Table 1 Pseudo-code for the K-OPLS model training algorithm. K denotes the original kernel matrix, K_i the kernel matrix deflated by i Y-orthogonal components and Q_i the K_i matrix deflated by A predictive components.

1.

Estimate the predictive Y-weights (C_p) by eigen-vector decomposition of Y^TKY

2.

Project Y onto C_p to achieve the predictive score matrix of Y: U_p ← YC_p

3.

Calculate the predictive score matrix of X: T_p ← KU_p

4.

Repeat for i : 1 to A_o

4.1

Estimate the Y-orthogonal loadings c_o by eigen-vector decomposition of T_p^TQ_iT_p.

4.2.

Calculate the Y-orthogonal score vector: t_o,i ← Q_iT_pc_o

4.3.

Deflate K_i by t_o,i, yielding K_i+1

4.4.

Update the predictive score matrix: T_p ← K_i+1U_p

5.

Predictions of Y: Y_hat ← T* _p (T_p^TT_p)^-1T_p^TU_pC_p^T. For predictions of future samples, T* _p originates from the prediction set.