Input: $x$ , $y$ , $r_0=y$ , $\mathcal{L}=\varnothing$ , $\lambda$ , threshold $ϵ$ .

Step 1: Implement a novel preprocessing strategy to obtain the PBOW matrix $D=\left[D_1,D_2,\cdots ,D_c\right]$ ;

Step 2: Compute sparse subset: $j^i={\text{argmax}}_{j\notin \mathcal{L}}\left|x^{\text{T}}{r}_{i-1}\right|\left(i=1,2,\cdots ,c\right)$ ;

Step 3: Sparse index set: $\mathcal{L}=\mathcal{L}\cup j^i$ ;

Step 4: Solve for the sparse parameter: ${\alpha }_i=\underset{x\in {ℝ}^n,i\in \mathcal{L}}{\arg \min }{\Vert y-D_{i}x\Vert }_2^2+\lambda {\Vert x\Vert }_2^2$ ;

Step 5: Calculate residuals: $r_i={\Vert y-D_i{\alpha }_i\Vert }_2^2\left(i=1,2,\cdots ,c\right)$ , if ${\Vert r_i\Vert }_2^2<ϵ$ break else continue.

Output: $label\left(y\right)=\arg {\min }_i{r}_i$ .