While googling about low distortion embeddings, I feel that there are two separate communities working on the subject of low distortion embedding, without much communication with each other.
In particular, I see a math community, refering to Johnson Lindenstrauss Lemma, Bourgain's theorem and its various refinements, some constructive methods for such low distortion embeddings with Frechet type embeddings, the work from Matousek or Indyk etc.
A typical paper would be:
Advances in Metric Embedding Theory
A typical lecture :
James Lee's lecture
or Indyk's lecture
On the other hand, I see a stat/CS community, working on Multi Dimensional Scaling (MDS) or IsoMaps, with method such as SMACOF, SparseMap, MetricMap, Landmark MDS etc. achieving similar results to embedd into $l_2$.
A typical paper would be :
Multidimensional Scaling Using Majorization: SMACOF in R
or FastMap, MetricMap, and Landmark MDS are all Nystrom Algorithms
A simple short lecture:
UToronto's lecture
The techniques are very different (Fréchet embedding vs optimization techniques or spectral methods).. and hence I wonder whether these problems are actually different ? The overlap in techniques, analysis and references is almost null whereas the goal looks the same to me.
Thanks!