Algorithm 3.

NNS-HTP

Input: Φ, Y, and S.

Output: X̂ and Λ̂SS.

Initialization: Set R(0) = Y and X̂(0) = 0

Iteration: for j = 1, 2, … until stopping criteria are satisfied

1. Set ${\alpha }^{(j)}=\frac{{\Vert {\mathbf{\Phi }}_{(j-1)}^T{\mathbf{R}}^{(j-1)}\Vert }_F^2}{{\Vert {\mathbf{\Phi }}_{(j-1)}{\mathbf{\Phi }}_{(j-1)}^T{\mathbf{R}}^{(j-1)}\Vert }_F^2}$, where ${\mathbf{\Phi }}_{(j-1)}^T$ is the matrix formed by taking the S columns of Φ corresponding to ${\widehat{\mathrm{\Lambda }}}_{SS}^{(j-1)}$.

2. Set G̃(j) = X̂(j−1) + α(j)ΦT R(j−1).

3. Set ${\widehat{\mathrm{\Lambda }}}_{SS}^{(j)}$ to be the indices of the S rows of [G̃(j)]+ with the largest Frobenius norms.

4. Update X̂(j) according to (11).

5. Update R(j) = Y − ΦX̂(j).