Nonlinear iterative partial least squares NIPALS algorithm

The nonlinear iterative partial least-squares (NIPALS) algorithm, also called power method, has been popular especially in the early time of PCA applications in chemistry an extended version is used in PLS regression. The algorithm is efficient if only a few PCA components are required because the components are calculated step-by-step. 

The simplest method for PCA used in analytics is the iterative nonlinear iterative partial least squares (NIPALS) algorithm explained in Example 5.1. More powerful methods are based on matrix diagonalization, such as SVD, or bidiagonalization, such as the partial least squares (PLS) method. 

During the calibration step, the PLS technique assumes that the spectral data set X can be decomposed in the form of Equation 6.16. PLS factors are then computed with the help of iterative numerical procedures, such as the popular nonlinear iterative partial least squares (NIPALS) algorithm, as described in standard texts [46,74,75]. The PLS factors can be regarded as rotations of the PCA factors computed in... 

A straightforward method for PCA is the NIPALS (nonlinear iterative partial least squares) algorithm it is quickly implemented and can be applied to large datasets [58, 79],... 

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