Algorithm 2 NCA Feature Selection

1. Input: $Z\in R^{d x L};\mathsf{\gamma }$ initial step length; σ: kernel width; ℷ: regularisation parameter; and η: small positive constant. 2. Initialization: $w^{\left[0\right]}=\left(1, 1, \dots , 1\right),{ϵ}^{\left(0\right)}=-\infty$$,t=0$. 3. Repeat 4. $for i=1, \dots , L do$ 5. Compute $p_{ij}$ and $p_i$ using $w^{\left(t\right)}$ according to (2) and (3) 6. $for r=1, \dots , d do$ 7. $\nabla \_r=2(1/\sigma (p_i{\displaystyle \sum }_{j\ne i}{p}_{ij}\left|z_{ir}-z_{jr}\right|-{\displaystyle \sum }_j{c}_{ij}\left|z_{ir}-z_{jr}\right|)-\gimel )w_r^{\left(t\right)}$ 8. t = t + 1 9. $w^{\left(t\right)}=w^{\left(t-1\right)}+\mathsf{\gamma }\mathsf{\Delta }$ 10. ${ϵ}^{\left(t\right)}=\xi \left(w^{\left(t-1\right)}\right)$ 11. $\mathrm{if}{ϵ}^{\left(t\right)}>{ϵ}^{\left(t-1\right)}\mathrm{then}\mathsf{\gamma }$ = 1.01 $\mathsf{\gamma }$ 12. else 13. $\mathsf{\gamma }=0.4\mathsf{\gamma }$ 14. $\mathrm{until}\left|{ϵ}^{\left(t\right)}-{ϵ}^{\left(t-1\right)}\right|<\eta$ 15. $w=w^t$ 16. $\mathrm{Return}w$