Knowledge Graph Embeddings

Outline

• Why embed the KG ?
• Notations
• General Algorithm
• Scoring Function
  • Translation Based
  • Semantic Matching Based
• KG embedding with additional resources
  • Entity types
  • Relation Paths
  • Textual Descriptions
• Conclusion

Outline

• Why embed the KG ?
• Notations
• General Algorithm
• Scoring Function
  • Translation Based
  • Semantic Matching Based
• KG embedding with additional resources
  • Entity types
  • Relation Paths
  • Textual Descriptions
• Conclusion

• Embedding the KG into a continuous space while preserving the properties and semantics of the whole KG.
• Applications
  • Link Prediction: 
  • Triple Classification:
  • Entity Resolution:
  • Relation Extraction:
  • Question Answering:

Why Embed the KG ?

Outline

• Why embed the KG ?
• Notations
• General Algorithm
• Scoring Function
  • Translation Based
  • Semantic Matching Based
• KG embedding with additional resources
  • Entity types
  • Relation Paths
  • Textual Descriptions
• Conclusion

Notations

• KG contains entities \(e \in \mathbb{E} \) and relationships \( r \in \mathbb{R} \)
• Each KB triple (fact) is represented by \( (h,r,t)\)
• \( h\): head entity, \(t\): tail entity and \(r\): relation
• Example:  (AlfredHitchcock, DirectorOf, Psycho)
• Scoring function \(f_r(h, t) \) : measures the plausibility of the fact \((h,r,t)\)

Outline

• Why embed the KG ?
• Notations
• General Algorithm
• Scoring Function
  • Translation Based
  • Semantic Matching Based
• KG embedding with additional resources
  • Entity types
  • Relation Paths
  • Textual Descriptions
• Conclusion

General Algorithm

Outline

• Why embed the KG ?
• Notations
• General Algorithm
• Scoring Function
  • Translation Based
  • Semantic Matching Based
• KG embedding with additional resources
  • Entity types
  • Relation Paths
  • Textual Descriptions
• Conclusion

Translation Based Approaches - TransE

• Head entity \(\mathbf{h}\) and tail entity \( \mathbf{t}\) of a fact \((h,r,t)\) are vectors in \(\mathbb{R}^d\)
• Relation \(\mathbf{r}\) is a translation in \(\mathbb{R}^d\)
• Scoring function: \(f_r(h,t) = -\lVert \mathbf{h}+\mathbf{r}-\mathbf{t}\lVert_{1/2}\)  
• Ranking Loss: \( \mathcal{L} = \)