State of the Art and Development Trend - Computational Intelligence in Time Series Forecasting - page 349

^ `

2

A exp V x x * ,

kj k j kj

where x kj * is the j th element of k th cluster centre v k * and the “and” operator is
implemented by multiplication.
The parameter V is crucial for the fuzzy model to perform well. It's initial
value can be estimated from

log 0.5

e

V

k

0.5 D

min

For each cluster centre we find its closest cluster centre and calculate the distance
D min between these two cluster centres. This formula implies that, in the fuzzy set
around a cluster centre, if there is a data point midway between the cluster and its
closest neighbouring cluster centre then the membership value of this data point
belonging to the fuzzy set should be 0.5. This estimation is further verified and
confirmed with the experimental evidence by Yao et al. (2000).

References

[1] Auflauf J and Biehl (1989) The Adatron: An adaptive perceptron algorithm

Europhysics Letters 10(7):687-692.

[2] Babuška (1996) Fuzzy modelling and identification, Ph.D Thesis, Control Laboratory,

Delft University of Technology, the Netherlands.

[3] Babuška R, Van der Veen PJ, and Kaymak, U (2002) Improved Covariance

Estimation for Gustafson-Kessel Clustering, FUZZ-IEEE 2002, vol. 2: 1081-1085.

[4] Bezdek JC (1974) Cluster validity with fuzzy sets. J. Cybernet.: 58-71.

[5] Bezdek JC, Tsao EC, and Pal N R (1992) Fuzzy Kohonen Clustering Networks. Proc.

of the IEEE Conf. on Fuzzy System: 1035-1043.

[6] Burges CJC (1998) A Tutorial on Support Vector Machines for Pattern Recognition.

Data Mining and Knowledge Discovery. Preprint: Kluwer Academic Publishers,
Boston.

[7] Cao L (2003) Support vector machines experts for time series forecasting,

Neurocomputing, 51:321-339.

[8] Cao L and Tay EHF (2001) Financial Forecasting Using Support Vector Machines.

Neural Computation & Application. 10:184-192.

[9] Chen J, Li Huai, Sun K, and Kim B (2003) How will Bioinformatics impact signal

processing research. IEEE Signal Processing Maga. 20(6): 16-26.

[10] Chen Z, Feng TJ, and Meng QC (1999) The Application of wavelet neural network in

time series prediction and system modelling based on multi-resolution learning.

[11] Chiu SL (1994) Fuzzy model identification based on cluster estimation: J. Intell.

Fuzzy Systems: 2: 267-278.

[12] Cover TM (1965) Geometrical and statistical properties of systems of linear

inequalities with applications in pattern recognition, IEEE Trans. on Electronic
Computers, vol. 14: 326-324.

[13] Cybenko G (1989) Approximation by superposition of a sigmoidal function.

Mathematics of Control, signals and systems 2:303-314.