We propose the convex factorization machine (CFM), which is a convex variant
of the widely used Factorization Machines (FMs). Specifically, we employ a
linear+quadratic model and regularize the linear term with the
$\ell_2$-regularizer and the quadratic term with the trace norm regularizer.
Then, we formulate the CFM optimization as a semidefinite programming problem
and propose an efficient optimization procedure with Hazan's algorithm. A key
advantage of CFM over existing FMs is that it can find a globally optimal
solution, while FMs may get a poor locally optimal solution since the objective
function of FMs is non-convex. In addition, the proposed algorithm is simple
yet effective and can be implemented easily. Finally, CFM is a general
factorization method and can also be used for other factorization problems
including including multi-view matrix factorization and tensor completion
problems. Through synthetic and movielens datasets, we first show that the
proposed CFM achieves results competitive to FMs. Furthermore, in a
toxicogenomics prediction task, we show that CFM outperforms a state-of-the-art
tensor factorization method.

本文提出了一种凸分解机方法（CFM），它是广泛使用的分解机（FM）的一个凸变体。该方法可以找到全局最优解，并已在应用于多视角矩阵分解和张量完成问题时获得成功。