How can I extract the residual array from the Scikit Learn PCA routine?
I'm not super familiar with PLS/NIPALS, but I think you need to construct it yourself. Multiply the scores by the loadings and subtract the resulting matrix from the data to get the residual matrix. See here for a more detailed discussion: https://learnche.org/pid/latent-variable-modelling/projection-to-latent-structures/how-the-pls-model-is-calculated