Algorithm 1 NIPALS.

1: Set K. 2: ${\mathit{X}}_0=\mathit{X}-\overline{\mathit{X}}$. 3: ${\mathit{y}}_0=\mathit{y}-\overline{\mathit{y}}$. 4: for$k=1$ to K do 5:  Derive the eigenvector ${\mathit{w}}_k$ which corresponds to the maximum eigenvalue of the following eigenvalue problem: ${\mathit{X}}_{k-1}^T{\mathit{y}}_{k-1}^T{\mathit{y}}_{k-1}{\mathit{X}}_{k-1}{\mathit{w}}_k=\lambda {\mathit{w}}_k$. 6:  ${\mathit{t}}_k=X_{k-1}{\mathit{w}}_k$. 7:  ${\mathit{p}}_k={\mathit{X}}_{k-1}^T{\mathit{t}}_k/{\mathit{t}}_k^T{\mathit{t}}_k$. 8:  $b_k={\mathit{y}}_{k-1}^T{\mathit{t}}_k/{\mathit{t}}_k^T{\mathit{t}}_k$. 9:  if $k=K$ then 10:   Output $\mathit{P}=[{\mathit{p}}_1,\cdots ,{\mathit{p}}_K]$ and $\mathit{b}={[b_1,\cdots b_K]}^T$. 11:  end if 12: end for