A Degeneracy Framework for Graph Similarity: グラフ類似度のための縮退フレームワーク

Transcript

1. "
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2. ࿦จʹ͍ͭͯ

3. "CPVU
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   w άϥϑΧʔωϧʹ
 ڵຯ͕͋ͬͨ

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   αϙʔτϕΫτϧϚγϯʣ
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   w ରশੑɿ
   w ਖ਼ఆ஋ੑɿ k : × → ℝ+ ∀x, y ∈ : k(x, y) = k(y, x) ∀n ∈ ℕ, x1 , …, xn ∈ : (Gij ) ≜ (k(xi , xj )) ∈ ℝn×n (
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5. ‣ άϥϑΧʔωϧ͸άϥϑͷϖΞΛೖྗͱ͢ΔΧʔωϧؔ਺
   w ͭ·ΓɺάϥϑΧʔωϧͰάϥϑಉ࢜ͷྨࣅ౓Λܭࢉ͢Δ͜ͱ͕Ͱ͖Δ
   ‣ ͳͥάϥϑΧʔωϧ͕ॏཁͳͷ͔ʁ
   w ੈͷதͷσʔλͷଟ͘͸ɺہॴతʹ΋େҬతʹ΋ԿΒ͔ͷߏ଄Λ͍࣋ͬͯΔ͜ͱ͕ଟ͘ɺ άϥϑ͸ϩεϨεͳσʔλදݱͷྑ͍ۙࣅ
   w

   w w w w άϥϑΧʔωϧ͸άϥϑΛ௚઀ೖྗͱͯ͠ѻ͑ΔΞϧΰϦζϜͷઃܭʹ໾ཱͭ άϥϑΧʔωϧͱ͸ʁ k( , ) = 100

6. άϥϑΧʔωϧͷԠ༻ྫ https://art.ist.hokudai.ac.jp/~takigawa/data/fpai94_takigawa.pdf

7. άϥϑΧʔωϧ͕΍͍ͬͯΔ͜ͱ k( , ) = ⟨ϕ( ), ϕ( )⟩ℋ =

   100 ࠶ੜ֩ώϧϕϧτۭؒ
   3,)4 σʔλۭؒʢू߹ʣ ℋ = (ℝd, ⟨ ⋅ , ⋅ ⟩ℋ ) ϕ : → ℋ ϕ( ) ϕ( ) ໌ࣔతʹಛ௃ྔΛੜ੒ʢJF
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   3,)4
   ٴͼП͕ʢඇ໌ࣔతʹʣҰҙʹܾఆ͞ΕΔ͜ͱ͕஌ΒΕ͍ͯΔʢΧʔωϧτϦοΫʣɻ ಛ௃ϕΫτϧ΁ͷม׵ʢҰൠʹ͸ඇઢܗࣸ૾ʣ Ұൠʹ͸࣍ݩ਺
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   w ֶशΞϧΰϦζϜͰඞཁͳܭࢉ͕ɺಛ௃ۭؒ಺Ͱͷσʔλಉ࢜ͷ಺ੵʢJF
   Χʔωϧؔ਺ͷग़ྗ஋ʣ ͷΈʹґଘ͢Δͱ͖
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9. ຊ୊ʹ໭Δ

10. ͜ͷ࿦จͰఏҊ͢Δ΋ͷ ‣ άϥϑͷ֊૚ߏ଄Λ໌ࣔతʹར༻͢Δ৽ͨͳάϥϑΧʔωϧΛఏҊ
    w ֊૚ߏ଄Λௐ΂Δͷʹ
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    w ͭ·Γɺ

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    BDDVSBDZ
    ͕޲্ͨ͠

11. άϥϑͷॖୀʢEFHFOFSBDZʣ ‣ ॖୀʢEFHFOFSBDZʣ͸άϥϑʹର͢Δੑ࣭
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12. LDPSF
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13. LDPSF
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    w ࠓߏங͍ͯ͠Δ
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14. LDPSF
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    w ྫ͑͹ιʔγϟϧωοτϫʔΫͰ͸ɺத৺త ਓ෺Ͱߏ੒͞ΕΔίϛϡχςΟʔ͕֘౰ Cδ*(G)

    ⊆ … ⊆ C1 ⊆ C0 = G LDPSF͕ߏஙͰ͖Δ࠷େͷL
    
    άϥϑͷॖୀ਺ άϥϑͷྨࣅ౓΋
    LDPSF
    ͝ͱͷྨࣅ౓ͰଌΔͷ͕ྑ͍ͷͰ͸ʁ

15. ఏҊख๏

16. ʲఏҊख๏ʳ$PSF
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    w ྫʣL
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    LDPSF
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17. $PNQVUBUJPOBM
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    Lʣͷখ͍͞ํ
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    w

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18. ࣮ݧ

19. ࣮ݧͷηοςΟϯά ‣ σʔληοτɿ
    w όΠΦΠϯϑΥϚςΟΫεͱιʔγϟϧ ωοτϫʔΫ༝དྷͷσʔληοτΛར༻
    ‣ ෼ྨ໰୊ɿ
    w 47.Λར༻ͯ͠෼ྨλεΫΛղ͘
    

    w ௒ύϥϝʔλ͸
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    w ϕʔεάϥϑΧʔωϧ
    
    छʷఏҊϑϨʔ ϜϫʔΫͷ༗ແ
    
    
    छྨ όΠΦΠϯϑΥ ιʔγϟϧωοτ https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets

20. ݁Ռʢฏۉ
    BDDVSBDZ
    ͱͦͷ෼ࢄʣ ଠࣈͷ਺ࣈ͸ɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ޲্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ

21. ݁Ռʢฏۉ
    BDDVSBDZ
    ͱͦͷ෼ࢄʣ ଠࣈͷ਺ࣈ͸ɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ޲্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ όΠΦܥͷσʔλΑΓ΋ιʔγϟϧ ωοτܥͷσʔλͷํ͕ੑೳ޲্͕ ΈΒΕͨ
    
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22. ݁Ռʢฏۉ
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    ͱͦͷ෼ࢄʣ ଠࣈͷ਺ࣈ͸ɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ޲্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ (3Ͱ͸ݦஶʹੑೳ޲্͕ΈΒΕ ΔҰํ 8-Ͱ͸͍·͍ͪޮՌͳ͠ 8-͸֤ϊʔυͷۙ઀Λཁ ໿͢ΔΑ͏ͳΧʔωϧͳͷ

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    ͷ ֓೦ͱ͋·Γ૬ҧແ͠
23. None

24. ࣮ߦ࣌ؒͷ૿େʹؔ͢Δߟ࡯ ‣ ϕʔεΧʔωϧͷ࣮ߦ࣌ؒʹର͢ΔɺLDPSF
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25. ιʔγϟϧωοτϫʔΫͰੑೳ޲্͕ݦஶͳཧ༝ ‣ ωοτϫʔΫͷ࣍਺෼෍͕ҟͳΔ ‣ ΂͖৐ଇʹै͏ωοτϫʔΫ͸ɺΑΓத৺ͷ
    LDPSF
    ʹ༗ӹͳ৘ใ͕٧ ·͍ͬͯΔͱߟ͑ΕΔ

26. ୯Ұ
    LDPSF
    Λ࢖ͬͨ
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    w L
    ͷ
    LDPSF
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    ‣ ؍ଌɿ
    w

    ʲ$PSF
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    w ʲ(3ʳL
    
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     ʢײ૝ʣඞཁ࠷௿ݶͷ৘ใ͕٧·͍ͬͯΔ࠷খͷ෦ ෼άϥϑ͕͜ͷ͋ͨΓͳͷͰ͸ʁ IMDB-BINARYͰͷGRͱCore GR

27. ·ͱΊ

28. ·ͱΊ LDPSF
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    ‣

    ຊ࿦จͰ͸άϥϑΧʔωϧʹద༻͕ͨ͠ɺ೚ҙͷάϥϑϚονϯάΞϧΰϦζϜʹద༻Ͱ͖Δ
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    ‣ ιʔγϟϧωοτϫʔΫͳͲͷɺεέʔϧϑϦʔωοτϫʔΫͰ༗ޮ
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