Local modelling with radial basis function networks

Chemometrics and Intelligent Laboratory Systems

Volumn 50, Issue 2, 2000, Pages 179-198

  Walczak, B ^a   Massart, D L ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Calibration; Classification; Neuro fuzzy systems; Radial basis function network

Indexed keywords

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; CALIBRATION; DISEASE CLASSIFICATION; HUMAN; INFORMATION PROCESSING; LABORATORY TEST; MODEL; PRIORITY JOURNAL; TECHNIQUE; THEORY; THYROID DISEASE; THYROID HORMONE BLOOD LEVEL;

EID: 0034642825     PISSN: 01697439     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0169-7439(99)00056-8     Document Type: Article

References (36)

1. J. Zupan, J. Gasteiger, Neural Networks for Chemists, VCH Publishers, New York, 1993.
2. Smits J.R., Breedveld L.W., Derksen M.W.J., Kateman G. Pattern classification with artificial neural networks: Classification of algae, based upon flow cytometer data. Anal. Chim. Acta. 258:1992;11-25.
3. Lewis I.R., Daniel N.W. Jr., Chaffin N.C., Griffiths P.R. Raman spectrometry and neural networks for the classification of wood types-1. Spectrochim. Acta. 50A:1994;1943-1958.
4. Borggaard C., Thodberg H.H. Optimal minimal neural interpretation of spectra. Anal. Chem. 64:1992;545.
5. Wu W., Walczak B., Massart D.L., Heuerding S., Erni F., Last I.R., Prebble K.A. Artificial neural networks in classification of NIR spectral data: design of the training set. Chemom. Intell. Lab. Syst. 33:1996;35-46.
6. Cense J.M., Diawara B., Legendre J.J., Roullet G. Neural networks prediction of partition coefficients. Chemom. Intell. Lab. Syst. 23:1994;301-308.
7. Naes T., Kvaal K., Isaksson T., Miller C. Artificial neural networks in multivariate calibration. J. Near Infrared Spectrosc. 1:1993;1-11.
8. Bos A., Bos M., van der Linden W.E. Artificial neural networks as a multivariate calibration tool: modeling the Fe-Cr-Ni system in X-ray fluorescence spectroscopy. Anal. Chim. Acta. 277:1993;289-295.
9. Watanabe K., Matsuura I., Abe M., Kubota M., Himmelblau D.M. Incipient fault diagnosis of chemical processes via artificial neural networks. AIChE J. 35:1989;1803-1812.
10. Gemperline P.J., Long J.R., Gregoriou V.G. Nonlinear multivariate calibration using principal components regression and artificial neural networks. Anal. Chem. 63:1991;2313-2323.
11. M.J.D. Powell, Radial basis functions for multivariable interpolation: A review, in: J.C. Mason, M.G. Cox (Eds.), Algorithms for Approximation, Clarendon Press, Oxford 1987, pp. 143-167.
12. Micchelli C.A. Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximations. 2:1986;11-22.
13. Broomhead D.S., Lowe D. Multivariable functional interpolation and adaptive networks. Complex Systems. 2:1988;321-355.
14. Moody T.J., Darken C.J. Fast learning in networks of locally tuned processing units. Neural Computing. 1:1989;151-160.
15. Girosi F., Pogio T. Networks and the best approximation property. Biological Cybernetics. 63:1990;169-176.
16. Girosi F., Jones M., Poggio T. Regularization theory and neural network architecture. Neural Computation. 7:1995;219-270.
17. J. Mac Queen, Some methods for classification and analysis of multivariate observations, in: L.M. leCam, J. Neyman (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, Berkeley, University of California Press, 1967.
18. Tarassenko L., Roberts S. Supervised and unsupervised learning in radial basis function classifiers. IEE Proc. Vis. Image Signal Process. 141:1994;210-216.
19. Y.H. Cheng, G. Jain, Learning algorithm for radial basis function network with the capability of adding and pruning neurons, Proc. ICNN, Orlando 1994, 797-801.
20. Platt J. A resource-allocating network for function interpretation. Neural Computation. 3:1991;213-225.
21. Kaminski W., Strumillo P. Kernel orthonormalization in radial basis function neural networks. IEEE Trans. Neural Networks. 8:1997;1177-1183.
22. S. Osowski, Neural Networks (in Polish) Wyd. NT, Warszawa, 1996
23. Chen S., Cowan C.F., Grant P.M. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans. Neural Networks. 2:1991;302-309.
24. Walczak B., Massart D.L. The radial basis functions - partial least squares approach as a flexible non-linear regression techniques. Anal. Chim. Acta. 331:1996;177-185.
25. Walczak B., Massart D.L. Application of radial basis functions - partial least squares to non-linear pattern recognition problems: Diagnosis of process faults. Anal. Chim. Acta. 331:1996;187-193.
26. D.L. Massart, B.G.M. Vandeginste, L.M.C. Buydens, S. de Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbbok of Chemometrics and Qualimetrics: Part A, Elsevier, Amsterdam, 1997.
27. S. de Jong, A comparison of algorithms for partial least squares regression, Chemom. Intell. Lab. Syst., to be submitted.
28. De Jong S. SIMPLS: an alternative approach to partial least squares regression. Chemom. Intell. Lab. Syst. 18:1993;251-263.
29. Kennard R.W., Stone L.A. Computer aided design of experiments. Technometrics. 11:1969;137-148.
30. D. Coomans, Patroonherkenning in de medische diagnose aan de hand vanklinische laboratoriumonderzoeken, VUB, Brussels, 1982.
31. Stokbro K., Umberger D.K., Hertz J.A. Exploiting neurons with localized receptive fields to learn chaos. Complex Systems. 4:1990;603-622.
32. Bakshi B.R., Stephanopoulos G. Wave-net: a multiresolution, hierarchical neural network with localized learning. AIChE J. 39:1993;57-81.
33. C.M. Bishop, Neural Networks for Pattern Recognition, Clarendon Press, Oxford, 1995.
34. J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and soft computing, Prentice-Hall, Englewood Cliffs, NJ, 1997.
35. Walczak B., Wegscheider W. Calibration of non-linear anlytical systems by a neuro fuzzy approach. Chemom. Intell. Lab. Syst. 22:1994;199-207.
36. Walczak B., Bauer-Wolf E., Wegscheider W. A neuro-fuzzy system for X-ray spectra interpretation. Microchim. Acta. 113:1994;153-169.