Translating embeddings for modeling multi-relational data

• https://papers.nips.cc/paper/2013/file/1cecc7a77928ca8133fa24680a88d2f9-Paper.pdf

This paper proposes “TransE” Graph embedding method, which “models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities.”

$$\mathcal{L} = \sum_{(h,l,t)\in S} \sum_{(h', l, t')\in S'} \left[ \gamma + d(\mathbf{h} + \mathbf{l}, \mathbf{t}) - d(\mathbf{h'}+\mathbf{l},\mathbf{t'}) \right]_{+}$$

where $S'$ is the set of ‘corrupted’ triples.

This is designed for Knowledge graph so that each type of edge would roughly aligned to the same direction in the space.