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:
- Random: project the points in $\mathbb{R}^d$ directly onto $\mathbb{R}^2$.
- 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?