Neural Network Implementation of the PLS Algorithm

The partial least squares algorithm is widely used for multivariate statistical process monitoring among other topics. The popular "bootstrap" algorithm, however, requires repeated iterative calculations of the residual matrix, which makestheoretical analyses difficult and hinders concise interpretations of the results. This paper presents a simplified algorithm based on an optimization objective function. The partial least squares algorithm can then be easily mapped to a linear neural network. A weight updating strategy is provided with a rigorous mathematical proof. The efficiency of the technique is demonstrated through a simulation which demonstrates that the latent structures and regression coefficients can be directly obtained from the original data matrices and the results can be easily interpreted.