TABLE III.

Algorithm 1 The detailed steps for computing an intra-inter class distance ratio as a separation measure. The Smaller ratio denotes higher intra-class compactness and label separation.

Input:Feature matrix X and the number of class C.

Step 1: Compute the mean feature vector for the i-th class, i.e., ${\overline{\mathbf{x}}}_i=\frac{1}{N_i}{\sum }_{j=1}^{N_i}{\mathbf{x}}_{ij}$ where xij denote the j-th sample from the i-th class, and Ni is the number of samples in the i-th class; Step 2: Compute the mean intra-class squared distance (i.e., intra-class variance) for the i-th class, i.e., ${\overline{d}}_i=\frac{1}{N_i}{\sum }_{j=1}^{N_i}{\Vert {\mathbf{x}}_{ij}-{\overline{\mathbf{x}}}_i\Vert }_2^2$, and then compute the mean intra-class variance, i.e., ${\overline{d}}_{intra}=\frac{1}{C}{\sum }_{i=1}^C{\overline{d}}_i$; Step 3: Compute the mean inter-class squared distance, i.e., ${\overline{d}}_{inter}=\frac{1}{C}{\sum }_{i=1}^C{\Vert {\overline{\mathbf{x}}}_i-\overline{\mathbf{x}}\Vert }_2^2$, where $\overline{\mathbf{x}}$ is the mean of the class means; Step 4: Compute the intra-inter class distance ratio, i.e., $r={\overline{d}}_{intra}/{\overline{d}}_{inter}$;

Output: Intra-inter class distance ratio r.