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## Swarm Intelligence Algorithms for Data Clustering

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Venue: | IN SOFT COMPUTING FOR KNOWLEDGE DISCOVERY AND DATA MINING BOOK, PART IV |

Citations: | 26 - 1 self |

### Citations

3702 |
Introduction to Statistical Pattern Recognition, 2nd ed
- Fukunaga
- 1990
(Show Context)
Citation Context ...ychology, archeology, education),280 Ajith Abraham, Swagatam Das, and Sandip Roy and economics (marketing, business) (Evangelou et al., 2001, Lillesand and Keifer, 1994,Rao, 1971,Duda and Hart, 1973,=-=Fukunaga, 1990-=-,Everitt, 1993). From a machine learning perspective, clusters correspond to the hidden patterns in data, the search for clusters is a kind of unsupervised learning, and the resulting system represent... |

3520 | Particle swarm optimization
- Kennedy, Eberhart
- 1995
(Show Context)
Citation Context ...ization problems including the traveling salesman, the quadratic assignment, scheduling, vehicle routing, etc., as well as to routing in telecommunication networks. Particle Swarm Optimization (PSO) (=-=Kennedy and Eberhart, 1995-=-) is another very popular SI algorithm for global optimization over continuous search spaces. Since its advent in 1995, PSO has attracted the attention of several researchers all over the world result... |

3416 |
UCI repository of machine learning databases. http://www.ics. uci.edu/ ∼ mlearn/MLRepository.html
- Blake, Merz
- 1998
(Show Context)
Citation Context ... and Maulik, 2000) and two real world datasets. The real world datasets used are the glass and the Wisconsin breast cancer data set, both of which have been taken from the UCI public data repository (=-=Blake et al., 1998-=-). The glass data were sampled from six different type of glass: building windows float processed (70 objects), building windows non float processed (76 objects), vehicle windows float processed (17 o... |

2968 | Some methods for classification and analysis of multivariate observations
- MacQueen
- 1967
(Show Context)
Citation Context ...e class in this case. In case of fuzzy clustering, a pattern may belong to all the classes with a certain fuzzy membership grade (Jain et al., 1999). The most widely used iterative K-means algorithm (=-=MacQueen, 1967-=-) for partitional clustering aims at minimizing the ICS (Intra-Cluster Spread) which for K cluster centers can be defined as ICS(C1, C2, ..., CK) = K∑ ∑ i=1 Xi∈Ci ‖Xi − mi‖ 2 (10) The K-means (or hard... |

2153 |
Finding Groups in Data: An Introduction to Cluster Analysis
- Kaufman, Rousseeuw
- 1990
(Show Context)
Citation Context ...n assigned to the closest cluster-centre. Centroids are updated by using the mean of the associated patterns. The process is repeated until some stopping criterion is met. In the c-medoids algorithm (=-=Kaufman and Rousseeuw, 1990-=-), on the other hand, each cluster is represented by one of the representative objects in the cluster located near the center. Partitioning around medoids (PAM) (Kaufman and Rousseeuw, 1990) starts fr... |

1699 | A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II - Deb, Pratap, et al. |

1354 |
Swarm intelligence: From natural to artificial systems
- Bonabeau, Dorigo, et al.
- 1999
(Show Context)
Citation Context ...ics for solving the clustering problems. Among other social movements, researchers have simulated the way, ants work collaboratively in the task of grouping dead bodies so, as to keep the nest clean (=-=Bonabeau et al., 1999-=-). It can be observed that, with time the ants tend to cluster all dead bodies in a specific region of the environment, thus forming piles of corpses. Larval sorting and corpse cleaning by ant was fir... |

1238 | The Ant System: Optimization by a colony of cooperating agents
- Dorigo, Maniezzo, et al.
- 1996
(Show Context)
Citation Context ...nning, and are solved by insect colonies without any kind of supervisor or controller. An example of particularly successful research direction in swarm intelligence is Ant Colony Optimization (ACO) (=-=Dorigo et al., 1996-=-, Dorigo and Gambardella, 1997), which focuses on discrete optimization problems, and has been applied successfully to a large number of NP hard discrete optimization problems including the traveling ... |

994 | Ant Colony System: A cooperative learning approach to the traveling salesman problem - Dorigo, Gambardella - 1997 |

812 | The particle swarm-explosion, stability, and convergence in a multidimensional complex space
- Clerc, Kennedy
- 2002
(Show Context)
Citation Context ...improved convergence properties. The Modification of the Classical PSO The canonical PSO has been subjected to empirical and theoretical investigations by several researchers (Eberhart and Shi, 2001, =-=Clerc and Kennedy, 2002-=-). In many occasions, the convergence is premature, especially if the swarm uses a small inertia weight ω or constriction coefficient (Clerc and Kennedy, 2002). As the global best found early in the s... |

773 |
Differential evolution a simple and efficient heuristic for global optimization over continuous spaces
- Storn, Price
- 1997
(Show Context)
Citation Context ...on data of Yeast and Rat Hepatocytes. Paterlini and Krink (Paterlini and Krink, 2006) have compared the performance of Kmeans, GA (Holland, 1975, Goldberg, 1975), PSO and Differential Evolution (DE) (=-=Storn and Price, 1997-=-) for a representative point evaluation approach to partitional clustering. The results show that PSO and DE outperformed the K-means algorithm.296 Ajith Abraham, Swagatam Das, and Sandip Roy Cui et ... |

695 | Efficient and effective clustering method for spatial data mining
- Ng, Han
- 1994
(Show Context)
Citation Context ...tal distance of the resulting clustering. Although PAM works effectively for small data, it does not scale well for large datasets. Clustering large applications based on randomized search (CLARANS) (=-=Ng and Han, 1994-=-), using randomized sampling, is capable of dealing with the associated scalability issue. The fuzzy c-means (FCM) (Bezdek, 1981) seems to be the most popular algorithm in the field of fuzzy clusterin... |

661 |
Pattern Recognition
- Theodoridis, Koutroumbas
- 1999
(Show Context)
Citation Context ...tracking its number of clusters. Finding an optimal number of clusters in a large dataset is usually a challenging task. The problem has been investigated by several researches (Halkidi et al., 2001, =-=Theodoridis and Koutroubas, 1999-=-) but the outcome is still unsatisfactory (Rosenberger and Chehdi, 2000). Lee and Antonsson (Lee and Antonsson, 2000) used an Evolutionary Strategy (ES) (Schwefel, 1995) based method to dynamically cl... |

602 |
Remote sensing and image interpretation
- Lillesand, Kiefer, et al.
- 1994
(Show Context)
Citation Context ... geology, remote sensing), social sciences (sociology, psychology, archeology, education),280 Ajith Abraham, Swagatam Das, and Sandip Roy and economics (marketing, business) (Evangelou et al., 2001, =-=Lillesand and Keifer, 1994-=-,Rao, 1971,Duda and Hart, 1973,Fukunaga, 1990,Everitt, 1993). From a machine learning perspective, clusters correspond to the hidden patterns in data, the search for clusters is a kind of unsupervised... |

581 |
Evolution and Optimum Seeking
- Schwefel
- 1995
(Show Context)
Citation Context ...et al., 2001, Theodoridis and Koutroubas, 1999) but the outcome is still unsatisfactory (Rosenberger and Chehdi, 2000). Lee and Antonsson (Lee and Antonsson, 2000) used an Evolutionary Strategy (ES) (=-=Schwefel, 1995-=-) based method to dynamically cluster a dataset. The proposed ES implemented variable-length individuals to search for both centroids and optimal number of clusters. An approach to classify a dataset ... |

480 | D.: Survey of Clustering Algorithms
- XU, WUNSCH
(Show Context)
Citation Context ...re coming up with new algorithms, on a regular basis, to meet the increasing complexity of vast real-world datasets. A comprehensive review of the state-of-the-art clustering methods can be found in (=-=Xu and Wunsch, 2005-=-) and (Rokach and Maimon, 2005). Data mining is a powerful new technology, which aims at the extraction of hidden predictive information from large databases. Data mining tools predict future trends a... |

319 | A discrete binary version of the particle swarm algorithm - Kennedy, Eberhart - 1997 |

316 |
Unsupervised optimal fuzzy clustering
- Gath, Geva
- 1989
(Show Context)
Citation Context ...ligence Algorithms for Data Clustering 291 uij = ⎡ ⎢ ⎣ c∑ ( ‖Xj − Vi‖ 2 ‖X − Vi‖ 2 ⎤ )1/(m − 1) ⎥ ⎦ k=1 −1 (13) Several modifications of the classical FCM algorithm can be found in (Hall et al., 1999,=-=Gath and Geva, 1989-=-,Bensaid et al., 1996,Clark et al., 1994,Ahmed et al., 2002, Wang et al., 2004). 3.3 Relevance of SI Algorithms in Clustering From the discussion of the previous section, we see that the SI algorithms... |

312 |
A validity measure for fuzzy clustering
- Xie, Beni
- 1991
(Show Context)
Citation Context ...ong the cluster centers (may be their Euclidean distance) gives an indication of cluster separation. In the present work we have based our fitness function on the Xie-Benni index. This index, due to (=-=Xie and Beni, 1991-=-), is given by: c∑ i=1 j=1 n∑ u2 ij ‖Xj − Vi‖ 2 XBm = n × mini̸=j ‖Vi − Vj‖ 2 (21) Using XBm the optimal number of clusters can be obtained by minimizing the index value. The fitness function may thus... |

279 | Particle swarm optimization: developments, applications and resources - Eberhart, Shi - 2001 |

188 | Arti neural networks for feature extraction and multivariate data projection - Mao, Jain - 1995 |

176 | Genetic Algorithms - DE - 1989 |

171 |
Genetic Algorithms and Grouping Problems
- Falkenauer
- 1998
(Show Context)
Citation Context ...orgy, 1965), graph theory (Zahn, 1971), expectation maximization algorithms (Mitchell, 1997), artificial neural networks (Mao and Jain, 1995, Pal et al., 1993, Kohonen, 1995), evolutionary computing (=-=Falkenauer, 1998-=-, Paterlini and Minerva, 2003) and so on. Researchers all over the globe are coming up with new algorithms, on a regular basis, to meet the increasing complexity of vast real-world datasets. A compreh... |

157 | Living in groups - Krause, Ruxton - 2002 |

136 |
A clustering technique for summarizing multivariate data
- Ball, Hall
- 1967
(Show Context)
Citation Context ...t al., 1999). Therefore, many clustering algorithms have widely been used to solve the segmentation problem (e.g., K-means (Tou and Gonzalez, 1974), Fuzzy C-means (Trivedi and Bezdek, 1986), ISODATA (=-=Ball and Hall, 1967-=-), Snob (Wallace and Boulton, 1968) and recently the PSO and DE based clustering techniques (Omran et al., 2005a, Omran et al., 2005b)). Here we illustrate the automatic soft segmentation of a number ... |

127 |
Genes VII
- Lewin
- 2000
(Show Context)
Citation Context ...hrough which the coded information of a gene is converted into structures operating in the cell. It provides the physical evidence that a gene has been ”turned on” or activated for protein synthesis (=-=Lewin, 1995-=-). Proper selection, analysis and interpretation of the gene expression data can lead us to the answers of many important problems in experimental biology. Promising results have been reported in (Xia... |

123 | Pattern classification and scene analysis - RO, PE - 1973 |

120 |
Diversity and Adaptation in Populations of Clustering Ants
- Lumer, Faieta
- 1994
(Show Context)
Citation Context ...based clustering algorithm (Handl et al., 2003). Lumer and Faieta modified the algorithm using a dissimilarity-based evaluation of the local density, in order to make it suitable for data clustering (=-=Lumer and Faieta, 1994-=-). This introduced standard Ant Clustering Algorithm (ACA). It has subsequently been used for numerical data analysis (Lumer and Faieta,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-min... |

112 | A Robust Competitive Clustering Algorithm With Applications in Computer Vision
- Frigui, Krishnapuram
- 1999
(Show Context)
Citation Context ... that the clustering problem is NPhard when the number of clusters exceeds 3. 3.2 The Classical Clustering Algorithms Data clustering is broadly based on two approaches: hierarchical and partitional (=-=Frigui and Krishnapuram, 1999-=-, Leung et al., 2000). Within each of the types, there exists a wealth of subtypes and different algorithms for finding the clusters. In hierarchical clustering, the output is a tree showing a sequenc... |

105 | Data mining in soft computing framework: a survey
- Mitra, SK
(Show Context)
Citation Context ... proactive, knowledge-driven decisions. The process of knowledge discovery from databases necessitates fast and automatic clustering of very large datasets with several attributes of different types (=-=Mitra et al., 2002-=-). This poses a severe challenge before the classical clustering techniques. Recently a family of nature inspired algorithms, known as Swarm Intelligence (SI), has attracted several researchers from t... |

92 |
Swarm Intelligence in Cellular Robotic Systems
- Beni, Wang
- 1989
(Show Context)
Citation Context ...living creatures motivated researchers to undertake the study of today what is known as Swarm Intelligence. Historically, the phrase Swarm Intelligence (SI) was coined by Beny and Wang in late 1980s (=-=Beni and Wang, 1989-=-) in the context of cellular robotics. A group of researchers in different parts of the world started working almost at the same time to study the versatile behavior of different living creatures and ... |

83 | Pattern Recognition with Fuzzy Objective Function Algorithms - JC - 1981 |

55 | Data clustering: A review - AK, MN, et al. - 1999 |

42 |
Genetic clustering for automatic evolution of clusters and application to image classification, Pattern Recognit
- Bandyopadhyay, Maulik
(Show Context)
Citation Context ...where two fitness functions are optimized simultaneously: one gives the optimal number of clusters, whereas the other leads to a proper identification of each cluster’s centroid. Bandopadhyay et al. (=-=Bandyopadhyay and Maulik, 2000-=-) devised a variable string-length genetic algorithm (VGA) to tackle the dynamic clustering problem using a single fitness function. Very recently, Omran et al. came up with an automatic hard clusteri... |

40 | Cluster Analysis - BS, Leese, et al. - 2001 |

40 | Clustering Validity Assessment: Finding the Optimal Partitioning of a Data Set
- Halkidi, Vazirgiannis
- 2001
(Show Context)
Citation Context ...ning the optimum number of classes is to run the algorithm repeatedly with different number of classes as input and then to select the partitioning of the data resulting in the best validity measure (=-=Halkidi and Vazirgiannis, 2001-=-). Ideally, a validity index should take care of the following aspects of the partitioning: 1. Cohesion: Patterns in one cluster should be as similar to each other as possible. The fitness variance of... |

37 | Improved ant-based clustering and sorting in a document retrieval interface
- Handl, Meyer
- 2002
(Show Context)
Citation Context ...,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-mining (Lumer and Faieta, 1995), graph-partitioning (Kuntz and Snyers, 1994, Kuntz and Snyers, 1999, Kuntz et al., 1998) and text-mining (=-=Handl and Meyer, 2002-=-, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, Ramos et al., 2002) proposed a number of modifications to improve the convergence rate and to get optimal number of cl... |

37 | Self-organized stigmergic document maps: Environment as mechanism for context learning - Ramos, Merelo - 2002 |

35 |
Self-organized data and image retrieval as a consequence of inter-dynamic synergistic relationships in artificial ant colonies
- Ramos, Muge, et al.
- 2002
(Show Context)
Citation Context ...rtitioning (Kuntz and Snyers, 1994, Kuntz and Snyers, 1999, Kuntz et al., 1998) and text-mining (Handl and Meyer, 2002, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, =-=Ramos et al., 2002-=-) proposed a number of modifications to improve the convergence rate and to get optimal number of clusters. Monmarche et al. hybridized the Ant-based clustering algorithm with K-means algorithm (Monma... |

30 | Differential evolution and particle swarm optimisation in partitional clustering
- Paterlini, Krink
- 2006
(Show Context)
Citation Context ...et al., 2003) for clustering gene expression data. They got promising results by applying the hybrid SOM-PSO algorithm over the gene expression data of Yeast and Rat Hepatocytes. Paterlini and Krink (=-=Paterlini and Krink, 2006-=-) have compared the performance of Kmeans, GA (Holland, 1975, Goldberg, 1975), PSO and Differential Evolution (DE) (Storn and Price, 1997) for a representative point evaluation approach to partitional... |

30 |
A clustering algorithm using an evolutionary programming-based approach
- Sarkar, Yegnanarayana, et al.
- 1997
(Show Context)
Citation Context ...individuals to search for both centroids and optimal number of clusters. An approach to classify a dataset dynamically using Evolutionary Programming (EP) (Fogel et al., 1966) can be found in Sarkar (=-=Sarkar et al., 1997-=-) where two fitness functions are optimized simultaneously: one gives the optimal number of clusters, whereas the other leads to a proper identification of each cluster’s centroid. Bandopadhyay et al.... |

28 |
Particle swarm optimization method for image clustering
- Omran, Engelbrecht, et al.
- 2005
(Show Context)
Citation Context ...st local optimum from the starting position of the search. PSO-based clustering algorithm was first introduced by Omran et al. in (Omran et al., 2002). The results of Omran et al. (Omran et al., 2002,=-=Omran et al., 2005-=-a) showed that PSO based method outperformed K-means, FCM and a few other state-of-the-art clustering algorithms. In their method, Omran et al. used a quantization error based fitness measure for judg... |

24 |
Emergent colonization and graph partitioning
- Kuntz, Snyers
- 1994
(Show Context)
Citation Context ...hm (ACA). It has subsequently been used for numerical data analysis (Lumer and Faieta,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-mining (Lumer and Faieta, 1995), graph-partitioning (=-=Kuntz and Snyers, 1994-=-, Kuntz and Snyers, 1999, Kuntz et al., 1998) and text-mining (Handl and Meyer, 2002, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, Ramos et al., 2002) proposed a num... |

20 | Differential evolution methods for unsupervised image classification
- Omran, Salman
(Show Context)
Citation Context ...st local optimum from the starting position of the search. PSO-based clustering algorithm was first introduced by Omran et al. in (Omran et al., 2002). The results of Omran et al. (Omran et al., 2002,=-=Omran et al., 2005-=-a) showed that PSO based method outperformed K-means, FCM and a few other state-of-the-art clustering algorithms. In their method, Omran et al. used a quantization error based fitness measure for judg... |

19 |
Unsupervised clustering method with optimal estimation of the number of clusters: application to image segmentation
- Rosenberger, Chehdi
- 2000
(Show Context)
Citation Context ... large dataset is usually a challenging task. The problem has been investigated by several researches (Halkidi et al., 2001, Theodoridis and Koutroubas, 1999) but the outcome is still unsatisfactory (=-=Rosenberger and Chehdi, 2000-=-). Lee and Antonsson (Lee and Antonsson, 2000) used an Evolutionary Strategy (ES) (Schwefel, 1995) based method to dynamically cluster a dataset. The proposed ES implemented variable-length individual... |

18 | A New Data Clustering Algorithm - Zhang, Ramakrishnan, et al. - 1997 |

17 | Artificial intelligence through simulated evolution - LJ, AJ, et al. - 1966 |

17 | Pattern recognition principles - JT, RC |

16 | Discovery of clusters in numeric data by an hybridization of an ant colony with the minimum distance classification, from ant colonies to artificial ants
- Steinberg, Venturini, et al.
- 1998
(Show Context)
Citation Context ... 2002) proposed a number of modifications to improve the convergence rate and to get optimal number of clusters. Monmarche et al. hybridized the Ant-based clustering algorithm with K-means algorithm (=-=Monmarche et al., 1999-=-) and compared it to traditional K-means on various data sets, using the classification error for evaluation purposes. However, the results obtained with this method are not applicable to ordinary ant... |

15 |
Homogenous ants for web document similarity modeling and categorization
- Hoe, Lai, et al.
- 2002
(Show Context)
Citation Context ...agatam Das, and Sandip Roy 1994), data-mining (Lumer and Faieta, 1995), graph-partitioning (Kuntz and Snyers, 1994, Kuntz and Snyers, 1999, Kuntz et al., 1998) and text-mining (Handl and Meyer, 2002, =-=Hoe et al., 2002-=-, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, Ramos et al., 2002) proposed a number of modifications to improve the convergence rate and to get optimal number of clusters. Monmarche ... |

15 |
Exploratory Database Analysis via Self-Organization”, Unpublished Manuscript
- Lumer, Faieta
- 1995
(Show Context)
Citation Context ...is introduced standard Ant Clustering Algorithm (ACA). It has subsequently been used for numerical data analysis (Lumer and Faieta,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-mining (=-=Lumer and Faieta, 1995-=-), graph-partitioning (Kuntz and Snyers, 1994, Kuntz and Snyers, 1999, Kuntz et al., 1998) and text-mining (Handl and Meyer, 2002, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Me... |

14 | Potok ―Document Clustering Analysis Based on Hybrid PSO+Kmeans Algorithm - Cui, Thomas |

14 | Ant-based clustering: a comparative study of its relative performance with respect to k-means, average link and 1D-SOM
- Handl, Knowles, et al.
- 2003
(Show Context)
Citation Context ...rval sorting and corpse cleaning by ant was first modeled by Deneubourg et al. for accomplishing certain tasks in robotics (Deneubourg et al., 1991). This inspired the Ant-based clustering algorithm (=-=Handl et al., 2003-=-). Lumer and Faieta modified the algorithm using a dissimilarity-based evaluation of the local density, in order to make it suitable for data clustering (Lumer and Faieta, 1994). This introduced stand... |

14 |
New results on an antbased heuristic for highlighting the organization of large graphs
- Kuntz, Snyers
- 1451
(Show Context)
Citation Context ...ently been used for numerical data analysis (Lumer and Faieta,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-mining (Lumer and Faieta, 1995), graph-partitioning (Kuntz and Snyers, 1994, =-=Kuntz and Snyers, 1999-=-, Kuntz et al., 1998) and text-mining (Handl and Meyer, 2002, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, Ramos et al., 2002) proposed a number of modifications to ... |

14 |
A stochastic heuristic for visualising graph clusters in a bidimensional space prior to partitioning
- Kuntz, Snyers, et al.
- 1999
(Show Context)
Citation Context ...rical data analysis (Lumer and Faieta,292 Ajith Abraham, Swagatam Das, and Sandip Roy 1994), data-mining (Lumer and Faieta, 1995), graph-partitioning (Kuntz and Snyers, 1994, Kuntz and Snyers, 1999, =-=Kuntz et al., 1998-=-) and text-mining (Handl and Meyer, 2002, Hoe et al., 2002, Ramos and Merelo, 2002). Many authors (Handl and Meyer, 2002, Ramos et al., 2002) proposed a number of modifications to improve the converge... |

12 | The sensory basis of fish schools: Relative roles of lateral line and vision - BL, TJ - 1980 |

10 |
Clustering by Space-Space Filtering
- Leung, Zhang, et al.
- 2000
(Show Context)
Citation Context ... NPhard when the number of clusters exceeds 3. 3.2 The Classical Clustering Algorithms Data clustering is broadly based on two approaches: hierarchical and partitional (Frigui and Krishnapuram, 1999, =-=Leung et al., 2000-=-). Within each of the types, there exists a wealth of subtypes and different algorithms for finding the clusters. In hierarchical clustering, the output is a tree showing a sequence of clustering with... |

9 | Cluster analysis of multivariate data: efficiency vs interpretability of classifications - EW - 1965 |

9 | Maulik U: A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification. Fuzzy Sets and Systems - MK, Bandyopadhyay - 2005 |

9 |
Evolutionary approaches for cluster analysis
- Paterlini, Minerva
(Show Context)
Citation Context ... theory (Zahn, 1971), expectation maximization algorithms (Mitchell, 1997), artificial neural networks (Mao and Jain, 1995, Pal et al., 1993, Kohonen, 1995), evolutionary computing (Falkenauer, 1998, =-=Paterlini and Minerva, 2003-=-) and so on. Researchers all over the globe are coming up with new algorithms, on a regular basis, to meet the increasing complexity of vast real-world datasets. A comprehensive review of the state-of... |

9 | An Information Measure for Classification - CS, DM - 1968 |

7 |
Clustering methods,” in Data mining and knowledge discovery handbook
- Rokach, Maimon
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(Show Context)
Citation Context ...rithms, on a regular basis, to meet the increasing complexity of vast real-world datasets. A comprehensive review of the state-of-the-art clustering methods can be found in (Xu and Wunsch, 2005) and (=-=Rokach and Maimon, 2005-=-). Data mining is a powerful new technology, which aims at the extraction of hidden predictive information from large databases. Data mining tools predict future trends and behaviors, allowing busines... |

6 | The three-dimensional structure of airborne bird flocks. Behavioral Ecology and Sociobiology - PF, LM - 1978 |

6 | Cluster analysis and mathematical programming - MR - 1971 |

6 | Ant colony clustering and feature extraction for anomaly intrusion detection - Tsang, Kwong - 2006 |

5 | Antonsson “Self-adapting vertices for mask-layout synthesis - Lee, K |

5 | Graph-theoretical methods for detecting and describing gestalt clusters - CT - 1971 |

4 | Alsultan K: A Simulated Annealing Algorithm for the Clustering Problem. Pattern Recognition - SZ - 1991 |

4 | Eberhart RC, Miled ZB and Oppelt RJ (2003) Gene Clustering Using Self-Organizing Maps and Particle Swarm Optimization - Xiao, ER |

3 | Swarms, phase transitions, and collective intelligence - MM - 1994 |

2 | Bezdek JC.and Clarke LP - AM, LO - 1996 |

2 |
On the complexity of clustering problems. Beckmenn M and Kunzi HP(Eds.), Optimization and
- Brucker
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(Show Context)
Citation Context ...widely used distance measure is the Euclidean distance, which between any two d-dimensional patterns Xi and Xj is given by, d(Xi, Xj) = √ d ∑ (Xi,p − Xj,p) 2 = ‖Xi − Xj‖ (9) p=1 It has been shown in (=-=Brucker, 1978-=-) that the clustering problem is NPhard when the number of clusters exceeds 3. 3.2 The Classical Clustering Algorithms Data clustering is broadly based on two approaches: hierarchical and partitional ... |

2 | Fuzzy Ants as a Clustering Concept - PM, LO - 2003 |

2 | A and Engelbrecht AP, (2002), Image Classification using Particle Swarm Optimization - Omran, Salman |

2 | A and Engelbrecht AP, (2005), Dynamic Clustering using Particle Swarm Optimization with Application in Unsupervised Image Classification - Omran, Salman |

2 | Merwe DW and Engelbrecht AP, (2003), Data clustering using particle swarm optimization - der |

1 | Farag AA and Moriarty TA, Modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data - MN, SM, et al. - 2002 |

1 | Guinot C and Venturini G, Data and text mining with hierarchical clustering ants - Azzag |

1 | Velthuizen RP and Silbiger MS , MRI segmentation using fuzzy clustering techniques - MC, LO, et al. - 1994 |

1 | Detrain C and Chetien L , The dynamics of collective sorting: Robot-like ants and ant-like robots - JL, Goss, et al. - 1991 |

1 | A and Monica C, Swarm Intelligence - Grosan, Abraham |

1 | Generalized clustering networks and Kohonen’s self-organizing scheme - NR, JC, et al. - 1993 |

1 | Low-level segmentation of aerial images with fuzzy clustering - MM, JC - 1986 |