Algorithm 1 Fp-2DPCA

Input: $A_i\in R^{m\times n}\left(i=1,\cdots ,N\right),k,{\displaystyle \sum _{i=1}^M{A}_i}=0,J\left(W^{\left(t\right)}\right)={\displaystyle \sum _{i=1}^M\frac{{\Vert E_i\Vert }_F^p}{{\Vert A_{i}W\Vert }_F^p}}$

Initialize: $W^{\left(t\right)}\in R^{m\times k},{\left(W^t\right)}^{\text{T}}{W}^t=I_k,t=1,\delta =\left|J\left(W^{\left(t\right)}\right)-J\left(W^{\left(t-1\right)}\right)\right|$

While: $\delta \ge \epsilon$

1. Calculate $d_i^{\left(t\right)}$ for each $A_i$ according to Equation (9),

Calculate $W:W=U{V}^{\text{T}}$ according to the conclusion of Equation (23),

2. Calculate $H^{\left(t\right)}$ according to Equation (9) and Equation (23),

3. SVD decomposition of $H^{\left(t\right)}$ : $H^{\left(t\right)}=U\Sigma V^{\text{T}}$ ,

4. Calculate $W:W=U{V}^{\text{T}}$ according to the conclusion of Equation (23),

5. Update $\delta$ ,

6. Update $t:t=t+1$ .

Output: $W^{t+1}\in R^{n\times d}$