Algorithm 4.

The RMFFS method.

Input: Data matrix $\mathbf{X}=[{\mathbf{f}}^1,{\mathbf{f}}^2,\dots ,{\mathbf{f}}^d]\in {\mathbb{R}}^{n\times d}$; the regularization parameter α; the number of selected features k.

1: Initialize $\mathbf{W}\in {\mathbb{R}}^{d\times k}$ and $\mathbf{H}\in {\mathbb{R}}^{k\times d}$.

2: while not converged do

3: Fix H and obtain W according to ${\mathbf{\text{W}}}_{\mathit{\text{ij}}}\leftarrow {\mathbf{\text{W}}}_{\mathit{\text{ij}}}\frac{{\left({\mathbf{X}}^T\mathbf{X}{\mathbf{H}}^T+\alpha \mathbf{W}\right)}_{\mathit{ij}}}{{\left({\mathbf{X}}^T\mathbf{X}\mathbf{W}\mathbf{H}{\mathbf{H}}^T+\alpha {\mathbf{1}}_d\mathbf{W}\right)}_{\mathit{ij}}}$.

4: Fix W and obtain H according to ${\mathbf{\text{H}}}_{\mathit{ij}}\leftarrow {\mathbf{\text{H}}}_{\mathit{ij}}\frac{{\left({\mathbf{W}}^T{\mathbf{X}}^T\mathbf{X}\right)}_{\mathit{ij}}}{{\left({\mathbf{W}}^T{\mathbf{X}}^T\mathbf{X}\mathbf{W}\mathbf{H}\right)}_{\mathit{ij}}}$.

5: end while

Output: Sort the values of ‖Wi‖2 in a descending order and put the rows of W in an order according to the order induced by the values of ‖Wi‖2, where i = 1, … , d. Next, from {f1, f2, …, fd}, select k features whose corresponding rows in W are evaluated as the top score rows according to the norm function.