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TransD[ACL 2015]

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.