Before revision:  This paper reviews a line of work that is grounded in theoretical computer science and numerical linear algebra, and which finds that an algorithmically desirable sketch  of the data must have a subspace embedding property .
After revision:  This paper reviews a line of work that is grounded in theoretical computer science and numerical linear algebra, and which finds that an algorithmically desirable sketch , which is a randomly chosen subset of the data must have a subspace embedding property .