With "sampling over documents," it is convenient to express the sampling rate in terms of D s and D, whereas with sketches, it is convenient to express the sampling rate in terms of k and f .
the following two approximations allow us to flip back and forth between the two views: using sketches with size k, the corresponding sample size D s in "sampling over documents" would be D s ≈ D f k, where D f represents the data sparsity.