A multiblock partial least squares algorithm for investigating complex chemical systems

Abstract The details of a general multiblock partial least squares (PLS) algorithm based on one originally presented by Wold et al. have been developed and are completely presented. The algorithm can handle most types of relationships between the blocks and constitutes a significant advancement in the modeling of complex chemical systems. The algorithm has been programmed in FORTRAN and has been tested on two simulated multiblock problems, a three‐block and a five‐block problem. The algorithm combines the score vectors for all blocks predicting a particular block into a new block. This new block is used to predict the predicted block in a manner analogous to the two‐block PLS. In a similar manner if one block predicts more than one other block, the score vectors of all predicted blocks are combined to form a new block, which is then predicted by the predictor block as in the two‐block PLS. Blocks that both predict and are predicted are treated in such a way that both of these roles can be taken into account when calculating interblock relationships. The results of numerical simulations indicate that the computer program is operating properly and that the multiblock PLS produces meaningful and consistent results.