Algorithm 1. Feature Selection

Input:   Original feature matrix ${\mathbf{X}}_M$ with M-dimensional features. Output:   Selected feature subset $\mathbf{S}$ with D-dimensional features $(D=1,2,\cdots ,M)$. Procedure:   1: D = 1. Compute $SI(f_i)(i=1,2,\cdots ,M)$ of each dimension of the original feature matrix and record the score1: $scor{e}_1=SI(f_i)$. Choose the feature with the largest $scor{e}_1$ as the first element of the optimal feature subset S. Then, the remaining feature element is $X_{M-\mathrm{D}}$.   2: do   Step 1: D = D + 1. Then, choose a feature element from $X_{M-\mathrm{D}}$ in turn, and combine the element with S into a new feature subset $X_T$, all subset $X_T$ make up a new feature matrix $X^{\prime }$. Compute the class separability index ($SI$) of each feature subset in the $X^{\prime }$ and the $SI$ is defined as $SI=\frac{2}{D}{\displaystyle \sum _{i=1}^{D}SI(f_i)}$.   Step 2: For the formed new feature matrix $X^{\prime }$ in Step 1, obtain $t=\left(\begin{array}{l}2\\ D\end{array}\right)$ subsets. Then, compute the average $DI$ of the pairwise dissimilarity of all the subsets.   Step 3: For each subset, compute the score2 defined as $scor{e}_2=SI+DI$, which reflects whether the feature subset is appropriate.   Step 4: Put the feature element with the largest value of $scor{e}_2$ into $\mathbf{S}$ and reset the remaining feature element $X_{M-\mathrm{D}}$.   Step 5: Input the selected feature subset $\mathbf{S}$ with D-dimensional features into the classifier. Then, the classification accuracy of the D-dimensional features $accuracy(D)$ will be obtained.   End while until the number of selected elements D reaches M.   3: Choose the best classification accuracy from $accuracy(D)(D=1,2,3\cdots M)$ as the final accuracy for this kind of feature after feature selection. If $accuracy(i)=accuracy(j)$ but $i\le j(i,j=1,2,3\cdots M)$, $i$ can be considered as the optimal feature dimension. Return: $\mathbf{S}$ = {s1, s2, …, sM}. Note: The larger score2 means the feature is more beneficial to increasing classification performance.