Algorithm 1 The procedure for MSFBEL framework.

Input: Number of scales s, number of classes c, training data $\mathit{X}\in {\mathbb{R}}^{d\times n}$, training data label   $\mathit{O}\in {\mathbb{R}}^{c\times n}$, a subset of training data ${\mathit{X}}_{sub}\in {\mathbb{R}}^{d\times m}$, the labels of subset ${\mathit{O}}_{sub}\in {\mathbb{R}}^{c\times m}$,   testing data $\mathit{y}\in {\mathbb{R}}^d$; Output: The label of testing data: l.  1: for $j=1:s$ do  2:  Compute the label of testing data under scale j via Algorithm 2;  3: end for  4: Compute decision matrix $\mathit{D}$ by Equation (4) with ${\mathit{X}}_{sub}$ and ${\mathit{O}}_{sub}$;  5: Compute $\mathit{M}={\mathit{D}}^T\mathit{D}$ and $\mathit{b}=2{\mathit{D}}^T{\mathbf{1}}_m$;  6: Compute the adaptive weight ${\mathit{w}}^{*}$ via Algorithm 3;  7: Compute $l={argmax}_{k\in \left[c\right]}\{{\sum }_{j=1}^s{w}_j^{*}\mathbb{I}(r_j=k)\}$.