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We introduce the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Speci cally, we employ a linear+quadratic model and regularize the linear term with the 2 -regularizer and the quadratic term with the trace norm regularizer. en, we formulate the CFM optimization as a semide nite programming problem and propose an e cient optimization procedure with Hazan's algorithm. A key advantage of CFM over existing FMs is that it can nd adoi:10.1145/3097983.3098103 dblp:conf/kdd/YamadaLGCWKKMC17 fatcat:yl4rses5cbcyph5icjqyufmvku