| There is a lot of fundamental work on random projections [0] from Dasgupta et al., Achlioptas et al., etc. For example, while random projections produced by sampling normal random variables like in the article are sufficient, there alternative approaches that produce transformations with "better" properties for big data- e.g. transformations with a sparse matrix representations. For the basic background see the JL Lemma [1]- it turns with high probability, random linear transformations that map from high to low-d Euclidean spaces preserve inner products. In the context of compressive sensing, it's very much related the restricted isometry property [2]. Recently, it's been shown that random projections also appear in nature- the olfactory mechanisms of certain insects behave very similarly to random projections [3]. [0] https://en.wikipedia.org/wiki/Random_projection [1] https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_... [2] https://en.wikipedia.org/wiki/Restricted_isometry_property [3] https://science.sciencemag.org/content/358/6364/793/tab-figu... |