Algorithm 1 Algorithm to solve Eq. (9)

$$\begin{array}{cc}\hfill & \mathbf{Require}:\hfill \\ \hfill & \mathbf{X}\in {\mathcal{R}}^{n\times p},{\mathbf{Y}}_j\in {\mathcal{R}}^{n\times q},j=1,\dots ,c,\beta ,{\lambda }_1,{\lambda }_2,{\gamma }_1,{\gamma }_2\hfill \\ \hfill & \mathbf{Ensure}:\hfill \\ \hfill & \text{Canonical weights}\mathbf{U}\text{and}\mathbf{V}.\hfill \\ \hfill & 1:\text{Initialize}\mathbf{U}\in {\mathcal{R}}^{p\times c},\mathbf{V}\in {\mathcal{R}}^{q\times c};\hfill \\ \hfill & 2:\mathbf{while}\text{not convergence}\mathbf{do}\hfill \\ \hfill & 3:\text{Update}{\underset{¯}{\tilde{\mathbf{D}}}}_{g_k}\text{and}{\underset{¯}{{\mathbf{D}}_1}}_{g_k};\hfill \\ \hfill & 4:\text{Solve}\mathbf{U}\text{according to Eq}.(13),\text{and normalize}{\mathbf{u}}_j\text{to}\hfill \\ \hfill & \Vert \mathbf{X}{\mathbf{u}}_j{\Vert }_2^2=1;\hfill \\ \hfill & 5:\text{Update}{\mathbf{D}}_2;\hfill \\ \hfill & 6:\text{Solve}{\mathbf{v}}_j(j=1,\cdots ,c)\text{according to Eq}.(16),\text{and}\hfill \\ \hfill & \text{normalize}{\mathbf{v}}_j\text{to}\Vert {\mathbf{Y}}_j{\mathbf{v}}_j{\Vert }_2^2=1;\hfill \\ \hfill & 7:\mathrm{end}\mathrm{while}\hfill \end{array}$$