Algorithm 2. SNN query.

1: Input: Query vector q; user-specified radius R; output from Algorithm 1

2: Compute $x_q:=q-\mu$

3: Compute the sorting score of xq, i.e., ${\alpha }_q:=x_q^T{v}_1$

4: Select candidate index range J so that $|{\alpha }_j-{\alpha }_q|\le R$ for all $j\in J$

5: Compute $d:=\overline{x}(J)-X(J,:{)}^T{x}_q$ using the precomputed $\overline{x}=[\overline{x_i}]$

6: Return: Points xj with $d_j\le (R^2-x_q^T{x}_q)/2$ according to Eq. (4)