Algorithm 1.

Feature selection for the GMM or the $k$-means

Input: Data set $𝒟=\left\{{\mathit{x}}_1,\dots ,{\mathit{x}}_n\right\}$ and the number of clusters $k$

Output: labels $1,\dots ,k$ for each ${\mathit{x}}_i\in 𝒟$ with the best $A\subseteq ℱ$

Initialization

1: Determine the first $j_{\min }^{(1)}$ by (7) with $loss(A)=d\left(𝒞,{𝒞}_A\right)$ given by (5) if the GMM method is adopted or $loss(A)=\tilde{d}\left(𝒞,{𝒞}_A\right)$ given by (6) if the $k$-means method is adopted

Begin Iteration

2: Let $A^{(t-1)}=\{j_{\min }^{(1)},j_{\min }^{(2)},\dots ,j_{\min }^{(t-1)}\}$ be the previous set of important features and determine the current $j_{\min }^{(t)}$ by (8) and update $A^{(t)}=A^{(t-1)}\cup \{j_{\min }^{(t)}\}$

3: Stop if $t=p$ or no important feature is found; otherwise continue

End Iteration

4: Output