Algorithm 1 F-TEST and RNCA.

Procedure F-TEST($\mathbf{X}$, $\mathbf{Y}$): training dataset 01: return $({\mathrm{w}}_f)$ that produces weighted feature vectors using F-test 02: select $({\mathrm{w}}_f)\ge$ threshold End procedure   Procedure RNCA ($\mathbf{X}$, $\mathbf{Y}$): a training dataset 01: partition training dataset into 5 folds for $i=1,n$ do: where n is the number of the ${\lambda }_{i,k}$ line space 02: ${\lambda }_{i,k}$: tuning using 5-fold cross-validation    for $k=1,5$ do: 03:    call NCA($\mathbf{X}$, $\mathbf{Y}$, ${\lambda }_{i,k}$): train NCA for $\lambda$ regularization parameter 04:    compute ${\mathcal{L}}_{i,k}$: record loss values    endfor endfor 05: ${\mathcal{L}}_{\mu }$ = mean(${\mathcal{L}}_{i,k}$): compute average loss value 06: ${\lambda }_b=arg{min}_{{\mathcal{L}}_{\mu }}(\mathrm{y}|\mathrm{x},{\lambda }_{i,k},{\mathcal{L}}_{\mu })$: find best ${\lambda }_b$ 07: call NCA($\mathbf{X}$, $\mathbf{Y}$, ${\lambda }_b$, $\zeta$): $\zeta$ = $@({\mathrm{y}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{j}})1-exp(-|{\mathrm{y}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{j}}|)$ 08: return $(\mathrm{w})$ that produces weighted feature vectors 09: select $(\mathrm{w})\ge$ (threshold) = 3; fixed threshold End procedure