  We propose a clustering method that involves chaining four known techniques
into a pipeline yielding an algorithm with stronger recovery guarantees than
any of the four components separately. Given $n$ points in $\mathbb R^d$, the
first component of our pipeline, which we call leapfrog distances, is
reminiscent of density-based clustering, yielding an $n\times n$ distance
matrix. The leapfrog distances are then translated to new embeddings using
multidimensional scaling and spectral methods, two other known techniques,
yielding new embeddings of the $n$ points in $\mathbb R^{d'}$, where $d'$
satisfies $d'\ll d$ in general. Finally, sum-of-norms (SON) clustering is
applied to the re-embedded points. Although the fourth step (SON clustering)
can in principle be replaced by any other clustering method, our focus is on
provable guarantees of recovery of underlying structure. Therefore, we
establish that the re-embedding improves recovery SON clustering, since SON
clustering is a well-studied method that already has provable guarantees.
