Graph: A Survey of Graph Neural Networks, Embedding, Tasks and Applications

グラフに関連する話題について幅広くサーベイを行い、30本の重要論文と70本の関連論文にまとめました。
※こちらは発表のための縮小版です
※ 発表はこちらで行いました。動画もあります（ https://nlpaper-challenge.connpass.com/event/136090/ ）
GNN, GCN, RelationalGCN and other GNNs, Link Prediction, Graph Classification, Graph Completion, Graph Representation/Embedding, Graph Kernel, Combinatorial/Logical, その他の最近の話題, CV, NLP, Molecular Graph Generation, Recommendation などの Application について、2016年以降の研究成果を中心に紹介します。

Transcript

1. (SBQI
   "4VSWFZPG(SBQI/FVSBM/FUXPSLT &NCFEEJOH
   5BTLTBOE"QQMJDBUJPOT
   

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2. Kenshi Uchihashi
   uchi_k @wednesdaymuse
   About me
   nlpaper.challenge ӡӦ
   Freelance Machine Learning
   ɹɹɹɹɹEngineer / Researcher
   former ະ౿16, ژେ৘ใӃ,
   FreakOut Machine Learning Engineer
   

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3. αʔϕΠํ๏
   • ؔ࿈Ωʔϫʔυ ݚڀऀͷચ͍ग़͠
   ◦ (PPHMF4DIPMBS΁
   • ॏཁ࿦จͷબఆ
   ◦ ͢ͰʹධՁ͕ఆ·ͬͨ΋ͷʹ͍ͭͯ͸Ҿ༻਺
   ◦ ೥ʹग़൛͞Εͨ΋ͷʹ͍ͭͯ͸಺༰ͰධՁ༗໊ݚڀऀ΍ϥϘ
   ◦ ༗ࣝऀʹฉ͘
   • $POGFSFODF
   ◦ /FVS*14
   *$-3
   *$.-
   """*
   ʜ
   ◦ ,%%
   888
   ʜ
   ◦ BSYJW
   ʜ
   • ࿦จͷ෼໺͸࠷΋ߩݙ͕େ͖͍ͱࢥͬͨ෼໺ʹׂΓৼΓ
   • ྫ͑͹$7΁ͷΞϓϦέʔγϣϯ࿦จͰ΋৽ͯ͘͠༗༻ͳ($/ͷϑϨʔϜ
   ϫʔΫΛఏҊ͍ͯ͠Ε͹෼໺͸($/ΛׂΓ౰ͯΔɺͳͲ
   

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4. ஫ҙ
   • ਤ΍਺ࣜ͸࿦จ͔ΒҾ༻͍ͯ͠·͢
   ◦ Ҿ༻ݩͷ࿦จ͸λΠτϧͷ࿦จͰ͢
   • ҎԼͷ஌ࣝΛલఏͱ͠·͢
   ◦ χϡʔϥϧωοτϫʔΫͷجૅ஌ࣝ
   ◦ .-1 DPOWPMVUJPO QPPMJOH $// 3// -45. ʜ
   ◦ άϥϑʹؔ͢Δجૅ༻ޠ
   ◦ ϊʔυ Τοδ ༗޲ແ޲ ॏΈ෇͖ͳ͠ ྡ઀ߦྻ άϥϑϥϓϥγΞϯ
   ◦ ͦͷଞ
   ◦ BEWFSTBSJBMBUUBDL TVCUSFF ʜ
   • ಛʹஅΓ͕ͳ͚Ε͹͍͍ͩͨϧʔϓ΍ଟॏΤοδΛ࣋ͨͳ͍άϥϑΛѻ͍ͬͯ·͢
   • ਺ࣜ͸௥Θͣɺ࿦จ಺Ͱॏཁͳ΋ͷʹߜͬͯղઆ͢ΔελΠϧͰ͢
   • ࿦จͷࡉ͔͍ͱ͜Ζ͸঺հͰ͖ͳ͍ͷͰɺݚڀͷେ͖ͳྲྀΕॏࢹͰ͢
   

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5. ஫ҙ
   • ॏཁ࿦จຊɺؔ࿈࿦จຊʹ·ͱΊ·ͨ͠ʢൃද൛Ͱ͸൒෼͘Β͍ʹݮΒͯ͠
   ͍·͢ʣ
   • ൃදͰ͸جૅతͳ಺༰ʹ͠΅Γ·ͨ͠
   ◦ (//
   ◦ ($/
   ◦ PUIFS(//T
   ◦ (SBQI3FQSFTFOUBUJPO&NCFEEJOH
   ◦ /PEFGPDVTFE5BTL
   ◦ (SBQIGPDVTFE5BTL
   ◦ 5BTLT
   ◦ $PNCJOBUPSJBM-PHJDBM "EWFSTBSJBM"UUBDL .BUDIJOH FUD
   ◦ "QQMJDBUJPOT
   ◦ $7 /-1 3FMBUJPO&YUSBDUJPO 3FDPNNFOEBUJPO .PMFDVMBS
   (SBQI(FOFSBUJPO 1IZTJDT
   • ൣғΛ޿͗ͨ͘͢͠ײ͋ΔΜͰ͕͢ɺޙ೔VQ͢ΔࢿྉͰิ׬͍ͩ͘͞
   

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6. /FVSBM/FUXPSLTPO(SBQI
   

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7. 5IF(SBQI/FVSBM/FUXPSL.PEFM
   #Graph Neural Network
   *&&&5// 4DBSTFMMJ 'SBODP 6OJWFSTJUZPG4JFOB
   BOE(PSJ .BSDPBOE5TPJ "I$BOE)BHFOCVDIOFS .BOE.POGBSEJOJ ( DJUBUJPOT
   ྡ઀Τοδϥϕϧ ϊʔυঢ়ଶ ྡ઀ϊʔυϥϕϧ
   ϊʔυϥϕϧ
   • ࠷ۙ๣ϊʔυͷ৘ใΛ࠶ؼతʹ
   BHHSFHBUF͢Δ
   • LճͷBHHSFHBUJPOʹΑͬͯɺLIPQ
   ͷ৘ใ͕औಘͰ͖Δ
   • ༧ΊܾΊΒΕͨλΠϜεςοϓͰֶश͕
   ऴྃ͢ΔͷͰԕ͘ͷϊʔυͷ৘ใ͕औΕ
   ͳ͍͜ͱ͕͋Δ
   ϊʔυ͕ϝοηʔδΛ఻೻͍ͯ͘͠࢓૊ΈͰ(//Λಋग़ͨ͠
   άϥϑߏ଄Λͦͷ··χϡʔϥϧωοτʹམͱ͠ࠐΊΔΑ͏ʹ
   

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8. w ೖྗϊʔυू߹ΛΫϥελϦϯά͍ͯ͘͠
   w ΛݸͷΫϥελʹ෼͚ͨ݁Ռ͕
   w ͸ྡ઀ؔ܎͕͋Δͱ͜ΖͷΈ஋Λ࣋ͭε
   ύʔεͳϑΟϧλʔ
   4QFDUSBM/FUXPSLTBOE-PDBMMZ$POOFDUFE/FUXPSLTPO(SBQIT
   #GCN #SpatialGCN #SpectralGCN #Spectral Clustering
   *$-3 +PBO#SVOB /FX:PSL6OJWFSTJUZ
   8PKDJFDI;BSFNCB "SUIVS4[MBN :BOO-F$VO DJUBUJPO
   άϥϑʹ͓͚Δہॴੑͱղ૾౓Λఆٛ͠ɺ$//Λάϥϑʹ֦ு͢Δํ๏Λ
   4QBUJBMͱ4QFDUSBMͷछྨఏҊ
   ྡ઀ߦྻΛ༻͍ͨہॴੑ
   NVMUJTDBMFDMVTUFSJOHʹΑΔղ૾౓
   ϊʔυू߹ ྡ઀ߦྻ
   ᮢ஋Λద౰ʹઃఆ͢Δ͜ͱͰہॴੑΛදݱ
   Ϋϥελʹؚ·ΕΔશϊʔυͷಛ௃ྔΛೖ
   ྗͱ͠ɺ୅ද஋ͱͯ͠Ұͭͷಛ௃ྔΛग़ྗ
   ϓʔϦϯά
   4QBUJBM$POTUSVDUJPO
   ϑΟϧλʔ
   

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9. 4QFDUSBM/FUXPSLTBOE-PDBMMZ$POOFDUFE/FUXPSLTPO(SBQIT
   #Graph Neural Network #Spectral Clustering #Fourier Transform
   *$-3 +PBO#SVOB /FX:PSL6OJWFSTJUZ
   8PKDJFDI;BSFNCB "SUIVS4[MBN :BOO-F$VO DJUBUJPO
   ϑʔϦΤม׵͸೾ܗΛप೾਺੒෼ʹ෼ղ͢Δ͕ɺάϥϑϑʔϦΤม׵͸άϥϑ্Ͱఆٛ͞Εͨ৴
   ߸ʹରͯ͠৴߸ͷٸफ़͞Λఆٛ͠ɺٸफ़͞͝ͱʹ੒෼෼ղ
   άϥϑϥϓϥγΞϯͷݻ༗஋ܭࢉͰٸफ़͞੒෼΁ͷ෼ղ͕Մೳ
   DPOWPMVUJPO͸'PVSJFSEPNBJOʹ͓͚Δཁૉੵʹ૬౰͢Δͱ͍͏ఆཧΛ༻͍ͯɺཁૉੵͰ
   DPOWPMVUJPO͢Δ͜ͱ͕Ͱ͖ΔΑ͏ʹͳΔ
   ཁૉੵʹରͯ͠ٯϑʔϦΤม׵ΛͱΔ
   ݻ༗஋ܭࢉͱݻ༗ϕΫτϧͷੵͷܭࢉίετ͕େ͖͍
   4QFDUSBM$POTUSVDUJPO
   ϑʔϦΤجఈʹରԠͨ͠άϥϑϥϓϥγΞϯͷݻ༗ϕΫτϧͷ݁߹܎਺ΛมԽ͞
   ͤΔ͜ͱͰάϥϑ্ͷಛ௃ྔม׵͕ఆٛͰ͖Δ
   ݻ༗ϕΫτϧ
   

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10. $POWPMVUJPOBM/FVSBM/FUXPSLTPO(SBQIT
    XJUI'BTU-PDBMJ[FE4QFDUSBM'JMUFSJOH
    #GCN #Spectral Filtering #Chebyshev Polynomials
    /FVS*14 .JDIBËM%F⒎FSSBSE &1'-
    9BWJFS#SFTTPO 1JFSSF7BOEFSHIFZOTU DJUBUJPOT
    ݻ༗஋ߦྻ
    νΣϏγΣϑଟ߲ࣜۙࣅʹΑͬͯݻ༗஋෼ղΛճආ͠ɺ($/ͷܭࢉྔΛԼ͛Δ
    νΣϏγΣϑଟ߲ࣜۙࣅ
    ݻ༗஋ܭࢉͱݻ༗ϕΫτϧͷੵͷܭࢉίετ͕
    େ͖͍໰୊Λ͔ͳΓղܾ
    'PVSJFSEPNBJOͰఆٛ͞ΕͨϑΟϧλ
    Λ༻͍ͨ৞ΈࠐΈ͸ɺ
    ݻ༗஋ͷεέʔϦϯά
    ଟ߲ࣜۙࣅͨ͠ํ͕ਫ਼౓΋্͕ͬͨ
    νΣϏγΣϑଟ߲ࣜͷ࣍਺,͕ϑΟϧλαΠζ
    ͱରԠ͍ͯ͠Δ
    

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11. 4FNJ4VQFSWJTFE$MBTTJpDBUJPOXJUI(SBQI$POWPMVUJPOBM/FUXPSLT
    #GCN #Semi-Supervised Learning
    *$-3 5IPNBT/,JQG .BY8FMMJOH DJUBUJPOT
    ྡ઀ϊʔυͷ৞ΈࠐΈͷΈͰ4QFDUSBM($/ͷۙࣅ͕Ͱ͖Δ͜ͱΛࣔͨ͠
    w νΣϏγΣϑଟ߲ࣜۙࣅͷϞσϧͷ,ͷ৔
    ߹ʢ࠷ۙ๣ͷΈࢀর͢Δʣ
    w Ϟσϧͷදݱೳྗ͸Լ͕Δ
    w %//ͷΑ͏ʹɺޯ഑ফࣦʹରԠ͢ΔςΫ
    χοΫΛಋೖʢSFOPSNBMJ[BUJPOUSJDLʣ
    աֶशͷ཈੍ޮՌʹΑͬͯɺۙࣅͨ͠΄͏͕ਫ਼౓͕ྑ͘ͳ͍ͬͯΔ
    ଟ߲ࣜۙࣅͨ͠ํ͕ਫ਼౓΋্͕ͬͨ
    ϥϕϧ͕෇͍͍ͯΔσʔλʹ͍ͭͯɺTPGUNBYDSPTTFOUSPQZʹΑֶͬͯश͢Δ
    ඪ४తͳ($/ͱͯ͠ҎԼͷఆࣜԽΛͨ͠
    

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12. (BUFE(SBQI4FRVFODF/FVSBM/FUXPSLT
    #GNN #LSTM #Sequence
    *$-3 :VKJB-J %FQBSUNFOUPG$PNQVUFS4DJFODF 6OJWFSTJUZPG5PSPOUP
    %BOJFM5BSMPX .BSD#SPDLTDINJEU BOE3JDIBSE;FNFM DJUBUJPOT
    w (//ͷঢ়ଶߋ৽͸࣮࣭3//͕ͩͬͨɺ͜͜Λ-45.΍(36ʹมߋ͢Δ
    w ޯ഑ܭࢉʹʢ"MNFJEB1JOFEBΞϧΰϦζϜͰ͸ͳ͘ʣ#155Λ࢖༻
    w 4FRVFODFͳग़ྗΛֶशՄೳʹͳΓɺେ͖͘Ԡ༻෯͕૿͑ͨ
    -45.΍(36Ͱঢ়ଶߋ৽Λߦ͏(//Λಋग़
    ίʔυͷ৴པੑධՁͳͲͷଟ༷ͳλεΫ΁ͷԠ༻Մೳੑ͕ੜ·Εͨ
    (36΍-45.ʹସ͑Δ
    ΑΓεϚʔτͳɺ࣌୅ʹԊͬͨఆࣜԽΛͨ͠
    

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13. )PX1PXFSGVMBSF(SBQI/FVSBM/FUXPSLT
    #GNN #WL test #Graph Isomorphism Network
    *$-3 ,FZVMV9V .*5
    8FJIVB)V +VSF-FTLPWFD 4UFGBOJF+FHFMLB DJUBUJPOT
    (//TΛఆࣜԽ͠ɺ8-UFTUͱಉ౳ͷੑೳΛಘΔͨΊʹඞཁͳ੍໿Λಋग़ͨ͠
    (//TͷఆࣜԽ
    ϊʔυWͷಛ௃ϕΫτϧ
    • "((3&("5&ͱ$0.#*/&ͷTUFQʹ෼͚Δ
    • (SBQIGPDVTFE5BTLͰ͸3&"%065Ͱશϊʔυ৘ใΛू໿
    FY
    (SBQI4"(&
    FY
    ($/
    "((3&("5&ͱ$0.#*/&ʹԿΛબͿ͔Ͱطଘͷ(//T͸هड़Ͱ͖Δ
    • $0.#*/&ͳ͠
    

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14. )PX1PXFSGVMBSF(SBQI/FVSBM/FUXPSLT
    #GNN #WL test #Graph Isomorphism Network
    *$-3 ,FZVMV9V .*5
    8FJIVB)V +VSF-FTLPWFD 4UFGBOJF+FHFMLB DJUBUJPOT
    "((3&("5&ͱ$0.#*/&Ͱهड़Ͱ͖Δ(//T͸άϥϑ෦෼ߏ଄ͷࣝผ
    ೳྗ͕8-TVCUSFFLFSOFMͱ౳ՁͰ͋Δ
    (//Tͷදݱೳྗͷߴ͞Λ෼ੳ͍ͨ͠
    ཧ૝తʹ͸ɺҟͳΔάϥϑΛ׬શʹࣝผͰ͖Δ͔Ͳ͏͔͕άϥϑͷදݱೳྗͷߴ͞
    Λද͕͢ɺ͜Ε͸ಉܕੑࣝผ໰୊ʢ/1ʣΛղܾͨ͜͠ͱʹͳΔʢʂʣ
    ݁࿦
    8-UFTUͰͷϊʔυͷಛ௃ϕΫτϧ͸POFIPUϕΫτϧͰTVCUSFFؒ
    ͷྨࣅੑͳͲΛಘΔ͜ͱ͸Ͱ͖ͳ͍ͷʹର͠ɺ(//TͰ͸Մೳ
    (//T͕8-UFTUΛֶशϕʔεͰ࿈ଓۭؒʹ֦ுͨ͠΋ͷʹͳ͍ͬͯΔ
    ͳͷͰɺFNCFEEJOH΍άϥϑߏ଄ؒͷEFQFOEFODZ΋औಘՄೳ
    

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15. )PX1PXFSGVMBSF(SBQI/FVSBM/FUXPSLT
    #GNN #WL test #Graph Isomorphism Network
    *$-3 ,FZVMV9V .*5
    8FJIVB)V +VSF-FTLPWFD 4UFGBOJF+FHFMLB DJUBUJPOT
    "((3&("5&ʹ.&"/΍."9Λ࢖͏ͱ8-UFTUʹྼΔͷͰɺ46.Λ࢖͍·͠ΐ͏
    ʢͨͩ͠ɺλεΫʹΑͬͯ͸͍͍ͱ͜Ζ΋͋Δʣ
    8-UFTUอূͷ͋Δ(*/ʢ(SBQI*TPNPSQIJTN/FUXPSLʣΛఏҊ
    ࣗ෼ࣗ਎ʹద౰ͳ܎਺Λ͔͚ͯɺશͯͷྡ઀ϊʔυͱͷ࿨Λͱͬͯ.-1ʹೖྗ͢
    Δͱ͍͏γϯϓϧͳߏ੒ʢ"((3&("5&ͷΈʣͰ΋ɺ
    ଞͷෳࡶͳϞσϧͱཧ࿦্ಉఔ౓ͷੑೳ͕ظ଴Ͱ͖Δɻ
    

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16. (SBQI/FVSBM/FUXPSL
    • "OFXNPEFMGPSMFBSOJOHJOHSBQIEPNBJOT
    ◦ *+$// .BSDP(PSJ 6OJWFSTJUZPG4JFOB
    FUBM DJUBUJPOT
    ◦ (SBQI/FVSBM/FUXPSLΛఏҊ
    • (SBQI8BSQ.PEVMFBO"VYJMJBSZ.PEVMFGPS#PPTUJOHUIF1PXFSPG
    (SBQI/FVSBM/FUXPSLT
    ◦ BS9JW ,BUTVIJLP*TIJHVSP 1SFGFSSFE/FUXPSLT
    FUBM
    DJUBUJPOT
    ◦ (//ͷදݱೳྗͷ௿͞Λ໰୊ࢹ͠ɺදݱೳྗΛ্͛Δ(SBQI8BSQ.PEVMF
    ʢ(81ʣΛఏҊɺখ͞ΊͷάϥϑͰ͋Δඞཁ͕͋Δ͕ɺಛʹ૑ༀͰ݁ՌΛग़͢
    • 8FJTGFJMFSBOEMFNBOHPOFVSBM)JHIFSPSEFSHSBQIOFVSBMOFUXPSLT
    ◦ """* $ISJTUPQIFS.PSSJT FUBM DJUBUJPOT
    ◦ )PX1PXFSGVM"SFʙͷ݁ՌΛड͚ͯɺߴ࣍ͷ8-TVCUSFFLFSOFMʹର͢Δ
    (//Λߏங
    

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17. (SBQI/FVSBM/FUXPSL
    • -FBSOJOH$POWPMVUJPOBM/FVSBM/FUXPSLTGPS(SBQIT
    ◦ *$.- .BUIJBT/JFQFSU /&$-BCT&VSPQF
    FUBM DJUBUJPOT
    ◦ 8-HSBQILFSOFMͰάϥϑΛલॲཧͯ͠$//ʹೖΕΔ1BUDIZTBOΛఏҊ
    • 8BWFMFUTPO(SBQITWJB4QFDUSBM(SBQI5IFPSZ
    ◦ "QQMJFEBOE$PNQVUBUJPOBM)BSNPOJD"OBMZTJT %BWJE,
    )BNNPOE FUBM DJUBUJPOT
    ◦ άϥϑ৴߸ॲཧͷจ຺ͰΑ͘Ҿ༻͞ΕΔ࿦จ
    • 5IF&NFSHJOH'JFMEPG4JHOBM1SPDFTTJOHPO(SBQIT&YUFOEJOH)JHI
    %JNFOTJPOBM%BUB"OBMZTJTUP/FUXPSLTBOE0UIFS*SSFHVMBS%PNBJOT
    ◦ "*&&&4JHOBM1SPDFTTJOH.BHB[JOF %*4IVNBO &1'-
    FUBM
    DJUBUJPOT
    ◦ άϥϑ৴߸ॲཧͷจ຺ͰΑ͘Ҿ༻͞ΕΔ࿦จ
    

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18. (SBQI/FVSBM/FUXPSL
    • )JHIFSPSEFS(SBQI$POWPMVUJPOBM/FUXPSLT
    ◦ *$.- 4BNJ"CV&M)BJKB 6OJWFSTJUZPG4PVUIFSO$BMJGPSOJB
    FUBM
    DJUBUJPOT
    ◦ POFIPQͳྡ઀ߦྻ͔ΒNVMUJIPQͳྡ઀ߦྻ΁֦ுͨ͠($/ΛఏҊ
    • %ZOBNJD(SBQI$POWPMVUJPOBM/FUXPSLT
    ◦ BS9JW 'SBODP.BOFTTJ 8BZOBVU
    FUBM DJUBUJPOT
    ◦ ಈతʹมԽ͢Δάϥϑͷղੳ͕Մೳʹͳͬͨ
    • (SBQI6/FUT
    ◦ *$.- )POHZBOH(BP 5FYBT".6OJWFSTJUZ
    4IVJXBOH+J
    DJUBUJPOT
    ◦ 6/FUTΛάϥϑͰ΋Ͱ͖ΔΑ͏ʹ͢ΔͨΊʹɺHSBQIQPPMJOHͱHSBQI
    VOQPPMJOHΛఆٛ
    

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19. (SBQI3FQSFTFOUBUJPO
    

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20. %FFQXBML0OMJOFMFBSOJOHPGTPDJBMSFQSFTFOUBUJPOT
    #Representation #Online Learning #Graph Embedding
    ,%% #SZBO1FSP[[J 3BNJ"M3GPV 4UFWFO4LJFOB DJUBUJPOT
    άϥϑ্ͰϥϯμϜ΢ΥʔΫΛߦ͍ɺಘΒΕͨܥྻΛ4LJQHSBNʹೖྗ͢Δ͜ͱͰ
    ϊʔυͷ෼ࢄදݱΛಘΔ
    જࡏදݱΛॳظԽ
    ͋Δϊʔυ͔Βग़ൃͯ͠ϥϯμϜ
    ΢ΥʔΫΛߦ͏
    ಘΒΕͨܥྻΛ4LJQHSBN΁
    ೖྗ
    ؔ܎ੑͷ͍ۙϊʔυΛ༧ଌ͠ɺ
    άϥϑͷϕΫτϧදݱΛಘΔ
    ڞىͷ֬཰͚ͩͰ͸ͳ͘ɺજࡏදݱ΋Ұॹʹֶश͍ͨ͠ͷͰɺ
    જࡏදݱͷܭࢉίετΛԼ͛Δ޻෉͕͞Ε͍ͯΔ
    άϥϑͷಛ௃Λଊ͑ɺؔ܎ੑͷ͍ۙϊʔυΛۙ͘ʹ഑ஔͰ͖Δ
    

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21. -*/&-BSHFTDBMF*OGPSNBUJPO/FUXPSL&NCFEEJOH
    #Graph Embedding #Edge Sampling
    888 +JBO5BOH .JDSPTPGU3FTFBSDI"TJB
    FUBM DJUBUJPOT
    ௚઀ϦϯΫΛ࣋ͨͳ͍ϊʔυͰ΋͍ۙ͠ಛ௃Λ༗͍ͯ͠ΔͳΒߟྀͯ͠
    &NCFEEJOH͢Δख๏ΛఏҊ
    ϩʔΧϧͳߏ଄ʢpSTUPSEFSQSPYJNJUZʣͱ
    άϩʔόϧͳߏ଄ʢTFDPOEPSEFSQSPYJNJUZ
    ڞ௨͍ͯ͠Δଞͷ௖఺͕ࣅ͍ͯΔ͔Ͳ͏͔Λධ
    Ձʣͷ྆ํΛߟྀͯ͠FNCFEEJOHΛߦ͏
    pSTUPSEFSQSPYJNJUZ
    ɹɹ௚઀؍ଌ͞ΕΔϊʔυಉ࢜ͷۙ઀ؔ܎
    second-order proximity:
    ɹɹಉ͡Α͏ͳྡ઀ؔ܎Λ࣋ͭۙ઀ϊʔυ
    ΤοδͷॏΈͷ෼ࢄ͕େ͖͘ͳΔͱֶश཰ͷௐ੔͕೉͘͠ͳΔͷͰΤοδαϯϓ
    ϦϯάΛ޻෉͍ͯ͠Δ
    888 ,%%͔ΒEBUBNJOJOH ੺
    /*14 *$.-͔ΒNBDIJOFMFBSOJOH ੨
    
    $713 *$$7͔ΒDPNQVUFSWJTJPO ྘
    ͰBVUIPSTOFUXPSLΛՄࢹԽ
    

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22. OPEFWFD4DBMBCMF'FBUVSF-FBSOJOHGPS/FUXPSLT
    #Graph Embedding #DFS #DeepWalk
    ,%% "EJUZB(SPWFS 4UBOGPSE6OJWFSTJUZ
    +VSF-FTLPWFD DJUBUJPOT
    %FFQ8BMLͷܥྻऔಘ͕3BOEPN8BMLͰ͋Δͱ͜ΖΛվળ͠ɺ
    άϥϑΒ͍͠ํ๏ΛఏҊ
    ෯༏ઌ୳ࡧͬΆ͍#SFBEUIpSTU
    4BNQMJOHʢ#'4ʣͱਂ͞༏ઌ୳ࡧͬΆ͍
    %FQUIpSTU4BNQMJOHʢ%'4ʣΛఆٛ
    #'4͹͔Γॏࢹɾɾɾۙྡͷؔ܎͔͠ݟΕͳ͍ɻ͜Ε·Ͱ͸͜Εͩͬͨɻ
    ɹɹɹɹɹɹɹɹɹɹಉ͡ϊʔυ͹͔Γࢀরͯ͠͠·͏
    %'4͹͔Γॏࢹɾɾɾۙ๣ΛΑΓԕ͘ͷϊʔυ͔Βߏ੒͢Δɻ
    ɹɹɹɹɹɹɹɹɹɹͨͩ͠෼ࢄ͕େ͖͘ͳΔ
    αϯϓϦϯάઓུΛ࣋ͭ%FFQ8BMLΛఆࣜԽ
    

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23. (SBQI("/(SBQI3FQSFTFOUBUJPO-FBSOJOH
    XJUI(FOFSBUJWF"EWFSTBSJBM/FUT
    #GAN #Graph Softmax
    """* )POHXFJ8BOH 4IBOHIBJ+JBP5POH6OJWFSTJUZ
    +JB8 +JBMJO8 .JBP; 8FJOBO; 'V[IFOH; 9JOH9JF .JOZJ(VP DJUBUJPOT
    w (ͱQ@USVF͕͍͍ۙͮͯ͘͜ͱΛظ଴
    w ੜ੒ϞσϧͷMPTTܭࢉͰɺάϥϑߏ଄
    ʹదͨ͠෯༏ઌ୳ࡧʹجͮ͘(SBQI
    4PGUNBYΛಋೖ
    w ܭࢉޮ཰΋্͕Δ
    ੜ੒͞ΕͨϊʔυΛࠞͥࠐΉੜ੒Ϟσϧͱɺάϥϑશମͷଥ౰ੑΛ൑ఆ͢ΔࣝผϞσϧ
    Λ༻͍ͯɺάϥϑͰ("/Λ΍Δ
    (SBQI4PGUNBYΛ৽ͨʹಋೖ
    ҟͳΔจ຺Ͱൃల͖ͯͨ͠ੜ੒ϞσϧͱࣝผϞσϧͷ༥߹
    

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24. 8FJTGFJMFS-FINBO(SBQI,FSOFMT
    #WL test #Graph Kernel #Graph Classification #Similarity
    +.-3 /JOP4IFSWBTIJE[F .BY1MBODL*OTUJUVUFT5VCJOHFO
    FUBM DJUBUJPOT
    (ͱ(`ͷશͯͷϊʔυʹ͍ͭͯɺࣗ
    ਎ͱۙ๣ϊʔυͷϥϕϧΛूΊΔ
    ूΊͨϥϕϧΛࣙॻॱͰιʔτ
    ϥϕϧू߹ʹϢχʔΫϥϕϧΛ෇༩
    ͢Δ
    ϥϕϧ਺Λͱͯ͠ɺ܁Γฦ͠ճ਺
    O͕Λຬͨ͢·Ͱଓ͚Δ
    ৽͘͠࡞ΒΕΔϥϕϧू߹͕Ұக͠
    ͍ͯΕ͹ಉܕ
    άϥϑͷಉܕੑΛ൑ఆ͢Δ8FJTGFJMFS-FINBO5FTUΛಋग़
    ಉܕੑ൑ఆͰ͓ͦΒ͘Ұ൪Ҿ༻͞Ε͍ͯΔ
    8-TVCUSFFLFSOFMʹΑΔಛ௃ྔԽ΋
    

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25. (SBQI3FQSFTFOUBUJPO
    • 1Z5PSDI#JH(SBQI"-BSHFTDBMF(SBQI&NCFEEJOH4ZTUFN
    ◦ 4ZT.- "EBN-FSFS 'BDFCPPL"*3FTFBSDI
    FUBM DJUBUJPOT
    ◦ 5SJMMJPOαΠζͷΤοδΛ࣋ͭάϥϑΛFNCFEEJOHͰ͖Δ044
    • *OEVDUJWF3FQSFTFOUBUJPO-FBSOJOHPO-BSHF(SBQIT
    ◦ /FVS*14 8JMMJBN-)BNJMUPO 4UBOGPSE6OJWFSTJUZ
    3FY:JOH +VSF
    -FTLPWFD DJUBUJPOT
    ◦ ۙ๣৘ใ͔ΒFNCFEEJOHΛٻΊΔͨΊͷBHHSFHBUFؔ਺Λֶश͢Δ͜ͱͰ
    ະ஌ϊʔυͷFNCFEEJOHΛֶशͰ͖Δɻ(SBQI4"(&
    • 3FQSFTFOUBUJPOMFBSOJOHPGLOPXMFEHFHSBQITXJUIFOUJUZ
    EFTDSJQUJPOT
    ◦ """* DJUBUJPOT
    ◦ &OUJUZؚ͕·Ε͍ͯͳͯ͘΋આ໌จΛ࢖ͬͯਪ࿦͢Δ[FSPTIPUʹऔΓ૊ΜͰ
    ͍Δ
    

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26. (SBQI3FQSFTFOUBUJPO
    • 3FQSFTFOUBUJPO-FBSOJOHPO(SBQITXJUI+VNQJOH,OPXMFEHF
    /FUXPSLT
    ◦ *$.- ,FZVMV9V FUBM DJUBUJPOT
    • -FBSOJOH-BQMBDJBO.BUSJYJO4NPPUI(SBQI4JHOBM3FQSFTFOUBUJPOT
    ◦ BS9JW 9JBPXFO%POH &1'-
    %PSJOB5IBOPV 1BTDBM'SPTTBSE
    BOE1JFSSF7BOEFSHIFZOTU DJUBUJPOT
    ◦ σʔλ͔Βάϥϑߏ଄Λֶश͍ͨ͠ɻJMMQPTFEQSPCMFN͕ͩάϥϑͷ׈Β͔͞
    Λ͍͍ײ͡ʹ࢖͏
    • 'BTU(SBQI3FQSFTFOUBUJPO-FBSOJOHXJUI1Z5PSDI(FPNFUSJD
    ◦ *$-3 .BUUIJBT'FZ+BO&-FOTTFO 56%PSUNVOE6OJWFSTJUZ
    
    DJUBUJPOT
    ◦ άϥϑ΍%఺܈ͱ͍ͬͨඇϢʔΫϦουߏ଄σʔλ޲͚ͷ%-ϥΠϒϥϦ
    1ZUPSDI(FPNFUSJDͷ঺հ
    

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27. /PEF(SBQIGPDVTFE
    

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28. .PEFMJOH3FMBUJPOBM%BUBXJUI(SBQI$POWPMVUJPOBM/FUXPSLT
    #RGCN #entity prediction #link prediction #relational data
    &48$ .JDIBFM44DIMJDIULSVMM 6OJWFSTJUZPG"NTUFSEBN
    5IPNBT/,JQG 1FUFS#MPFN 3JBOOFWBOEFO#FSH *WBO5JUPW .BY8FMMJOH DJUBUJPOT
    άϥϑߏ଄ͷ෼ੳʹओ؟Λஔ͍ͨ3($/ΛఏҊ͠ɺ
    FOUJUZMJOLQSFEJDUJPOͷ༷ʑͳσʔλͰ4P5"
    w ੺͍ϊʔυ͕ิ׬͞ΕΔ΂͖ϊʔυɺΤοδͰ͋Ε
    ͹ิ׬͞ΕΔ΂͖ؔ܎ੑ
    w ؔ܎ੑʹԠͯۙ͡๣͕มΘΔͱߟ͑ͯɺ৽͍͠৞ࠐ
    ΈΛఆٛ͢Δ
    w ߋ৽͞Εͨ৴߸͔Βϊʔυͷଐੑ༧ଌʢFOUJUZ
    QSFEJDUJPOʣ΍
    BDUJWBUJPOGVODUJPO
    ਖ਼نԽ܎਺
    ຒΊࠐΈϕΫτϧ
    SFMBUJPOSΛ৞ΈࠐΉॏΈߦྻ
    ؔ܎ੑΛߟྀͨ͠($/ΛఆࣜԽ
    

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29. άϥϑ্ͷQPPMJOHΛιϑτΫϥελϦϯάͱͯ͠ఆࣜԽͯ͠HSBQIDMBTTJpDBUJPO
    ֤ϊʔυ͕࣍ͷϨΠϠʔͰͲͷΫϥελʹଐ͢Δ͔Λผͷ//Ͱ༧ଌ
    ྡ઀͢Δϊʔυ͕ಉ͡Ϋϥελʹଐ͢ΔΑ͏ͳਖ਼ଇԽΛ͔͚Δ
    Τϯτϩϐʔਖ਼ଇԽʹΑͬͯͲΕ͔ҰͭͷΫϥελʹଐ͢Δ֬཰Λ্͛Δ
    #graph classification #graph pooling
    )JFSBSDIJDBM(SBQI3FQSFTFOUBUJPO-FBSOJOHXJUI%J⒎FSFOUJBCMF1PPMJOH
    /FVS*14 3FY:JOH 4UBOGPSE6OJWFSTJUZ
    +JBYVBO:PV $ISJTUPQIFS.PSSJT 9JBOH3FO 8JMMJBN-)BNJMUPO +VSF-FTLPWFD DJUBUJPO
    

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30. طଘͷώϡʔϦεςΟΫεΛಋग़Ͱ͖Δ(//Λ༻͍ͨTVCHSBQIʹΑΔϦϯΫ༧ଌ
    ର৅ϊʔυपลͷ৘ใͷΈΛ࢖ͬͯ΋ޡࠩΛগͳ͘Ͱ͖ΔͷͰ͸ɺͱ͍͏ΞΠσΟΞ
    &ODMPTJOHTVCHSBQIΛ࢖ͬͨ༧ଌ͕ྑ͍ۙࣅʹͳ͍ͬͯͨ
    -JOL1SFEJDUJPO#BTFEPO(SBQI/FVSBM/FUXPSLT
    #link prediction #enclosed subgraph
    /FVS*14 .VIBO;IBOH 8BTIJOHUPO6OJWFSTJUZ
    :JYJO$IFO DJUBUJPOT
    

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31. "QQMJDBUJPOT
    

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32. άϥϑͷ௿࣍ݩຒΊࠐΈΛֶश͠ɺάϥϑ΁ͷ࿦ཧԋࢉΛຒΊࠐΈۭؒͰͷ
    زԿૢ࡞ʹஔ͖׵͑Δ͜ͱͰઢܗ࣌ؒͰͷ୳ࡧΛߦ͏
    ɾ࿦ཧૢ࡞ͱزԿֶૢ࡞͕׬શͳରԠΛ͍ͯ͠ͳ͍ʢ࿦ཧ൱ఆͳͲ͸ѻ͑ͳ͍ʣ
    ɾΤοδͷಛ௃Λ࢖༻͢Δ͜ͱ͕Ͱ͖ͳ͍
    ͱ͍͏໰୊͸͋Δ͕ɺෆ׬શͳLOPXMFEHFCBTFʹର͢ΔޮՌతͳΤοδ༧ଌख๏ɻ
    DPOKVODUJWFRVFSZΛ%"(ʹม׵
    BODIPSOPEFΛ௿࣍ݩ΁ຒΊࠐΈ
    FEHFΛͨͲΔ࿦ཧૢ࡞ΛຒΊࠐΈۭؒͰͷ
    زԿૢ࡞Ͱ͋ΔQSPKFDUJPOͱͯ͠ߦ͏
    ಘΒΕͨϕΫτϧͷJOUFSTFDUJPOʢ࿦ཧ
    ੵʣΛܭࢉ͢Δ
    1SPKFDUJPOΛߦ͏
    ࠷ۙ๣๏ͰRVFSZΛຬͨ͢OPEFΛ୳͢
    #Graph Querying #Embedding
    &NCFEEJOH-PHJDBM2VFSJFTPO,OPXMFEHF(SBQIT
    /FVS*14 8JMMJBN-)BNJMUPO 4UBOGPSE6OJWFSTJUZ %FQBSUNFOUPG$PNQVUFS4DJFODF
    FUBM DJUBUJPOT
    άϥϑΛܦ༝ͨ͠FNCFEEJOHΛߦ͏͜ͱͰɺ࿦ཧԋࢉՄೳͳੑ࣭͕࢒Δ
    

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33. *OUFSBDUJPO/FUXPSLTGPS-FBSOJOHBCPVU0CKFDUT 3FMBUJPOTBOE1IZTJDT
    #Physics
    /FVS*14 1FUFS8#BUUBHMJB %FFQ.JOE
    3B[WBO1BTDBOV .BUUIFX-BJ %BOJMP3F[FOEF ,PSBZ,BWVLDVPHMV DJUBUJPOT
    5SVF .PEFM
    ෺ཧ๏ଇΛɺ෺ମͱͦͷؔ܎ੑʹ෼ղ͢Δ͜ͱͰਪଌͰ͖ΔΑ͏ʹͨ͠
    w ෺ମͷ૬ޓ࡞༻ΛϞσϧԽ͢ΔͨΊʹɺ෺ମ
    ʢϊʔυʣͱ෺ମؒͷؔ܎ʢΤοδʣͷάϥϑ
    Λར༻
    w ෺ମʹର͢ΔޮՌྔΛܭࢉ͢ΔϞσϧͱɺ֎ྗ
    ͳͲͷ૬ޓ࡞༻Λߟྀͨ͠ঢ়ଶਪఆΛߦ͏Ϟσ
    ϧΛ࡞Δ
    ܭࢉྔ͕͔ͳΓେ͖͘ɺେن໛ͳ෺ཧ
    γϛϡϨʔγϣϯ͸Ͱ͖ͳ͍
    ൚༻ੑ͕ߴ͘ɺҰൠతͳ෺ཧ๏ଇʹద
    ༻Մೳ
    

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34. ݚڀऀ঺հ
    • 5IPNBT/,JQG
    ◦ ($/
    • .BY8FMMJOH
    ◦ 4FNJTVQFSWJTFEDMBTTJpDBUJPOXJUIHSBQIDPOWPMVUJPOBMOFUXPSLT
    Ͱ($/ͷσϑΝΫτʹ
    ◦ 7"&
    • :VKJB-J
    ◦ (BUFE(//
    ◦ (SBQI.BUDIJOH//
    • 1FUFS#BUUBHMJB
    ◦ 3FMBUJPOBMJOEVDUJWFCJBTFT EFFQMFBSOJOH BOEHSBQIOFUXPSLT
    • 4UFQIBO(ÛOOFNBOO
    ◦ BEWFSTBSJBMBUUBDL
    

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35. ݚڀऀ঺հ
    • ,FZVMV9V
    ◦ ·ֶͩੜͱࢥΘΕΔ͕ࠓޙ͍͢͝࿦จΛॻ͖ͦ͏
    ◦ Տݪྛڊେάϥϑ1+ͰབྷΈ͕͋Δʁ
    ◦ )PX1PXFSGVMBSF(SBQI/FVSBM/FUXPSLT
    • /JOP4IFSWBTIJE[F SJTJLPOEPS
    ◦ HSBQILFSOFM
    • 8JMMJBN-)BNJMUPO
    ◦ *OEVDUJWF3FQSFTFOUBUJPO-FBSOJOHPO-BSHF(SBQIT
    ◦ ໰୊ఏىͳͲಠಛͷ੾Γޱ
    • FUDʜ
    

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36. 8FMDPNF
    άϥϑ࿦จͷαʔϕΠ΍ݚڀΛ͍ͨ͠ਓɺ
    σʔληοτΛ࡞Γ͍ͨਓɺڞಉݚڀߟ͑ͯΈ͍ͨਓɺ
    ·ͣ͸࿈བྷ͍ͩ͘͞ʂ
    

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