Algorithm 1: The calculation algorithm of KPLS [19]
Step 1	Set $i=1$, ${\mathbf{Y}}_1=\mathbf{Y}$, ${\overline{\mathbf{K}}}_1=\overline{\mathbf{K}}$
Step 2	Select the first column of ${\mathbf{Y}}_i$ as ${\mathit{u}}_i$.
Step 3	${\mathbf{t}}_i={\overline{\mathbf{K}}}_i{\mathit{u}}_i$
Step 4	${\mathbf{t}}_i=\frac{{\mathbf{t}}_i}{‖{\mathbf{t}}_i‖}$
Step 5	${\mathbf{c}}_i={\mathbf{Y}}_i^{\mathrm{T}}{\mathbf{t}}_i$, ${\mathbf{u}}_i={\mathbf{Y}}_i{\mathbf{t}}_i$
Step 6	${\mathbf{u}}_i=\frac{{\mathbf{u}}_i}{‖{\mathbf{u}}_i‖}$
Step 7	Repeat step 3 to step 6 until ${\mathbf{t}}_i$ converges.
Step 8	${\overline{\mathbf{K}}}_{i+1}=\left({\mathbf{I}}_N-{\mathbf{t}}_i{\mathbf{t}}_i^{\mathrm{T}}\right){\overline{\mathbf{K}}}_i\left({\mathbf{I}}_N-{\mathbf{t}}_i{\mathbf{t}}_i^{\mathrm{T}}\right)$; ${\mathbf{Y}}_{i+1}=\left({\mathbf{I}}_N-{\mathbf{t}}_i{\mathbf{t}}_i^{\mathrm{T}}\right){\mathbf{Y}}_i$
Step 9	Get parameters $\mathbf{T}=\left[\mathbf{T},{\mathbf{t}}_i\right]$, $\mathbf{U}=\left[\mathbf{U},{\mathbf{u}}_i\right]$
Step 10	Set $i=i+1$ and repeat step 2 to step 9 until $i>r$