NIPALS-PLS Algorithm

Here we summarize the steps needed to compute the PLS model 

Slightly different implementations of the above PLS-NIPALS algorithm exist. They mostly differ in the chosen normalization of w, t or p (here Iwl = 1). This is not an important issue, but it may be a cause of confusion when comparing results from different (software) implementations. That the normalization is of no real importance can be seen as follows. Let us say we choose to multiply the weight 

A slight alternative to the above NIPALS algorithm is replacing the iteration loop (line 8-14) by  

As an example we try to model the relation between the sensory data of Table 35.1 and the instmmental measurements of Table 35.4. The PLS analysis results are shown in Table 35.8. The first PLS dimension loads about equally high on 

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PLS-components can be calculated as the eigenvectors of the matrix X yy X or by the NIPALS algorithm. In the standard version of PLS the directions of the PLS components are orthogonal and necessarily the corresponding scores correlate to some extent. As in PCR the number of components considered is essential for a good PLS-based model. Numerous aspects and variations of the NIPALS-PLS algorithm have been discussed but are beyond the scope of this contribution. 

The NIPALS PLS algorithm automatically accounts for the missing values, in principle by iteratively substituting the missing values by predictions from the model. This corresponds to giving the missing data values that have zero residuals and thus have no influence on the model parameters. 

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