Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with ApplicationsRecently many researchers are working on cluster analysis as a main tool for exploratory data analysis and data mining. A notable feature is that specialists in di?erent ?elds of sciences are considering the tool of data clustering to be useful. A major reason is that clustering algorithms and software are ?exible in thesensethatdi?erentmathematicalframeworksareemployedinthealgorithms and a user can select a suitable method according to his application. Moreover clusteringalgorithmshavedi?erentoutputsrangingfromtheolddendrogramsof agglomerativeclustering to more recent self-organizingmaps. Thus, a researcher or user can choose an appropriate output suited to his purpose,which is another ?exibility of the methods of clustering. An old and still most popular method is the K-means which use K cluster centers. A group of data is gathered around a cluster center and thus forms a cluster. The main subject of this book is the fuzzy c-means proposed by Dunn and Bezdek and their variations including recent studies. A main reasonwhy we concentrate on fuzzy c-means is that most methodology and application studies infuzzy clusteringusefuzzy c-means,andfuzzy c-meansshouldbe consideredto beamajortechniqueofclusteringingeneral,regardlesswhetheroneisinterested in fuzzy methods or not. Moreover recent advances in clustering techniques are rapid and we requirea new textbook that includes recent algorithms.We should also note that several books have recently been published but the contents do not include some methods studied herein. |
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... Absolute Deviation 4.4.1 Termination of Algorithm Based on Least Absolute Deviation 90 91 4.4.2 An Illustrative Example 5 Miscellanea .. 5.1 More on Similarity and Dissimilarity Measures 5.2 Other Methods of Fuzzy Clustering 5.2.1 ...
... Absolute Deviation 4.4.1 Termination of Algorithm Based on Least Absolute Deviation 90 91 4.4.2 An Illustrative Example 5 Miscellanea .. 5.1 More on Similarity and Dissimilarity Measures 5.2 Other Methods of Fuzzy Clustering 5.2.1 ...
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Contents
Introduction | 1 |
BasicMethods for cMeans Clustering | 9 |
Variations and Generalizations I | 43 |
Variations and Generalizations II | 67 |
Miscellanea | 99 |
Application to Classifier Design | 118 |
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Common terms and phrases
agglomerative arg max arg min arg min J(Ū c-means clustering Calculate classification function cluster centers clustering algorithm component analysis consider constraint convergence covariance matrix crisp c-means D(Xk data points data set defined denote derived dimensional dissimilarity distance EM algorithm entropy entropy-based method estimate Euclidean Euclidean distance external criteria FCM classifier FCMAS FCRM FCV algorithm FCV clustering Find optimal fuzzy c-means fuzzy clustering Gaussian golden section search IEEE initial values iteration k-NN kernelized least absolute deviation least squares linear fuzzy clustering log Uki Mahalanobis distance measure membership method of fuzzy minimization missing values Miyamoto Note number of clusters objective function optimal solution parameters partition possibilistic clustering principal component problem prototype regression models robust samples support vector machines technique Uki)m updating variables W₁ Wdet ΣΣ