Robust partial least-squares regression: a modular neural network approach

We have developed a robust Partial Least-Squares Regression (PLSR) neural network approach to statistical calibration model development. Generalized neural network learning rules derived from a weighted statistical representation error criterion that grows less than quadratically are presented. This optimization criterion allows for higher-order statistics associated with the inputs to be taken into account and also serves to robustify the results when the empirical data contains impulsive and colored noise and outliers. The learning rules presented are considered generalized because they can be used to implement several specialized cases including: robust PLSR, linear PLSR, weighted least-squares, and variance scaling. The same learning rules also implement steepest descent or Newton's method. Newton's method can be used to formulate an adaptive learning rate for training the network.