The Radial Basis Functions - Partial Least Squares approach as a flexible non-linear regression technique

Analytica Chimica Acta

Volumn 331, Issue 3, 1996, Pages 177-185

  Walczak, B ^a   Massart, D L ^b  

^a UNIVERSITY OF SILESIA   (Poland)

^b PHARMACEUTICAL INSTITUTE   (Belgium)

Author keywords

chemometrics; non linear regression; Radial Basis Functions Networks (RBFN); Spline PLS

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; CHEMOMETRICS; PRIORITY JOURNAL; REGRESSION ANALYSIS; STATISTICS; THEORY;

EID: 0030607269     PISSN: 00032670     EISSN: None     Source Type: Journal    
DOI: 10.1016/0003-2670(96)00202-4     Document Type: Article

References (28)

1. [1] I.E. Frank, Modern non-linear regression methods: a tutorial, Chemometrics and Intelligent Laboratory Systems, 27 (1995) 1-9.
2. [2] B.J. Wythoff, Backpropagation neural networks: a tutorial, Chemometrics and Intelligent Laboratory Systems, 18 (1993) 115-155.
3. [3] J. Zupan and J. Gasteiger, Neural networks: a new method for solving chemical problems or just a passing phase?, Anal. Chim. Acta, 248 (1991) 1-30.
4. [4] J. Zupan and J. Gasteiger, Neural Networks for Chemists: an Introduction, VCH, Weinheim, 1993.
5. [5] J.R.M. Smits, W.J. Melssen, L.M.C. Buydens and G. Kateman, Using artificial neural networks for solving chemical problems, Part I. Multilayer feed-forward networks, Chemometrics and Intelligent Laboratory Systems, 22 (1994) 165-189.
6. [6] G. Kateman, Neural networks in analytical chemistry, Chemometrics and Intelligent Laboratory Systems, 19 (1993) 135-142.
7. [7] E.P.P.A. Derks, M.S. Sanchez Pastor and L.M.C. Buydens, Robustness analysis of radial base function and multi-layered feed-forward neural networks models, Chemometrics and Intelligent Laboratory Systems, 28 (1995) 49-60.
8. [8] D.S. Broomhead and D. Lowe, Multivariable functional interpolation and adaptive networks, Complex Systems, 2 (1988) 312-355.
9. [9] J. Moody and C.J. Darken, Fast learning in networks of locally-tuned processing units, Neural Computation, 1 (1989) 151-160.
10. [10] S. Renals and R. Rohwer, Phoneme Classification Experiments Using Radial Basis Functions, Proc. Int. Joint Conf. Neural Networks, Washington, DC, June 1989, p. 461-467.
11. [11] S.C. Yao and E. Zafiriou, Control system sensor failure detection via networks of localized receptive fields, Amer. Control Conf., San Diego, CA, May 1990.
12. [12] P.A. Jokinen, A non-linear network model for continuous learning, Neurocomputing, 3 (1991) 157-176.
13. [13] L. Xu, A. Krzyzak and A. Yuille, On radial basis function nets and kernel regression: Statistical consistency, convergence rates, and receptive field size, Neural Networks, 7 (1994) 60-628.
14. [14] J.H. Holland, Adaptation in Natural and Artificial Systems, The University of Michigan Press, Ann Arbor, 1975.
15. [15] D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, New York, 1989.
16. [16] C.B. Lucasius and G. Kateman, Understanding and using genetic algorithms, Part 1. Concepts, properties and context, Chemometrics and Intelligent Laboratory Systems, 19 (1993) 1-33.
17. [17] C.B. Lucasius and G. Kateman, Understanding and using genetic algorithms, Part 2. Representation, configuration and hybridization, Chemometrics and Intelligent Laboratory Systems, 25 (1994) 99-145.
18. [18] S. Chen, C.F.N. Cowan and P.M. Grant, Orthogonal least squares learning algorithm for radial basis function networks, IEEE Transactions on Neural Networks, 2 (1991) 302-309.
19. [19] V.D. Sanchez A., On the number and the distribution of RBF centers, Neurocomputing, 7 (1995) 17-202.
20. [20] K.G. Joreskog and H. Wold (Eds.) Systems under indirect observation, Vol.I and II, North Holland Publishing Co, Amsterdam, 1982.
21. [21] H. Martens and T. Neas, Multivariate calibration, Wiley, Chichester, 1989.
22. [22] The MathWorks, Inc., Version 4.0, 1984.
23. [23] M. Stone, Cross-validation choice and assessment of statistical prediction, J. Roy. Stat. Soc., B (1974) 111-133.
24. [24] K. Stokbro, D.K, Umberger and J.A. Hertz, Exploiting neurons with localized receptive fields to learn chaos, Complex Systems, 4 (1990) 603-622.
25. [25] B.R. Bakshi and G. Stephanopoulos, Wave-net: a multiresolution, hierarchical neural network with localized learning, AIChE Journal, 39 (1993) 57-81.
26. [26] A.S. Lapedes and R. Farber, Non-linear signal processing using neural networks: Prediction and system modeling, Technical Report, Los Alamos National Laboratory, Los Alamos, New Mexico, 1987.
27. [27] B.E. Ydstie, Forecasting and control using adaptive connectionist networks, Comp. Chem. Eng., 14 (1990) 583.
28. [28] F. Lindgren, P. Geladi, S. Rannar and S. Void, Interactive variable selection (IVS) for PLS. Part 1: Theory and algorithms, J. Chemometrics, 8 (1994) 349-363.