Improved covariance estimation for Gustafson-Kessel clustering

R. Babuska, P.J. Veen, van der, U. Kaymak

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

176 Citations (Scopus)
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This article presents two techniques to improve the calculation of the fuzzy covariance matrix in the Gustafson-Kessel (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 fixing 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 extraction of Takagi-Sugeno fuzzy model from data. It reduces the risk of overfitting when the number of training samples is low in comparison to the number of clusters. This is achieved by adding a scaled unity matrix to the calculated covariance matrix. Numerical examples are presented to demonstrate the benefits of the proposed techniques
Original languageEnglish
Title of host publicationProceedings of the 2002 IEEE international conference on fuzzy systems
Place of PublicationHonolulu
Publication statusPublished - 2002
Event2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002) - Honolulu, HI, United States
Duration: 12 May 200217 May 2002


Conference2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002)
Abbreviated titleFUZZ-IEEE 2002
CountryUnited States
CityHonolulu, HI

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