Algorithm A2 Distinct feature vector identifier (DFI)

Input: A set of feature vectors $H=\{h_1,h_2,\dots ,h_{n_H}\}$ and a similarity threshold $\sigma \in \left(0,1\right)$, where $h_j\in {\mathbb{R}}^{D\times 1}$ for $j=1,2,\dots ,n_H$. Moreover, set $DF=\left\{\right\}$ (empty set).

Step 1: Compute $\mathrm{B}=\{b_1,\hspace{0.25em}{b}_2,.b_{n_F}\}$, where $b_j=\frac{h_j}{\parallel h_j\parallel }\in {\mathbb{R}}^{D\times 1}$, for $j=1,2,\dots ,n_H$.

Step 2: While $\mathrm{B}\ne \left\{\right\}$ (empty set) do

Step 2.1: Set $b_R=popRand\left(\mathrm{B}\right)$, where $popRand\left(.\right)$ is a function that randomly selects only one element of its input set, i.e., $H$.

Step 2.2: Compute

$C=\left[\begin{array}{c}{c}_1,\hspace{0.25em}{c}_2,\dots ,\hspace{0.25em}{c}_{\left(R-1\right)},\hspace{0.25em}{c}_{\left(R+1\right)},\dots ,\hspace{0.25em}{c}_{n_H}\end{array}\right]\in {\mathbb{R}}^{1\times \left(n_H-1\right)},$

where $c_j=b_R^T{b}_j$ for $j=1,2,\dots ,R-1,R+1,\dots ,n_H.$

Step 2.3: for $j=1,2,\dots ,R-1,R+1,\dots ,n_H,$ do

If ($c_{\mathrm{j}}$ $\ge \sigma$), then

$\mathrm{B}=\mathrm{B}.\hspace{0.25em}remove\left(b_j\right)$,

where $A.\hspace{0.25em}remove\left(a\right)$ is a function that removes element $a$ from set $A$.

End (for).

Step 2.4: Set

$DF\hspace{0.25em}=\hspace{0.25em}DF\hspace{0.25em}\cup \hspace{0.25em}{h}_R,$

And

$\mathrm{B}=\mathrm{B}.\hspace{0.25em}remove\left(b_R\right).$

End (While)

Output: $DF\hspace{0.25em}$