Algorithm 1. SNN index.

1: Input: Data matrix $P=[p_1,p_2,\dots ,p_n{]}^T\in {\mathbb{R}}^{\times }$

2: Compute $\mu :=\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}(\{p_j\})$

3: Compute the mean-centered matrix X with rows $x_i:=p_i-\mu$

4: Compute the singular value decomposition of $X=U\mathrm{\Sigma }{V}^T$

5: Compute the sorting keys ${\alpha }_i=x_i^T{v}_1$ for $i=1,2,\dots ,n$

6: Sort data points X such that ${\alpha }_1\le {\alpha }_2\le \cdots \le {\alpha }_n$

7: Compute $\overline{x_i}=(x_i^T{x}_i)/2$ for $i=1,2,\dots ,n$

8: Return: μ, X, v1, $[{\alpha }_i]$, $[\overline{x_i}]$