. 2022 May 25;16:832276. doi: 10.3389/fnins.2022.832276

Algorithm 2.

DCL

Input:

X_{1} \in ℝ^{p \times n}

X_{2} \in ℝ^{s \times n}

//Input of sMRI and fMRI, respectively.
Output:

{\hat{X}}_{1}

{\hat{X}}_{2}

{\tilde{X}}_{1}, L a m b d a_{1}, U_{1} \leftarrow S-POET (X_{1})

//processed by S-POET method

{\tilde{X}}_{2}, L a m b d a_{2}, U_{2} \leftarrow S-POET (X_{2})

//processed by S-POET method

3: Lambda₁₁ ← Construct diag(Lambda₁)

4: Lambda₂₂ ← Construct diag(Lambda₂)

T h e t a \leftarrow (L a m b d a_{11} @ U_{1} . T @ {\tilde{X}}_{1}) @ ({\tilde{X}}_{2} . T @ U_{2} @ L a m b d a_{22}) / n

6: V_theta, D_theta ← SVD(Theta, full_matrices = True) //Singular Value Decomposition

7: Gamma₁ ← U₁@Lambda₁₁@V_theta

8: Gamma₂ ← U₂@Lambda₂₂@V_theta

9: A_mat ← diag(D_theta) //Diagonal matrix

10: C_base ← Common variables

corr ({\tilde{X}}_{1}, {\tilde{X}}_{2})

11:

{\tilde{C}}_{1} \leftarrow

Common matrix

({\tilde{X}}_{1}, C_{b a s e}, A_{m a t})

12:

{\tilde{C}}_{2} \leftarrow

Common matrix

({\tilde{X}}_{2}, C_{b a s e}, A_{m a t})

13:

{\tilde{D}}_{1} \leftarrow

Distinctive matrix

({\tilde{X}}_{1}, {\tilde{C}}_{1})

14:

{\tilde{D}}_{2} \leftarrow

Distinctive matrix

({\tilde{X}}_{2}, {\tilde{C}}_{2})

15:

{\tilde{X}}_{1} \leftarrow

Combination of common and distinctive matrices

16:

{\tilde{X}}_{2} \leftarrow

Combination of common and distinctive matrices

17: return

{\hat{X}}_{1}

{\hat{X}}_{2}