Piyush Sao

Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models

The Johnson–Lindenstrauss (JL) lemma guarantees that a random projection of n points to m = O(ε⁻² log n) dimensions preserves pairwise squared distances within relative error ε with high probability. This dimension order is asymptotically optimal. In high dimensions, however, dis...