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Survey of clustering algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2005
"... Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the ..."
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Cited by 483 (4 self)
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Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
Variable Neighborhood Search
, 1997
"... Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications a ..."
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Cited by 342 (26 self)
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Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications are briefly summarized. They comprise heuristic solution of a variety of optimization problems, ways to accelerate exact algorithms and to analyze heuristic solution processes, as well as computerassisted discovery of conjectures in graph theory.
Variable neighborhood search: Principles and applications
, 2001
"... Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using an ..."
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Cited by 180 (16 self)
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Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and effective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its effectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a twolevel VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an efficient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear
Iterated local search
 Handbook of Metaheuristics, volume 57 of International Series in Operations Research and Management Science
, 2002
"... Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions th ..."
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Cited by 168 (14 self)
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Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for a given optimization engine. The success of Iterated Local Search lies in the biased sampling of this set of local optima. How effective this approach turns out to be depends mainly on the choice of the local search, the perturbations, and the acceptance criterion. So far, in spite of its conceptual simplicity, it has lead to a number of stateoftheart results without the use of too much problemspecific knowledge. But with further work so that the different modules are well adapted to the problem at hand, Iterated Local Search can often become a competitive or even state of the art algorithm. The purpose of this review is both to give a detailed description of this metaheuristic and to show where it stands in terms of performance. O.M. acknowledges support from the Institut Universitaire de France. This work was partially supported by the “Metaheuristics Network”, a Research Training Network funded by the Improving Human Potential programme of the CEC, grant HPRNCT199900106. The information provided is the sole responsibility of the authors and does not reflect the Community’s opinion. The Community is not responsible for any use that might be made of data appearing in this publication. 1 1
Ymeans: A Clustering Method for Intrusion Detection
 Proceedings of Canadian Conference on Electrical and Computer Engineering
, 2003
"... As the Internet spreads to each corner of the world, computers are exposed to miscellaneous intrusions from the World Wide Web. We need effective intrusion detection systems to protect our computers from these unauthorized or malicious actions. Traditional instancebased learning methods for Intrusi ..."
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Cited by 37 (1 self)
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As the Internet spreads to each corner of the world, computers are exposed to miscellaneous intrusions from the World Wide Web. We need effective intrusion detection systems to protect our computers from these unauthorized or malicious actions. Traditional instancebased learning methods for Intrusion Detection can only detect known intrusions since these methods classify instances based on what they have learned. They rarely detect the intrusions that they have not learned before. In this paper, we present a clustering heuristic for intrusion detection, called Ymeans. This proposed heuristic is based on the Kmeans algorithm and other related clustering algorithms. It overcomes two shortcomings of Kmeans: number of clusters dependency and degeneracy. The result of simulations run on the KDD99 data set shows that Ymeans is an effective method for partitioning large data space. A detection rate of 89.89 % and a false alarm rate of 1.00 % are achieved with Ymeans. 1 Keywords: Clustering; intrusion detection; Kmeans;
Solving the pCenter Problem with Tabu Search and Variable Neighborhood Search
, 2000
"... The pCenter problem consists in locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. In this paper we present a basic Variable Neighborhood Search and two Tabu Search heuristics for the pCenter ..."
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Cited by 20 (0 self)
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The pCenter problem consists in locating p facilities and assigning clients to them in order to minimize the maximum distance between a client and the facility to which he is allocated. In this paper we present a basic Variable Neighborhood Search and two Tabu Search heuristics for the pCenter problem without triangle inequality. Both proposed methods use the 1interchange (or vertex substitution) neighborhood structure.
Fuzzy JMeans: a new heuristic for fuzzy clustering
, 2002
"... A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called ..."
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Cited by 16 (5 self)
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A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called FuzzyJMeans, where the neighbourhood is defined by all possible centroidtopattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the wellknown FuzzyCMeans heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.
A Tutorial on Variable Neighborhood Search
 LES CAHIERS DU GERAD, HEC MONTREAL AND GERAD
, 2003
"... Variable Neighborhood Search (VNS) is a recent metaheuristic, or framework for building heuristics, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. In this tutorial we first present the ingre ..."
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Cited by 16 (3 self)
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Variable Neighborhood Search (VNS) is a recent metaheuristic, or framework for building heuristics, which exploits systematically the idea of neighborhood change, both in the descent to local minima and in the escape from the valleys which contain them. In this tutorial we first present the ingredients of VNS, i.e., Variable Neighborhood Descent (VND) and Reduced VNS (RVNS) followed by the basic and then the general scheme of VNS itself which contain both of them. Extensions are presented, in particular Skewed VNS (SVNS) which enhances exploration of far away valleys and Variable Neighborhood Decomposition Search (VNDS), a twolevel scheme for solution of large instances of various problems. In each case, we present the scheme, some illustrative examples and questions to be addressed in order to obtain an efficient implementation.
A genetic algorithm using hyperquadtrees for lowdimensional kmeans clustering
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—The kmeans algorithm is widely used for clustering because of its computational efficiency. Given n points in ddimensional space and the number of desired clusters k, kmeans seeks a set of k cluster centers so as to minimize the sum of the squared Euclidean distance between each point an ..."
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Cited by 15 (1 self)
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Abstract—The kmeans algorithm is widely used for clustering because of its computational efficiency. Given n points in ddimensional space and the number of desired clusters k, kmeans seeks a set of k cluster centers so as to minimize the sum of the squared Euclidean distance between each point and its nearest cluster center. However, the algorithm is very sensitive to the initial selection of centers and is likely to converge to partitions that are significantly inferior to the global optimum. We present a genetic algorithm (GA) for evolving centers in the kmeans algorithm that simultaneously identifies good partitions for a range of values around a specified k. The set of centers is represented using a hyperquadtree constructed on the data. This representation is exploited in our GA to generate an initial population of good centers and to support a novel crossover operation that selectively passes good subsets of neighboring centers from parents to offspring by swapping subtrees. Experimental results indicate that our GA finds the global optimum for data sets with known optima and finds good solutions for large simulated data sets. Index Terms—kmeans algorithm, clustering, genetic algorithms, quadtrees, optimal partition, center selection. 1
Fuzzy JMeans and VNS Methods for Clustering Genes from Microarray Data
 Bioinformatics
, 2004
"... Motivation: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression ..."
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Cited by 13 (1 self)
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Motivation: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression patterns. Crisp clustering methods assign each gene to one cluster, thereby omitting information about the multiple roles of genes. Results: Here we present the application of a local search heuristic, Fuzzy JMeans, embedded into the Variable Neighborhood Search metaheuristic for the clustering of microarray gene expression data. We show that for all data sets studied this algorithm outperforms the standard Fuzzy CMeans heuristic. Different methods for the utilization of cluster membership information in determining gene coregulation are presented. The clustering and data analyses were performed on simulated data sets as well as experimental cDNA microarray data for breast cancer and human blood from the Stanford Microarray Database. Availability: The source code of the clustering software (C programming language) is freely available