知識グラフの埋め込みとその応用 (第10回ステアラボ人工知能セミナー)

1. G = ( , ) = ⊆ × R× −→ = ( , , ) R +

2. + +

3. → ≈ ∗ , || − || , ≈

4. , , = ( , , ) ∈ ( , , ) ̸∈ ⇒ , , ≈ ( , , ;Θ)

5. ( , , ;Θ) Θ ⟨ , , ⟩ , , ∈ R + ⟨ , , ⟩ , , ∈ R , ∈ R ∈ R × ( ⋆ ) , , ∈ R + (⟨ , , ⟩) , , ∈ C , ∈ R + ∈ R( + )×( + ) −|| , − , || , ∈ R , , , ∈ R × + −||( + )− || , , ∈ R −||( − )+ −( − )|| , , , ∈ R + −|| + − || , ∈ R ∈ R ∈ R × ( ) , ∈ R ∈ R ∈ R × + ( ⎡ ⎣ ⎤ ⎦) , , ∈ R ∈ R ∈ R × ( [ ... ] + + ) , ∈ R , ∈ R ∈ R × [ ... ] ∈ R × × ⇒

6. , , Θ ( |Θ) = | | ∏ = | | ∏ = |R| ∏ = ( , , |σ( ( , , ;Θ))) ∗ σ( ) = + (− ) ∗ ( | ) = = − = ˆΘ = Θ {− ( |Θ)} = Θ − ∑ ( , , ) , , σ( ( , , ;Θ)) +( − , , ) ( −σ( ( , , ;Θ)))

7. ( , , ) ∈ ∀ ∈ ( , , ) ̸∈

8. ( , , ;Θ)

9. + ( , , ) (?, , ) ( , ,?) = | | | | ∑ = @ ≤ ( , , ) ∈

10. ( , , ) ∈ ( , , ;Θ) = Θ = { }∀ ∈R ∪{ } | | | | ≈ | | | |

11. ∈ R| |× ∈ R × | | | | ≈ | | | | ⇒

12. ⊗ R ×R → R × = [ , , ] = [ , , ] = ( ⊗ ) = [ , , , , , , , , ] ( ) ⇒ ( , , ) = = ( ⊗ ) ⇒

13. ∈ R × ∈ R × ∈ R × = = = =

14. + | | | | ≈ | | | | = ( ) ( , , ) = = = ⟨ , , ⟩ ∗ = ( )

15. = , = ( , , ) = ( , , ) ⇒ +

16. ∗ : R ×R → R = ∗ = + + = + + = + + ∗ = ∗ ( ) ∗ = F− (F( )⊙F( ))

17. ⋆ : R ×R → R = ⋆ = + + = + + = + + ⋆ ̸= ⋆ ( ) ⋆ = F− (F( )⊙F( ))

18. , ∈ , ∈ R ∈ R ∈ R ( , , ) = ( ⋆ ) ( ) ( ) ( , , ) ̸= ( , , )

19. ∈ C × ∗ = ∗ ∗ = = = − = − ∗ = ∗ = − ⇒

20. ∈ C × ∈ C × ∈ C × ∗ = ∗ = = ∗ = ∗

21. + + ∈ R × = ( ∗ ) ∈ C × ∈ C × = ⎛ ⎜ ⎝ , + , ··· , + , , + , ··· , + , ⎞ ⎟ ⎠ ∈ C × ′ = ⎛ ⎜ ⎝ , , ··· , , , , ··· , , ⎞ ⎟ ⎠ ∈ R ×

22. + = ⎛ ⎜ ⎝ , + , ··· ··· , + , ⎞ ⎟ ⎠ ∈ C × ′′ = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ , − , ··· , , ··· ··· , − , ··· , , ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ∈ R × ( ∗ ) = ′ ′′ ′

23. + | | | | ≈ | | | | = ′ ′′ ′ ( ) .( , , ) = ′ ′′ ′ = ′ ′′ ′ = ( ) = (⟨ , , ⟩)

24. ω = F( ) ψ = F( ) ψ = F( ) ( , , ) = ( ⋆ ) = ω (ψ ⊙ψ ) α ←→ α F( ) + ←→ F( )+F( ) ∗ ←→ F( )⊙F( ) ⋆ ←→ F( )⊙F( ) · = F( )·F( ) ( , , ) = .( , , )

25. − ∈ R( + )×( + ) = + × = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ , − , ··· ··· , , ··· ··· ··· , − , ··· ··· , , ··· ··· ··· ··· ··· ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

26. | | | | ≈ | | | | = + ,+ + + ( , , ) = ( , , )+ .( , , )

27. ( ) ✓ ( ) ✗ ( ) ✓ ( ) ✓ ( ) ✓ + = +

28. , ,... = ∀ , ∀ ∈ R

29. 0.4 0.5 0.6 0.7 0.8 0.9 1 ANALOGY ComplEx HolE DistMult RESCAL TransE MRR Hits at 3 Hits at 5 ⇒

30. + ( , )∧ ( , ) ⇒ ( , ) = , X Y S = { : X ∩ X ̸= /0} O = { : Y ∩ Y ̸= /0} S O ,..., ≈ ≈ ≈ ( , ... )

31. =: / / /.../ =: { } / =: { : ∃ ∈ ,( , , ) ∈ } =: / =: T ( ) ( , ) = M( , ) ⇒ T M

32. T ( ) = M( , ) = ( / / /.../ , ) = ... T ( ) = + M( , ) = −|| − || ( / / /.../ , ) = −|| + +···+ − ||

33. ( , , ) (?, , ) (?, , ) (?, , ) ( , ,?) ( , ,?) ( , ,?) ( , ) = ( ) ( ) ∈ { , } ∈ { , } ∈ R × ∈ R ×

34. + +

36. + +

37. + ¨

38. + +

知識グラフの埋め込みとその応用 (第10回ステアラボ人工知能セミナー)

You are reading a preview.

Check these out next

知識グラフの埋め込みとその応用 (第10回ステアラボ人工知能セミナー)

More Related Content

Slideshows for you (20)

Viewers also liked (20)

Similar to 知識グラフの埋め込みとその応用 (第10回ステアラボ人工知能セミナー) (20)

More from STAIR Lab, Chiba Institute of Technology (6)

Recently uploaded (20)