# SVD versus RSVD

In the so-called incremental SVD used for collaborative filtering: http://www.machinelearning.org/proceedings/icml2007/papers/407.pdf http://www2.research.att.com/~volinsky/papers/ieeecomputer.pdf http://www.quuxlabs.com/blog/2010/09/matrix-factorization-a-simple-tutorial-and-implementation-in-python/

The user-item matrix $$R$$ is factored as $$P^{T}Q$$ using gradient descent. In the classical SVD there is the diagonal matrix $$S$$ which holds the singular values. What happens(ed) to that matrix in this formulation? Is it just omitted and they still call it SVD or is it implicitly part of $$Q$$ and/or $$P$$ ?