Semantically Invariant Tensor Factorization

Raphaël Bailly (1, 2) , Antoine Bordes (3) , Nicolas Usunier (1, 2)

1 Labex MS2T - Laboratoire d'Excellence "Maîtrise des Systèmes de Systèmes Technologiques"
2 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]
3 FAIR - Facebook AI Research [Paris]

Multi-relational data can usually be represented as three-mode tensors with each slice (matrix) representing one relation (not necessarily symmetric) between two nodes. In this paper, we study factorization algorithms for such tensors that are semantically invariant, which means that they commute with the transposition of their frontal slices. We describe why this property is crucial for conveniently approximating such data and we demonstrate what are the necessary and sufficient conditions that any algorithm should have to fulfill it. Then, we introduce SITAR, a convex and semantic invariant algorithm, which produces low-rank approximations of tensors. We show empirically on three benchmarks that this well-defined algorithm outperforms previously presented low-rank factorization algorithm like RESCAL.

Domaines: Informatique [cs]

Raphaël Bailly, Antoine Bordes, Nicolas Usunier. Semantically Invariant Tensor Factorization. 2015. ⟨hal-01128021⟩