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

1. "
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2. ࿦จʹ͍ͭͯ
3. "CPVU
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 ڵຯ͕͋ͬͨ
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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਺
   E
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8. Χʔωϧؔ਺ͷ࢖ΘΕ͔ͨ ‣ Χʔωϧؔ਺͕ྗΛൃش͢Δͷ͸ɿ
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   w ֶशΞϧΰϦζϜͰඞཁͳܭࢉ͕ɺಛ௃ۭؒ಺Ͱͷσʔλಉ࢜ͷ಺ੵʢJF
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   w ໨తؔ਺Λࣜมܗͨ͠Γ࠷దԽ໰୊ͷ૒ର໰୊Λղ͘͜ͱͰɺಛ௃ϕΫτϧ͕಺ੵͷܗͰ͔͠ݱΕ ͳ͍ࣜͷΈͷΞϧΰϦζϜΛߏ੒͢Δ
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10. ͜ͷ࿦จͰఏҊ͢Δ΋ͷ ‣ άϥϑͷ֊૚ߏ଄Λ໌ࣔతʹར༻͢Δ৽ͨͳάϥϑΧʔωϧΛఏҊ
    w ֊૚ߏ଄Λௐ΂Δͷʹ
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    w ͭ·Γɺ ఏҊάϥϑΧʔωϧ
    
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11. άϥϑͷॖୀʢEFHFOFSBDZʣ ‣ ॖୀʢEFHFOFSBDZʣ͸άϥϑʹର͢Δੑ࣭
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12. LDPSF
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13. LDPSF
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14. LDPSF
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    LDPSF
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    w άϥϑͷ࠷େ࣍਺
    w ྡ઀ߦྻͷ࠷େݻ༗஋
    
    ‣ ɹɹ͸ϊʔυ਺ΑΓे෼ʹখ͍͞ʢɹɹɹɹʣ͜ͱ͕ଟ͍ͷͰɺLDPSF
    ϑϨʔϜϫʔΫʹཁ͢Δ௥Ճܭࢉ͸ൺֱత୹ͯ͘ࡁΉ c = A × δ* min A δ* min λmax λmax λmax ≪ n
18. ࣮ݧ
19. ࣮ݧͷηοςΟϯά ‣ σʔληοτɿ
    w όΠΦΠϯϑΥϚςΟΫεͱιʔγϟϧ ωοτϫʔΫ༝དྷͷσʔληοτΛར༻
    ‣ ෼ྨ໰୊ɿ
    w 47.Λར༻ͯ͠෼ྨλεΫΛղ͘
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    छྨ όΠΦΠϯϑΥ ιʔγϟϧωοτ https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets
20. ݁Ռʢฏۉ
    BDDVSBDZ
    ͱͦͷ෼ࢄʣ ଠࣈͷ਺ࣈ͸ɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ޲্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ
21. ݁Ռʢฏۉ
    BDDVSBDZ
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22. ݁Ռʢฏۉ
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24. ࣮ߦ࣌ؒͷ૿େʹؔ͢Δߟ࡯ ‣ ϕʔεΧʔωϧͷ࣮ߦ࣌ؒʹର͢ΔɺLDPSF
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25. ιʔγϟϧωοτϫʔΫͰੑೳ޲্͕ݦஶͳཧ༝ ‣ ωοτϫʔΫͷ࣍਺෼෍͕ҟͳΔ ‣ ΂͖৐ଇʹै͏ωοτϫʔΫ͸ɺΑΓத৺ͷ
    LDPSF
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26. ୯Ұ
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    w L
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    LDPSF
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    w ʲ$PSF
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     ʢײ૝ʣඞཁ࠷௿ݶͷ৘ใ͕٧·͍ͬͯΔ࠷খͷ෦ ෼άϥϑ͕͜ͷ͋ͨΓͳͷͰ͸ʁ IMDB-BINARYͰͷGRͱCore GR
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28. ·ͱΊ LDPSF
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    ‣ ຊ࿦จͰ͸άϥϑΧʔωϧʹద༻͕ͨ͠ɺ೚ҙͷάϥϑϚονϯάΞϧΰϦζϜʹద༻Ͱ͖Δ
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