Joint European Conference on Machine Learning and Knowledge Discovery in Databases

ECML PKDD 2015: Machine Learning and Knowledge Discovery in Databases pp 19-35

Convex Factorization Machines

Conference paper

DOI: 10.1007/978-3-319-23525-7_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9285)
Cite this paper as:
Blondel M., Fujino A., Ueda N. (2015) Convex Factorization Machines. In: Appice A., Rodrigues P., Santos Costa V., Gama J., Jorge A., Soares C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2015. Lecture Notes in Computer Science, vol 9285. Springer, Cham


Factorization machines are a generic framework which allows to mimic many factorization models simply by feature engineering. In this way, they combine the high predictive accuracy of factorization models with the flexibility of feature engineering. Unfortunately, factorization machines involve a non-convex optimization problem and are thus subject to bad local minima. In this paper, we propose a convex formulation of factorization machines based on the nuclear norm. Our formulation imposes fewer restrictions on the learned model and is thus more general than the original formulation. To solve the corresponding optimization problem, we present an efficient globally-convergent two-block coordinate descent algorithm. Empirically, we demonstrate that our approach achieves comparable or better predictive accuracy than the original factorization machines on 4 recommendation tasks and scales to datasets with 10 million samples.


Factorization machines Feature interactions Recommender systems Nuclear norm 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.NTT Communication Science LaboratoriesKyotoJapan

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