There are ways to do that from linear algebra, like orthogonalization processes (e.g., Gram-Schmidt process) followed by basis expansion. Or random projections

There are ways to do that from linear algebra, like orthogonalization processes (e.g., Gram-Schmidt process) followed by basis expansion. Or random projections can also be used in a similar way. And I’m sure there are much fancier techniques that draw upon higher math (like Grassmannians or Teichmuller mappings).