Both our approach and the methods of <cite>Primadhanty et al. (2015)</cite> address the problem of incorporating sparse combinatorial features by dimension reduction (i.e., matrix factorization); however, they differ in terms of the objective function to be optimized. <cite>Primadhanty et al. (2015)</cite> use maximum likelihood estimation as an objective function; whereas other objective functions such as hinge loss can be used in factorization machines.