Algorithm 1.

Algorithm to solve problem (11).

Input:

SNP matrix X ∈ ℝd×n, longitudinal phenotype matrix Y = [Y1 Y2 … YT] where ${Y_t|}_{t=1}^T\in {ℝ}^{n\times c}$, parameter δ1 = 10−12 and δ2 = 10−12, number of groups g.

Output:

Weight matrix W = [W1 W2 … WT] where ${W_t|}_{t=1}^T\in {ℝ}^{d\times c}$ and g different group matrices ${Q_i|}_{i=1}^g\in {ℝ}^{\mathit{\text{cT}}\times \mathit{\text{cT}}}$ which groups the tasks into exactly g subspaces.

Initialize W by the optimal solution to the ridge regression problem: $\underset{W}{\text{min}}{\Vert W^{T}X-Y\Vert }_F^2+{\Vert W\Vert }_F^2$

Initialize Q matrices randomly

while not converge do

1. Update D according to the definition in Eq. (12).

2. Update Q according to the solution in Eq. (14)

3. Update B according to the definition in Eq. (13).

4. Update W, where the solution to the k-th column of W is displayed in Eq. (15).

end while