Table 1 Multi-label sorting calculation algorithm

Algorithm: Multi-label sorting calculation algorithm

Enter: Training sample set \( \mathrm{X}={\left\{{x}_i\in {R}^d\right\}}_{i=1}^n \) , corresponding to the age label set \( \mathrm{Y}={\left\{{y}_i\in {\left\{0,1\right\}}^m\right\}}_{i=1}^n \) , and parameter λ initialized: η₀ = 1, γ = 2, α₁ = 1, W₀ = Z₀ = Z₁ = R^d × n.

Cycling when conditions do not converge:

 1. Set up \( \overline{\eta}={\eta}_{k-1} \)

 2. When \( \mathrm{F}\left({P}_{\overline{\eta}}\left({Z}_{k-1}\right)\right)>{Q}_{\overline{\eta}}\left({P}_{\overline{\eta}}\left({Z}_{k-1}\right),{Z}_{k-1}\right)\Big) \), so that \( \overline{\eta}:= \frac{\overline{\eta}}{\gamma } \)

 3. Set \( {\eta}_k=\overline{\eta} \), and update \( {\eta}_k=\overline{\eta} \):

   W_k = P_ηk(Z_k)

   \( {\alpha}_{k+1}=\frac{1+\sqrt{1+4{\alpha}_k^2}}{2} \)

   \( {Z}_{k+1}={W}_k+\left(\frac{\alpha_k-1}{\alpha_{k+1}}\right)\left({W}_k-{W}_{k-1}\right) \)

End Cycle