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We thank all reviewers for comments. The following is the response to each reviewer. To Reviewer_1: The setting of lambda, lambda2 is implicitly stated in Thm 1, as a particular setting of {\mathcal M} and {\mathcal N} in (3) corresponds to a setting of lambda, lambda2 in (2). However, admittedly, since the setting of \mathcal M (and \mathcal N) are related to feature quality (i.e. To Reviewer_2: In our formulation, we break the target matrix into two parts, R XMY T N. As noted, there are infinite solutions if we don't constrain on the solution space of M and N, as for any M we can let N R-XMT T. However, since R is low rank (says rank k), it is natural to seek a simple and explanatory solution where some of R's subspace (says rank r) is spanned by feature part XMY T and the remaining subspace (rank k-r) is spanned by N. And since XMY T is low rank, it is reasonable to assume M is also low rank, i.e.