Tensor factorization have shown to be a very efficient way to learn such data. It can be done either in a 3-way factorization style (trigram, e.g. RESCAL) or by sum of 2-way factorization (bigram, e.g TransE). Those methods usually achieve state-of-the-art accuracy on benchmarks. Though, all those learning methods suffer from regularization processes which are not always adequate.

We show that both 2-way and 3-way factorization of a relational tensor can be formulated as a simple matrix factorization problem. This class of problems can naturally be relaxed in a convex way. We show that this new method outperforms RESCAL on two benchmarks.

**Bio**

R. Bailly is currently post-doc at Heudiasyc (since march 2014), Compiègne. He works with Antoine Bordes and Nicolas Usunier on multi-relational learning and word embeddings. He was previously in Barcelona for a post-doc with Xavier Carreras, whith whom he worked on spectral methods applied to unsupervised setting.

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