# The HPPRINCOMP Procedure

#### NIPALS

The nonlinear iterative partial least squares (NIPALS) method extracts the principal components successively based on the data matrix . The NIPALS method starts by calculating the loadings, , as , where is the score vector. It then calculates an improved score vector, . The method iteratively computes the improved and until convergence is reached.

This process accounts for how the first principal component is extracted. The second component is extracted in the same way, by replacing with the residual from the first component: .

For large data matrices or matrices that have a high degree of column collinearity, the NIPALS method suffers from loss of orthogonality because of the machine-precision errors that accumulate at each iteration step. In practice, the NIPALS method is used to extract only the first few principal components.