A collaborative convex framework for factoring a data matrix $X$ into a
non-negative product $AS$, with a sparse coefficient matrix $S$, is proposed.
We restrict the columns of the dictionary matrix $A$ to coincide with certain
columns of the data matrix $X$, thereby guaranteeing a physically meaningful
dictionary and dimensionality reduction. We use $l_{1,\infty}$ regularization
to select the dictionary from the data and show this leads to an exact convex
relaxation of $l_0$ in the case of distinct noise free data.