  We study one-way matching of a pair of datasets with low rank signals. Under
a stylized model, we first derive information-theoretic limits of matching
under a mismatch proportion loss. We then show that linear assignment with
projected data achieves fast rates of convergence and sometimes even minimax
rate optimality for this task. The theoretical error bounds are corroborated by
simulated examples. Furthermore, we illustrate practical use of the matching
procedure on two single-cell data examples.
