2015/07/04 by Makoto Yamada, Yamada, Makoto, Lian, Wenzhao +9
Engineering · Mathematics · #Advanced MIMO Systems Optimization #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1507.01073
openalex publication_date 2015/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓ2-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.