ott.geometry.grid.Grid.to_LRCGeometry#

Grid.to_LRCGeometry(rank, tol=0.01, seed=0)#

Factorize the cost matrix in sublinear time .

Uses the implementation of , algorithm 4.

It holds that with probability 0.99, $$||A - UV||_F^2 \leq || A - A_k ||_F^2 + tol \cdot ||A||_F^2$$, where $$A$$ is n x m cost matrix, $$UV$$ the factorization computed in sublinear time and $$A_k$$ the best rank-k approximation.

Parameters
Return type

LRCGeometry

Returns

Low-rank geometry.