Universality laws for randomized dimension reduction, with applications

Understand

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis.

• In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data.
• This dimension reduction procedure succeeds when it preserves certain geometric features of the set.
• The question is how large the embedding dimension must be to ensure that randomized dimension reduction succeeds with high probability.