TransD

TransD[ACL 2015]

• paper: Knowledge Graph Embedding via Dynamic Mapping Matrix

Basic Idea

• Entities are embedded in a continuous low dimensional vector space and each relations are embedded in different vector space.
• Judge whether triplet (entities, relationships, entities) can be considered as a fact by similarity based on distance.
• First, the entity vector is projected onto the vector space related to both the entitiy and relation, and then use L2 normal form as the similarity calculation method, and the formula is as follows: ($\textbf{I}$ is the identity matrix)

$$ f(\textbf{h},\textbf{r},\textbf{t}) = | (\textbf{r}{p}\textbf{h}{p}^{\top }+\textbf{I})\textbf{h}+\textbf{r}-(\textbf{r}{p}\textbf{t}{p}^{\top }+\textbf{I})\textbf{t}|_{2}^{2} $$

• The negative samples are constructed by destroying the fact triples to train the model.

$$ S' = \left { (h',r,t) \right |h'\in E } \cup \left { (h,r,t') \right |t'\in E } $$

• The loss calculation method is as follows:

$$ Loss = \sum_{(\textbf{h},\textbf{r},\textbf{t}) \in S}\sum_{(\textbf{h}',\textbf{r},\textbf{t}') \in S'}[\gamma - f(\textbf{h},\textbf{r},\textbf{t}) + f(\textbf{h}',\textbf{r},\textbf{t}')]_{+} $$

• Finally, use BP to update the model.

• What`s more, the dimensions of the entity embedding vector and the relationship embedding vector can be different.

How to run

• Clone the Openhgnn-DGL

  # For link prediction task
  python main.py -m TransD -t link_prediction -d FB15k -g 0 --use_best_config

  If you do not have gpu, set -gpu -1.

  Supported dataset

  • FB15k

    • Number of entities and relations

      entities	relations
      14,951	1,345

    • Size of dataset

      set type	size
      train set	483,142
      validation set	50,000
      test set	59,071

  • WN18

    • Number of entities and relations

      entities	relations
      40,493	18

    • Size of dataset

      set type	size
      train set	141,442
      validation set	5,000
      test set	5,000

Performance

Task: Link Prediction

Evaluation metric: mrr

Dataset	Mean Rank	Hits@10
FB15k(raw)	187	50.0
FB15k(filt.)	67	67.3
WN18(raw)	464	56.1
WN18(filt.)	212	60.3

TrainerFlow: TransX flow

Hyper-parameter specific to the model

You can modify the parameters[TransE] in openhgnn/config.ini

More

Contirbutor

Xiaoke Yang

If you have any questions

Submit an issue or email to x.k.yang@qq.com.