of data provides better clustering? The answer depends on the quality of clusterings to be combined as well as the properties of the fusion method. First, we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem. As a result, we show that the consensus function is related to the classical intra-class variance criterion using the generalized mutual information definition. Second, we show the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits. A simple explanatory model is offered for the behavior of combinations of such weak clustering components. We analyze the combination accuracy as a function of parameters controlling the power and resolution of component partitions as well as the learning dynamics vs. the number of clusterings involved. Finally, some empirical studies compare the effectiveness of several consensus functions.
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paper_title: To Combine Steady-State Genetic Algorithm and Ensemble Learning for Data Clustering

paper_content:

This paper proposes a data clustering algorithm that combines the steady-state genetic algorithm and the ensemble learning method, termed as genetic-guided clustering algorithm with ensemble learning operator (GCEL). GCEL adopts the steady-state genetic algorithm to perform the search task, but replaces its traditional recombination operator with an ensemble learning operator. Therefore, GCEL can avoid the problems of clustering invalidity and context insensitivity of the traditional recombination operator of genetic algorithms. In addition, GCEL generates its initial population of candidate clustering solutions by using the random subspaces method. Therefore, less fitness evaluations are required to converge. The proposed GCEL is tested on one synthetic and several real data sets. Experimental results demonstrate that GCEL is able to achieve a comparative or better clustering solution with less fitness evaluations when compared with several other existing genetic-guided clustering algorithms.
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paper_title: Heterogeneous clustering ensemble method for combining different cluster results

paper_content:

Biological data set sizes have been growing rapidly with the technological advances that have occurred in bioinformatics. Data mining techniques have been used extensively as approaches to detect interesting patterns in large databases. In bioinformatics, clustering algorithm technique for data mining can be applied to find underlying genetic and biological interactions, without considering prior information from datasets. However, many clustering algorithms are practically available, and different clustering algorithms may generate dissimilar clustering results due to bio-data characteristics and experimental assumptions. In this paper, we propose a novel heterogeneous clustering ensemble scheme that uses a genetic algorithm to generate high quality and robust clustering results with characteristics of bio-data. The proposed method combines results of various clustering algorithms and crossover operation of genetic algorithm, and is founded on the concept of using the evolutionary processes to select the most commonly-inherited characteristics. Our framework proved to be available on real data set and the optimal clustering results generated by means of our proposed method are detailed in this paper. Experimental results demonstrate that the proposed method yields better clustering results than applying a single best clustering algorithm.
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paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
---
paper_title: Comparison of Steady State and Generational Genetic Algorithms for Use in Nonstationary Environments

paper_content:

The objective of this study is a comparison of two models of the genetic algorithm, the generational and incremental/steady state genetic algorithms, for use in nonstationary/dynamic environments. It is experimentally shown that the choice of a suitable version of the genetic algorithm can improve its performance in such environments. This can extend the ability of the genetic algorithm to track environmental changes which are relatively small and occur with low frequency without the need to implement an additional technique for tracking changing optima.
---
paper_title: Novel clustering approach that employs genetic algorithm with new representation scheme and multiple objectives

paper_content:

In this paper, we propose a new encoding scheme for GA and employ multiple objectives in handling the clustering problem. The proposed encoding scheme uses links so that objects to be clustered form a linear pseudo-graph. As multiple objectives are concerned, we used two objectives: 1) to minimize the Total Within Cluster Variation (TWCV); and 2) minimizing the number of clusters in a partition. Our approach obtains the optimal partitions for all the possible numbers of clusters in the Pareto Optimal set returned by a single GA run. The performance of the proposed approach has been tested using two well-known data sets: Iris and Ruspini. The obtained results demonstrate improvement over classical approaches.
---
paper_title: Exploiting the trade-off — the benefits of multiple objectives in data clustering

paper_content:

In previous work, we have proposed a novel approach to data clustering based on the explicit optimization of a partitioning with respect to two complementary clustering objectives [6]. Here, we extend this idea by describing an advanced multiobjective clustering algorithm, MOCK, with the capacity to identify good solutions from the Pareto front, and to automatically determine the number of clusters in a data set. The algorithm has been subject to a thorough comparison with alternative clustering techniques and we briefly summarize these results. We then present investigations into the mechanisms at the heart of MOCK: we discuss a simple example demonstrating the synergistic effects at work in multiobjective clustering, which explain its superiority to single-objective clustering techniques, and we analyse how MOCK's Pareto fronts compare to the performance curves obtained by single-objective algorithms run with a range of different numbers of clusters specified.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: Genetic K-means algorithm

paper_content:

In this paper, we propose a novel hybrid genetic algorithm (GA) that finds a globally optimal partition of a given data into a specified number of clusters. GA's used earlier in clustering employ either an expensive crossover operator to generate valid child chromosomes from parent chromosomes or a costly fitness function or both. To circumvent these expensive operations, we hybridize GA with a classical gradient descent algorithm used in clustering, viz. K-means algorithm. Hence, the name genetic K-means algorithm (GKA). We define K-means operator, one-step of K-means algorithm, and use it in GKA as a search operator instead of crossover. We also define a biased mutation operator specific to clustering called distance-based-mutation. Using finite Markov chain theory, we prove that the GKA converges to the global optimum. It is observed in the simulations that GKA converges to the best known optimum corresponding to the given data in concurrence with the convergence result. It is also observed that GKA searches faster than some of the other evolutionary algorithms used for clustering.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: A Novel Framework for Discovering Robust Cluster Results

paper_content:

We propose a novel method, called heterogeneous clustering ensemble (HCE), to generate robust clustering results that combine multiple partitions (clusters) derived from various clustering algorithms. The proposed method combines partitions of various clustering algorithms by means of newly-proposed the selection and the crossover operation of the genetic algorithm (GA) during the evolutionary process.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: Recursive Self Organizing Maps with Hybrid Clustering

paper_content:

We introduce the concept of a neural network based recursive clustering which creates an ensemble of clusters by recursive decomposition of data. The work involves a hybrid combination of a global clustering algorithm followed by a corresponding local clustering algorithm. Evolutionary Self Organizing Maps are used to create clusters. A set of core patterns is isolated and separately trained using a SOM. The process is recursively applied to the remaining patterns to create an ensemble of clusters. The partition of each recursion is integrated with the partition of the previous recursion. The correlation of the clusters with ground truth information (in the form of class labels) is used to measure algorithm robustness. The paper shows that a hybrid combination of evolutionary algorithms and neural network based clustering techniques is efficient in finding good partitions of clusters and in finding suitable resultant cluster shapes. The recursive self organizing map proposed aims to improve the clustering accuracy of the self organizing map. Empirical studies show that superior results are obtained when clustering artificially generated data as well as real world problems such as the Iris, Glass and Wine datasets.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: To Combine Steady-State Genetic Algorithm and Ensemble Learning for Data Clustering

paper_content:

This paper proposes a data clustering algorithm that combines the steady-state genetic algorithm and the ensemble learning method, termed as genetic-guided clustering algorithm with ensemble learning operator (GCEL). GCEL adopts the steady-state genetic algorithm to perform the search task, but replaces its traditional recombination operator with an ensemble learning operator. Therefore, GCEL can avoid the problems of clustering invalidity and context insensitivity of the traditional recombination operator of genetic algorithms. In addition, GCEL generates its initial population of candidate clustering solutions by using the random subspaces method. Therefore, less fitness evaluations are required to converge. The proposed GCEL is tested on one synthetic and several real data sets. Experimental results demonstrate that GCEL is able to achieve a comparative or better clustering solution with less fitness evaluations when compared with several other existing genetic-guided clustering algorithms.
---
paper_title: Integration analysis of diverse genomic data using multi-clustering results

paper_content:

In modern data mining applications, clustering algorithms are among the most important approaches, because these algorithms group elements in a dataset according to their similarities, and they do not require any class label information. In recent years, various methods for ensemble selection and clustering result combinations have been designed to optimize clustering results. Moreover, conducting data analysis using multiple sources, given the complexity of data objects, is a much more powerful method than evaluating each source separately. Therefore, a new paradigm is required that combines the genome-wide experimental results of multi-source datasets. However, multi-source data analysis is more difficult than single source data analysis. In this paper, we propose a new clustering ensemble approach for multi-source bio-data on complex objects. In addition, we present encouraging clustering results in a real bio-dataset examined using our proposed method.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: To Combine Steady-State Genetic Algorithm and Ensemble Learning for Data Clustering

paper_content:

This paper proposes a data clustering algorithm that combines the steady-state genetic algorithm and the ensemble learning method, termed as genetic-guided clustering algorithm with ensemble learning operator (GCEL). GCEL adopts the steady-state genetic algorithm to perform the search task, but replaces its traditional recombination operator with an ensemble learning operator. Therefore, GCEL can avoid the problems of clustering invalidity and context insensitivity of the traditional recombination operator of genetic algorithms. In addition, GCEL generates its initial population of candidate clustering solutions by using the random subspaces method. Therefore, less fitness evaluations are required to converge. The proposed GCEL is tested on one synthetic and several real data sets. Experimental results demonstrate that GCEL is able to achieve a comparative or better clustering solution with less fitness evaluations when compared with several other existing genetic-guided clustering algorithms.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: A Novel Framework for Discovering Robust Cluster Results

paper_content:

We propose a novel method, called heterogeneous clustering ensemble (HCE), to generate robust clustering results that combine multiple partitions (clusters) derived from various clustering algorithms. The proposed method combines partitions of various clustering algorithms by means of newly-proposed the selection and the crossover operation of the genetic algorithm (GA) during the evolutionary process.
---
paper_title: Combining multiple clusterings using evidence accumulation

paper_content:

We explore the idea of evidence accumulation (EAC) for combining the results of multiple clusterings. First, a clustering ensemble?a set of object partitions, is produced. Given a data set (n objects or patterns in d dimensions), different ways of producing data partitions are: 1) applying different clustering algorithms and 2) applying the same clustering algorithm with different values of parameters or initializations. Further, combinations of different data representations (feature spaces) and clustering algorithms can also provide a multitude of significantly different data partitionings. We propose a simple framework for extracting a consistent clustering, given the various partitions in a clustering ensemble. According to the EAC concept, each partition is viewed as an independent evidence of data organization, individual data partitions being combined, based on a voting mechanism, to generate a new n \times n similarity matrix between the n patterns. The final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix. We have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation, based on the concept of mutual information between data partitions. Stability of the results is evaluated using bootstrapping techniques. A detailed discussion of an evidence accumulation-based clustering algorithm, using a split and merge strategy based on the K-means clustering algorithm, is presented. Experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies, and with individual clustering results produced by well-known clustering algorithms.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
---
paper_title: Multi-objective clustering and cluster validation

paper_content:

An electrostatic record material comprising an electroconductive base sheet and a record layer formed on the base sheet and consisting essentially of an insulating resin, the record material being characterized in that the base sheet includes (i) an electroconductive layer comprising an ionic-conductive substance as its main electroconductive component, and (ii) an electroconductive layer comprising an electronic-conductive substance as its main electroconductive component. The electrostatic record material has excellent recording characteristics at usual humidity.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: To Combine Steady-State Genetic Algorithm and Ensemble Learning for Data Clustering

paper_content:

This paper proposes a data clustering algorithm that combines the steady-state genetic algorithm and the ensemble learning method, termed as genetic-guided clustering algorithm with ensemble learning operator (GCEL). GCEL adopts the steady-state genetic algorithm to perform the search task, but replaces its traditional recombination operator with an ensemble learning operator. Therefore, GCEL can avoid the problems of clustering invalidity and context insensitivity of the traditional recombination operator of genetic algorithms. In addition, GCEL generates its initial population of candidate clustering solutions by using the random subspaces method. Therefore, less fitness evaluations are required to converge. The proposed GCEL is tested on one synthetic and several real data sets. Experimental results demonstrate that GCEL is able to achieve a comparative or better clustering solution with less fitness evaluations when compared with several other existing genetic-guided clustering algorithms.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
---
paper_title: To Combine Steady-State Genetic Algorithm and Ensemble Learning for Data Clustering

paper_content:

This paper proposes a data clustering algorithm that combines the steady-state genetic algorithm and the ensemble learning method, termed as genetic-guided clustering algorithm with ensemble learning operator (GCEL). GCEL adopts the steady-state genetic algorithm to perform the search task, but replaces its traditional recombination operator with an ensemble learning operator. Therefore, GCEL can avoid the problems of clustering invalidity and context insensitivity of the traditional recombination operator of genetic algorithms. In addition, GCEL generates its initial population of candidate clustering solutions by using the random subspaces method. Therefore, less fitness evaluations are required to converge. The proposed GCEL is tested on one synthetic and several real data sets. Experimental results demonstrate that GCEL is able to achieve a comparative or better clustering solution with less fitness evaluations when compared with several other existing genetic-guided clustering algorithms.
---
paper_title: Recursive Self Organizing Maps with Hybrid Clustering

paper_content:

We introduce the concept of a neural network based recursive clustering which creates an ensemble of clusters by recursive decomposition of data. The work involves a hybrid combination of a global clustering algorithm followed by a corresponding local clustering algorithm. Evolutionary Self Organizing Maps are used to create clusters. A set of core patterns is isolated and separately trained using a SOM. The process is recursively applied to the remaining patterns to create an ensemble of clusters. The partition of each recursion is integrated with the partition of the previous recursion. The correlation of the clusters with ground truth information (in the form of class labels) is used to measure algorithm robustness. The paper shows that a hybrid combination of evolutionary algorithms and neural network based clustering techniques is efficient in finding good partitions of clusters and in finding suitable resultant cluster shapes. The recursive self organizing map proposed aims to improve the clustering accuracy of the self organizing map. Empirical studies show that superior results are obtained when clustering artificially generated data as well as real world problems such as the Iris, Glass and Wine datasets.
---
paper_title: Exploiting the trade-off — the benefits of multiple objectives in data clustering

paper_content:

In previous work, we have proposed a novel approach to data clustering based on the explicit optimization of a partitioning with respect to two complementary clustering objectives [6]. Here, we extend this idea by describing an advanced multiobjective clustering algorithm, MOCK, with the capacity to identify good solutions from the Pareto front, and to automatically determine the number of clusters in a data set. The algorithm has been subject to a thorough comparison with alternative clustering techniques and we briefly summarize these results. We then present investigations into the mechanisms at the heart of MOCK: we discuss a simple example demonstrating the synergistic effects at work in multiobjective clustering, which explain its superiority to single-objective clustering techniques, and we analyse how MOCK's Pareto fronts compare to the performance curves obtained by single-objective algorithms run with a range of different numbers of clusters specified.
---
paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
---
paper_title: Multi-Objective Clustering Ensemble with Prior Knowledge

paper_content:

In this paper, we introduce an approach to integrate prior knowledge in cluster analysis, which is different from the existing ones for semi-supervised clustering methods. In order to aid the discovery of alternative structures present in the data, we consider the knowledge of some existing complete classification of such data. The approach proposed is based on our Multi-Objective Clustering Ensemble algorithm (MOCLE). This algorithm generates a concise and stable set of partitions, which represents different trade-offs between several measures of partition quality. The prior knowledge is automatically integrated in MOCLE by embedding it into one of the objective functions. In this case, the function gives as output the quality of a partition, considering the prior knowledge of one of the known structures of the data.
---
paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

paper_content:

This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
---
paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
---
paper_title: Incremental genetic K-means algorithm and its application in gene expression data analysis

paper_content:

BackgroundIn recent years, clustering algorithms have been effectively applied in molecular biology for gene expression data analysis. With the help of clustering algorithms such as K-means, hierarchical clustering, SOM, etc, genes are partitioned into groups based on the similarity between their expression profiles. In this way, functionally related genes are identified. As the amount of laboratory data in molecular biology grows exponentially each year due to advanced technologies such as Microarray, new efficient and effective methods for clustering must be developed to process this growing amount of biological data.ResultsIn this paper, we propose a new clustering algorithm, Incremental Genetic K-means Algorithm (IGKA). IGKA is an extension to our previously proposed clustering algorithm, the Fast Genetic K-means Algorithm (FGKA). IGKA outperforms FGKA when the mutation probability is small. The main idea of IGKA is to calculate the objective value Total Within-Cluster Variation (TWCV) and to cluster centroids incrementally whenever the mutation probability is small. IGKA inherits the salient feature of FGKA of always converging to the global optimum. C program is freely available at http://database.cs.wayne.edu/proj/FGKA/index.htm.ConclusionsOur experiments indicate that, while the IGKA algorithm has a convergence pattern similar to FGKA, it has a better time performance when the mutation probability decreases to some point. Finally, we used IGKA to cluster a yeast dataset and found that it increased the enrichment of genes of similar function within the cluster.
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paper_title: Recursive Self Organizing Maps with Hybrid Clustering

paper_content:

We introduce the concept of a neural network based recursive clustering which creates an ensemble of clusters by recursive decomposition of data. The work involves a hybrid combination of a global clustering algorithm followed by a corresponding local clustering algorithm. Evolutionary Self Organizing Maps are used to create clusters. A set of core patterns is isolated and separately trained using a SOM. The process is recursively applied to the remaining patterns to create an ensemble of clusters. The partition of each recursion is integrated with the partition of the previous recursion. The correlation of the clusters with ground truth information (in the form of class labels) is used to measure algorithm robustness. The paper shows that a hybrid combination of evolutionary algorithms and neural network based clustering techniques is efficient in finding good partitions of clusters and in finding suitable resultant cluster shapes. The recursive self organizing map proposed aims to improve the clustering accuracy of the self organizing map. Empirical studies show that superior results are obtained when clustering artificially generated data as well as real world problems such as the Iris, Glass and Wine datasets.
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paper_title: Exploiting the trade-off — the benefits of multiple objectives in data clustering

paper_content:

In previous work, we have proposed a novel approach to data clustering based on the explicit optimization of a partitioning with respect to two complementary clustering objectives [6]. Here, we extend this idea by describing an advanced multiobjective clustering algorithm, MOCK, with the capacity to identify good solutions from the Pareto front, and to automatically determine the number of clusters in a data set. The algorithm has been subject to a thorough comparison with alternative clustering techniques and we briefly summarize these results. We then present investigations into the mechanisms at the heart of MOCK: we discuss a simple example demonstrating the synergistic effects at work in multiobjective clustering, which explain its superiority to single-objective clustering techniques, and we analyse how MOCK's Pareto fronts compare to the performance curves obtained by single-objective algorithms run with a range of different numbers of clusters specified.
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paper_title: Combining Multiple Clusterings using Information Theory based Genetic Algorithm

paper_content:

Clustering ensembles have emerged as a powerful method for improving both the robustness and the stability of unsupervised classification solutions. However, finding a consensus clustering from multiple clusterings is a difficult problem that can be approached from graph-based, combinatorial or statistical perspectives. A consensus scheme via the genetic algorithm based on information theory is proposed in this paper. A combined clustering is found by minimizing an information-theoretical criterion function using genetic algorithm. This study compares the performance of the information-theoretical consensus algorithm with other fusion approaches for clustering ensembles. Experimental results demonstrate the effectiveness of the proposed method.
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paper_title: Multi-Objective Clustering Ensemble with Prior Knowledge

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In this paper, we introduce an approach to integrate prior knowledge in cluster analysis, which is different from the existing ones for semi-supervised clustering methods. In order to aid the discovery of alternative structures present in the data, we consider the knowledge of some existing complete classification of such data. The approach proposed is based on our Multi-Objective Clustering Ensemble algorithm (MOCLE). This algorithm generates a concise and stable set of partitions, which represents different trade-offs between several measures of partition quality. The prior knowledge is automatically integrated in MOCLE by embedding it into one of the objective functions. In this case, the function gives as output the quality of a partition, considering the prior knowledge of one of the known structures of the data.
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paper_title: Parallel clustering of high dimensional data by integrating multi-objective genetic algorithm with divide and conquer

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This paper applies divide and conquer approach in an iterative way to handle the clustering process. The target is a parallelized effective and efficient approach that produces the intended clustering result. We achieve scalability by first partitioning a large dataset into subsets of manageable sizes based on the specifications of the machine to be used in the clustering process; then cluster the partitions separately in parallel. The centroid of each obtained cluster is treated like the root of a tree with instances in its cluster as leaves. The partitioning and clustering process is iteratively applied on the centroids with the trees growing up until we get the final clustering; the outcome is a forest with one tree per cluster. Finally, a conquer process is performed to get the actual intended clustering, where each instance (leaf node) belongs to the final cluster represented by the root of its tree. We use multi-objective genetic algorithm combined with validity indices to decide on the number of classes. This approach fits well for interactive online clustering. It facilitates for incremental clustering because chunks of instances are clustered as stand alone sets, and then the results are merged with existing clusters. This is attractive and feasible because we consider the clustering of only centroids after the first clustering stage. The reported test results demonstrate the applicability and effectiveness of the proposed approach.
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paper_title: Unsupervised Feature Selection Using Clustering Ensembles and Population Based Incremental Learning Algorithm

paper_content:

This paper describes a novel feature selection algorithm for unsupervised clustering, that combines the clustering ensembles method and the population based incremental learning algorithm. The main idea of the proposed unsupervised feature selection algorithm is to search for a subset of all features such that the clustering algorithm trained on this feature subset can achieve the most similar clustering solution to the one obtained by an ensemble learning algorithm. In particular, a clustering solution is firstly achieved by a clustering ensembles method, then the population based incremental learning algorithm is adopted to find the feature subset that best fits the obtained clustering solution. One advantage of the proposed unsupervised feature selection algorithm is that it is dimensionality-unbiased. In addition, the proposed unsupervised feature selection algorithm leverages the consensus across multiple clustering solutions. Experimental results on several real data sets demonstrate that the proposed unsupervised feature selection algorithm is often able to obtain a better feature subset when compared with other existing unsupervised feature selection algorithms.
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paper_title: An Evolutionary Approach to Clustering Ensemble

paper_content:

In this paper we propose a clustering ensemble algorithm based on genetic algorithm. The most important feature of our method is ability to extract the number of clusters. Genetic algorithms have been known as methods with high ability to find the solution of optimization problems. One of these problems is clustering, a process that receives a dataset as input and divides its members into several subsets called cluster (partition or group). The members of each cluster would be alike while members of two different clusters would be as different as possible. One of the common ways to do this is combinational clustering. Combinational clustering will combine the results of different clustering methods or some executions of a clustering method to calculate final clusters. In this paper, an evolutionary combinational clustering method is proposed to find the number of clusters. The evaluation of this method on several common datasets shows the proper performance of proposed method to find final clusters as well as the exact number of clusters.
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Title: A review: accuracy optimization in clustering ensembles using genetic algorithms 

Section 1: Introduction
Description 1: Explain the motivations behind clustering ensembles, their benefits, and the limitations of classical clustering algorithms. Introduce the concept of using genetic algorithms to enhance clustering ensembles' performance.

Section 2: Clustering ensemble and its challenges
Description 2: Discuss the rationale behind clustering ensembles, consensus function issues, diversity of clustering, and the strength of constituent models. Explain the NP-complete nature of finding a consensus partition.

Section 3: Clustering ensemble algorithms (CEAs)
Description 3: Provide an overview of different consensus functions used in CEAs such as co-association, graph-based methods, mutual information, and voting. Summarize existing research and datasets used for validating these methods.

Section 4: Employing genetic algorithms and their components in clustering ensembles
Description 4: Analyze the application of genetic algorithms in clustering ensembles. Discuss various genetic operations including genotype encoding, population initialization, fitness function, selection operator, crossover operator, mutation operator, and replacement.

Section 5: Genetic-guided clustering ensemble algorithms (GCEAs) and their clustering accuracy
Description 5: Summarize existing research on GCEAs and highlight their advantages, disadvantages, and future work. Compare the accuracy of GCEAs with classical CEAs based on various datasets.

Section 6: Comparison of clustering accuracy between CEA and GCEA algorithms
Description 6: Compare and contrast the clustering accuracy between traditional CEAs and GCEAs across benchmark datasets. Present empirical results and evaluate the performance improvements offered by GCEAs.

Section 7: Conclusions and future works
Description 7: Summarize the impact of using genetic algorithms in clustering ensembles. Discuss the main findings, improvements in clustering accuracy, and outline potential future research directions.