Table 1.

Alternative optimization of the joint brain decomposition model

1.	Input: Xi, i = 1,2,…,n: functional data of n subjects
	α: group sparsity parameter, β: data locality parameter, K: number of FNs
	R: number of iterations at the population level, L: number of iterations at subject level
2.	Output: Vi and Ui for each subject
3.	Initialize Vi and Ui as described in the Robust initialization section
4.	Alternative updates
	for r = 1,2,…,R
	for i = 1,2,…,n:
	for j = 1,2,…,L: (subscripts for voxels/time points and FNs were omitted for clarity)
	Update Vi as in eqn.8
	Update Ui as in eqn.6
	Update λi as in eqn.7
	end j
	end i
	if $\frac{{\mathit{obj}}_{r-1}-{\mathit{obj}}_r}{{\mathit{obj}}_{r-1}}<\mathit{tol}$; break; end if; (obj calculated as in eqn.5)
	end r