Algorithm 2 Bilateral Fp-2DPCA

Input: $A_i\in R^{m\times n}\left(i=1,\cdots ,N\right),{\displaystyle \sum _{i=1}^M{A}_i}=0$

1. Taking $A_i\left(i=1,\cdots ,N\right)$ as the input of algorithm 1, the right projection matrix $R\in {ℝ}^{n\times r}$ is obtained, and the characteristic matrix $Y_i=A_{i}R$ of $A_i$ is calculated;

2. Taking $Y_i^{\text{T}}\left(i=1,\cdots ,N\right)$ as the input of algorithm 1, the left projection matrix $L\in {ℝ}^{m\times l}$ is obtained, and the characteristic matrix $B_i^{\text{T}}=Y_i^{\text{T}}L$ of $Y_i^{\text{T}}$ is calculated;

Output: Output: output left projection matrix $L\in {ℝ}^{m\times l}$ , right projection matrix $R\in {ℝ}^{n\times r}$ , and characteristic matrix $B_i=L^{\text{T}}{A}_{i}R\in {ℝ}^{l\times r},i=1,2,\cdots ,N$ .