Improved covariance estimation for Gustafson-Kessel clustering

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

doi:10.1109/FUZZ.2002.1006654

Improved covariance estimation for Gustafson-Kessel clustering

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

Information Systems IE&IS

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

212 Citations (Scopus)

735 Downloads (Pure)

Abstract

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 language	English
Title of host publication	Proceedings of the 2002 IEEE international conference on fuzzy systems
Place of Publication	Honolulu
Pages	1081-1085
DOIs	https://doi.org/10.1109/FUZZ.2002.1006654
Publication status	Published - 2002
Event	2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002) - Honolulu, HI, United States Duration: 12 May 2002 → 17 May 2002

Conference

Conference	2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002)
Abbreviated title	FUZZ-IEEE 2002
Country/Territory	United States
City	Honolulu, HI
Period	12/05/02 → 17/05/02

Access to Document

10.1109/FUZZ.2002.1006654

Metis256338Final published version, 414 KB

Cite this

@inproceedings{52d2828c581745af952fba6d1da163b3,

title = "Improved covariance estimation for Gustafson-Kessel clustering",

abstract = "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",

author = "R. Babuska and {Veen, van der}, P.J. and U. Kaymak",

year = "2002",

doi = "10.1109/FUZZ.2002.1006654",

language = "English",

isbn = "0-7803-7280-8",

pages = "1081--1085",

booktitle = "Proceedings of the 2002 IEEE international conference on fuzzy systems",

note = "2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002), FUZZ-IEEE 2002 ; Conference date: 12-05-2002 Through 17-05-2002",

}

Babuska, R, Veen, van der, PJ & Kaymak, U 2002, Improved covariance estimation for Gustafson-Kessel clustering. in Proceedings of the 2002 IEEE international conference on fuzzy systems. Honolulu, pp. 1081-1085, 2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002), Honolulu, HI, Hawaii, United States, 12/05/02. https://doi.org/10.1109/FUZZ.2002.1006654

TY - GEN

T1 - Improved covariance estimation for Gustafson-Kessel clustering

AU - Babuska, R.

AU - Veen, van der, P.J.

AU - Kaymak, U.

PY - 2002

Y1 - 2002

N2 - 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

AB - 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

U2 - 10.1109/FUZZ.2002.1006654

DO - 10.1109/FUZZ.2002.1006654

M3 - Conference contribution

SN - 0-7803-7280-8

SP - 1081

EP - 1085

BT - Proceedings of the 2002 IEEE international conference on fuzzy systems

CY - Honolulu

T2 - 2002 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2002)

Y2 - 12 May 2002 through 17 May 2002

ER -

Improved covariance estimation for Gustafson-Kessel clustering

Abstract

Conference

Access to Document

Fingerprint

Cite this