Robust back propagation algorithm as a chemometric tool to prevent the overfitting to outliers

Abstract The ordinary back propagation algorithm for the artificial network is non-robust. It has been shown in a straightforward way that the BP algorithm can be robustified by introducing some kind of transform on the residual term r p . Using the proposed robust BP algorithm, the problem of overfitting to outlier points can effectively be circumvented. The feasibility of the proposed method has been testified by treating simulated examples and a real chemical data.

[1]  Zheng. Li,et al.  Nonlinear fitting by using a neural net algorithm , 1993 .

[2]  Ramesh C. Jain,et al.  A robust backpropagation learning algorithm for function approximation , 1994, IEEE Trans. Neural Networks.

[3]  Bruce R. Kowalski,et al.  MARS: A tutorial , 1992 .

[4]  Yu-Long Xie,et al.  Maximum sum of binary‐coded residuals (MASBR) regression as a robust procedure for treatment of spectral data , 1995 .

[5]  Bruce R. Kowalski,et al.  Nonlinear calibration using projection pursuit regression: application to an array of ion-selective electrodes , 1988 .

[6]  Guoying Li,et al.  Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo , 1985 .

[7]  N. B. Vogt.  Polynomial Principal Component Regression: An approach to Analysis and Interpretation of Complex Mixture Relationships in Multivariate Environmental Data , 1989 .

[8]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

[9]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[10]  G. Kateman,et al.  Neural networks in analytical chemistry , 1993 .

[11]  Steven D. Brown,et al.  Nonlinear multivariate mapping of chemical data using feed-forward neural networks , 1993 .

[12]  J. Zupan,et al.  Neural networks: A new method for solving chemical problems or just a passing phase? , 1991 .

[13]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[14]  H. J. H. Macfie,et al.  A robust PLS procedure , 1992 .

[15]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[16]  Yu-Long Xie,et al.  Robust Kalman filter as a chemometric method for analytical data processing , 1992 .

[17]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[18]  I. E. Frank.  A nonlinear PLS model , 1990 .

[19]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[20]  Paul J. Gemperline,et al.  Nonlinear multivariate calibration using principal components regression and artificial neural networks , 1991 .

[21]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .

[22]  A. Bos,et al.  Processing of signals from an ion-elective electrode array by a neural network , 1990 .