Algorithm 1 DRFS

Input: Data matrix $\mathbf{X}$, label matrix $\mathbf{Y}$, $\alpha , \beta$. Initialize $\mu =1, \rho =1.1, {\mu }_{max}={10}^8$. Output: Feature weight matrix $\mathbf{W}$.   1:Compute feature similarity matrices ${\mathbf{M}}^{(1)}, \dots , {\mathbf{M}}^{(r)}$, $\mathbf{M}$   2:while not converaged do   3:   Update $\mathbf{W}$ by $W_{ij}\leftarrow W_{ij}{\displaystyle \frac{{\left({({\mathbf{X}}^T\mathbf{X}+\mu \mathbf{I}+\lambda \mathbf{D})}^{-}\mathbf{W}+{({\mathbf{X}}^T\mathbf{Y}-\mu \mathbf{Z}+\mathrm{\Lambda })}^{+}\right)}_{ij}}{{\left({({\mathbf{X}}^T\mathbf{X}+\mu \mathbf{I}+\lambda \mathbf{D})}^{+}\mathbf{W}+{({\mathbf{X}}^T\mathbf{Y}-\mu \mathbf{Z}+\mathrm{\Lambda })}^{-}\right)}_{ij}}}$;   4:   Compute diagonal matrix $\mathbf{D}$ as $D_{ii}=1/2{\parallel {\mathbf{W}}^i\parallel }_2$;   5:   for $l=1$to r do   6:       Update ${\mathbf{z}}_l$ by ${\mathbf{z}}_l={\left({\displaystyle \frac{1}{r}}{\mathbf{L}}_{{\mathbf{M}}^{(l)}}+\mu \mathbf{I}\right)}^{-1}(\mu {\mathbf{w}}_l+{\mathrm{\Lambda }}_l-{\displaystyle \frac{1}{r(r-1)}}{\sum }_{k\ne l}^r{\mathbf{Mz}}_k)$;   7:       ${\mathbf{z}}_l=max({\mathbf{z}}_l,0)$;   8:   end for   9:   Update $\mathrm{\Lambda }\leftarrow \mathrm{\Lambda }+\mu (\mathbf{W}-\mathbf{Z})$; 10:   Update $\mu =min(\rho \mu ,{\mu }_{max})$; 11:end while