Knowledge Graph Embedding¶

Introduction for KGE¶

A knowledge graph contains a set of entities $\mathbb{E}$ and relations $\mathbb{R}$ between entities. The set of facts $\mathbb{D}^+$ in the knowledge graph are represented in the form of triples $(h, r, t)$ , where $h,t\in\mathbb{E}$ are referred to as the head (or subject) and the tail (or object) entities, and $r\in\mathbb{R}$ is referred to as the relationship (or predicate).

The problem of KGE is in finding a function that learns the embeddings of triples using low dimensional vectors such that it preserves structural information, $f:\mathbb{D}^+\rightarrow\mathbb{R}^d$ . To accomplish this, the general principle is to enforce the learning of entities and relationships to be compatible with the information in $\mathbb{D}^+$ . The representation choices include deterministic point, multivariate Gaussian distribution, or complex number. Under the Open World Assumption (OWA), a set of unseen negative triplets, $\mathbb{D}^-$ , are sampled from positive triples $\mathbb{D}^+$ by either corrupting the head or tail entity. Then, a scoring function, $f_r(h, t)$ is defined to reward the positive triples and penalize the negative triples. Finally, an optimization algorithm is used to minimize or maximize the scoring function.

KGE methods are often evaluated in terms of their capability of predicting the missing entities in negative triples $(?, r, t)$ or $(h, r, ?)$ , or predicting whether an unseen fact is true or not. The evaluation metrics include the rank of the answer in the predicted list (mean rank), and the ratio of answers ranked top-k in the list (hit-k ratio).

Implemented KGE Algorithms¶

We aim to implement as many latest state-of-the-art knowledge graph embedding methods as possible. From our perspective, by so far the KGE methods can be categorized based on the ways that how the model is trained:

Pairwise (margin) based Training KGE Models: these models utilize a latent feature of either entities or relations to explain the triples of the Knowledge graph. The features are called latent as they are not directly observed. The interaction of the entities and the relations are captured through their latent space representation. These models either utilize a distance-based scoring function or similarity-based matching function to embed the knowledge graph triples. (please refer to pykg2vec.models.pairwise for more details)
Pointwise based Training KGE Models: (please refer to pykg2vec.models.pointwise for more details).
Projection-Based (Multiclass) Training KGE Models: (please refer to pykg2vec.models.projection for more details).

Supported Dataset¶

We support various known benchmark datasets in pykg2vec.

FreebaseFB15k: Freebase dataset.
WordNet18: WordNet18 dataset.
WordNet18RR: WordNet18RR dataset.
YAGO3_10: YAGO Dataset.
DeepLearning50a: DeepLearning dataset.

We also support the use of your own dataset. Users can define their own datasets to be processed with the pykg2vec library.

Benchmarks¶

Some metrics running on benchmark dataset (FB15k) is shown below (all are filtered). We are still working on this table so it will be updated.

	MR	MRR	Hit1	Hit3	Hit5	Hit10
TransE	69.52	0.38	0.23	0.46	0.56	0.66
TransH	77.60	0.32	0.16	0.41	0.51	0.62
TransR	128.31	0.30	0.18	0.36	0.43	0.54
TransD	57.73	0.33	0.19	0.39	0.48	0.60
KG2E_EL	64.76	0.31	0.16	0.39	0.49	0.61
Complex	96.74	0.65	0.54	0.74	0.78	0.82
DistMult	128.78	0.45	0.32	0.53	0.61	0.70
RotatE	48.69	0.74	0.67	0.80	0.82	0.86
SME_L	86.3	0.32	0.20	0.35	0.43	0.54
SLM_BL	112.65	0.29	0.18	0.32	0.39	0.50