A Non-iterative Partial Least Squares Algorithm for Supervised Learning with Collinear Data

Partial least squares (PLS) has gained popularity in many domains such as industrial internet of things, bio-informatics, and econometrics due to its ability to deal with limited data, collinearity, and relevance to supervised machine learning. PLS has also been applied to system identification and subspace identification where the model is high-order, high-dimension, or collinear due to the lack of rich excitation. How-ever, all PLS algorithms to date are iterative in calculating the sequence of latent variables, unlike other related methods such as principal component regression. The iterative PLS estimation has made it difficult to perform statistical analysis. In this paper, we propose a novel non-iterative PLS algorithm based on the Krylov sequence used in PLS algorithms. Only a singular value decomposition is needed to obtain an equivalent PLS model for multiple PLS latent factors. The non-iterative PLS algorithm extracts the same latent space as the conventional PLS, which is demonstrated with a couple of industrial application cases.