In CSSP, the goal is similar, with the added constraint that the approximation to A must be obtained by projecting onto the subspace spanned by a k-subset of the original rows of A.
5 Formally, the goal is to produce a (k × m) matrix S formed from rows of A, such that is minimized over all n k possible choices for S. Here S + is the (m × k) Moore-Penrose pseudoinverse of S, and S + S gives the orthogonal projector onto the rowspace of S. our goal is to select k data points which serve as a good approximate basis for all the data points.