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 of the data , must preserve the eigenstructure of the data, a property known as a subspace embedding .