Title :
Improved covariance estimation for Gustafson-Kessel clustering
Author :
Babuka, R. ; van der Veen, P.J. ; Kaymak, U.
Author_Institution :
Fac. ITS, Delft Univ. of Technol., Netherlands
fDate :
6/24/1905 12:00:00 AM
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
Keywords :
covariance matrices; eigenvalues and eigenfunctions; fuzzy logic; GK algorithm; Gustafson-Kessel clustering; Takagi-Sugeno fuzzy model; covariance matrix; eigenvalue; fuzzy covariance matrix; improved covariance estimation; scaled unity matrix; Clustering algorithms; Control systems; Covariance matrix; Data mining; Eigenvalues and eigenfunctions; Partitioning algorithms; Power generation economics; Shape; Systems engineering and theory; Takagi-Sugeno model;
Conference_Titel :
Fuzzy Systems, 2002. FUZZ-IEEE'02. Proceedings of the 2002 IEEE International Conference on
Conference_Location :
Honolulu, HI
Print_ISBN :
0-7803-7280-8
DOI :
10.1109/FUZZ.2002.1006654