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I have several (dozens) of vectors in $\mathbb{R}^d$ (with $d$ being in millions). My goal is to project them into a 2-dimensional space. A couple of things that I know:

  • I know that projection from high-dimensional space could be pretty tricky, since we might be losing lots of information (that are encoded in high-dimensional space but might be representable in a 2d space).
  • I know that there are several tools for projection. For example, t-SNE or random projections.

I am looking for suggestions as to what is an efficient/practical way to do this. As of know, here are the two settings I have in mind:

  1. Random: project the points in $\mathbb{R}^d$ directly onto $\mathbb{R}^2$.
  2. Random + t-SNE: the points in $\mathbb{R}^d$ to an intermediate dimension (say, $1000$ dimensional space), followed by a projection onto a $\mathbb{R}^2$ space with t-SNE.

I don't apply t-SNE directly since I think it wouldn't scale to large-scale vectors.

Any suggestions or thoughts on how I can do a better projection?

Daniel
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  • Calculate the covariance matrix and project onto the eigenvectors corresponding to the largest eigenvalues. ... works for me. – Donald Splutterwit Dec 16 '19 at 23:33
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    I think this is an unanswerable question unless you can [edit] it to tell us what you want to achieve with this projection. What problem do you want to solve with this projection? You ask for something "better" but that's not a mathematical criterion. – Ethan Bolker Dec 16 '19 at 23:33

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