I’ve been looking at some recent embeddings work, and am struck by how beautiful the theory and algorithms are. It also makes me wonder, what are embeddings good for?<\/p>\n
A few things immediately come to mind:<\/p>\n
(1) For visualization of high-dimensional data sets.<\/p>\n
In this case, one would like good algorithms for embedding specifically into 2- and 3-dimensional Euclidean spaces.<\/p>\n
(2) For nonparametric modeling.<\/p>\n
The usual nonparametric models (histograms, nearest neighbor) often require resources which are exponential in the dimension. So if the data actually lie close to some low-dimensional
\nsurface, it might be a good idea to first identify this surface and embed the data before applying the model.<\/p>\n
Incidentally, for applications like these, it’s important to have a functional mapping from high to low dimension, which some techniques do not yield up.<\/p>\n
(3) As a prelude to classifier learning.<\/p>\n
The hope here is presumably that learning will be easier in the low-dimensional space, because of (i) better generalization and (ii) a more “natural” layout of the data.<\/p>\n
I’d be curious to know of other uses for embeddings.<\/p>\n","protected":false},"excerpt":{"rendered":"
I’ve been looking at some recent embeddings work, and am struck by how beautiful the theory and algorithms are. It also makes me wonder, what are embeddings good for? A few things immediately come to mind: (1) For visualization of high-dimensional data sets. In this case, one would like good algorithms for embedding specifically into … <\/p>\n