UniPROT reformulates uniform prototype selection as a partial optimal transport problem that yields a submodular objective admitting a greedy algorithm with (1-1/e) approximation guarantee.
The proof follows along similar lines of the non-negativity proof in Lemma 1
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UniPROT: Uniform Prototype Selection via Partial Optimal Transport with Submodular Guarantees
UniPROT reformulates uniform prototype selection as a partial optimal transport problem that yields a submodular objective admitting a greedy algorithm with (1-1/e) approximation guarantee.