Algorithm 1 Update procedures of model parameters

Input: Observed variables $\mathit{X}=\{{\mathit{X}}^{\left(f\right)},{\widehat{\mathit{X}}}^{\left(v\right)},{\widehat{\mathit{X}}}^{\left(s\right)}\}$  Initialize ${\mathit{X}}_{\mathrm{miss}}^{\left(f\right)}$, $\mathit{Z}$, ${\mathit{W}}^{\left(k\right)}$, ${\mathit{\alpha }}^{\left(k\right)}$, and ${\beta }_k$$(k\in \{f,v,s\left\}\right)$ by prior distributions in Equations (1), (2), (4), (5)  for number of training iterations do    Update the projection matrix ${\mathit{W}}^{\left(k\right)}$ in Equation (7)    Update the shared latent variables $\mathit{Z}$ in Equation (10)    Update the missing values ${\mathit{X}}_{\mathrm{miss}}^{\left(f\right)}$ in Equation (14)    Update the inverse variances ${\mathit{\alpha }}^{\left(k\right)}$ in Equation (15)    Update the inverse variance ${\beta }_k$ in Equation (18)  end for Output: Updated distributions of ${\mathit{X}}_{\mathrm{miss}}^{\left(f\right)}$, $\mathit{Z}$, ${\mathit{W}}^{\left(k\right)}$, ${\mathit{\alpha }}^{\left(k\right)}$, and ${\beta }_k$$(k\in \{f,v,s\left\}\right)$