Algorithm 1 Naive Computation of Euclidean Distance Matrix

1:Input:$X\in {\mathbb{R}}^{d\times n}$ 2:$D\leftarrow \mathrm{ZeroMatrix}(n,n)$       ▹ Initialize the distance matrix 3:for$i=1$tondo 4:    for $j=1$ton do 5:        $\mathrm{sum}\leftarrow 0$ 6:        for $k=1$tod do 7:           $\mathrm{diff}\leftarrow X[k,i]-X[k,j]$  ▹ Compute difference between vectors 8:           $\mathrm{sum}\leftarrow \mathrm{sum}+{\mathrm{diff}}^2$    ▹ Accumulate squared differences 9:        end for 10:        $D[i,j]\leftarrow \mathrm{sum}$          ▹ Store the squared distance 11:    end for 12:end for 13:Output:D