2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proc
DOI: 10.1109/fuzz.2002.1006654
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Improved covariance estimation for Gustafson-Kessel clustering

Abstract: -This article presents two techniques to improve the calculation of the fuzzy covariance matrix in the GustafsonKessel (GK) clustering algorithm. The first one overcomes problems that occur in the standard GK clustering when the number of data samples is small or when the data within a cluster are linearly correlated. The improvement is achieved by k i n g the ratio between the maximal and minimal eigenvalue of the covariance matrix. The second technique is useful when the GK algorithm is employed in the extra… Show more

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Cited by 104 publications
(106 citation statements)
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“…Improved covariance estimation for Gustafson-Kessel algorithm has been introduced in [20]. The objective function of GK algorithm is described by:…”
Section: Gustafson-kessel Clustering Approach (Gk)mentioning
confidence: 99%
“…Improved covariance estimation for Gustafson-Kessel algorithm has been introduced in [20]. The objective function of GK algorithm is described by:…”
Section: Gustafson-kessel Clustering Approach (Gk)mentioning
confidence: 99%
“…where i A is the norm inducing matrix, which allows the distance norm to adapt to the local topological structure of the data (see (Babuska et al, 2002)). The GK algorithm iteratively optimizes the following objective function to derive ij and i A adapts the local topological structure of the cluster shape as follows:…”
Section: Appendix a The Gustafson-kessel (Gk) Algorithmmentioning
confidence: 99%
“…where i A is the norm inducing matrix that allows the distance norm to adapt to the local topological structure of the data [12], A is used to adapt to the local topological structure of the data:…”
Section: Shape-based Clustering Algorithmsmentioning
confidence: 99%
“…The GK algorithm is characterised by adapting automatically the local data distance metric to the shape of the cluster using a covariance matrix [7], [12], which is based on the iterative optimization of the following objective function:…”
Section: Shape-based Clustering Algorithmsmentioning
confidence: 99%