ストリートスナップデータに 統計的ネットワーク分析の適用を試みた

TokyoR #78 LT

Transcript

1. ετϦʔτεφοϓσʔλʹ

   ౷ܭతωοτϫʔΫ෼ੳͷద༻ΛࢼΈͨ
   5PLZP3

   !TBMUDPPLZ
   

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2. ୭ʁ
   • !TBMUDPPLZ
   • 3ྺɿ೥͙Β͍͔ͳ
   • ۈઌɿݪ॓ʹ͋Δ*5ܥͷձࣾ
   • ࢓ࣄ಺༰ɿ3%తͳ෦ॺͰ3Λ࢖ͬͨ

   ɾσʔλ෼ੳ ׂ
   

   ɾػցֶश ׂ
   

   ɾલॲཧ ׂ
   
   • झຯɿ෰ϑΝογϣϯඒज़ؗ८Γ
   

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3. ωοτϫʔΫ෼ੳͱ͸
   ਓؒؔ܎ɺاۀؒͷؔ܎ɺੜ෺ؒͷؔ܎ɺίϯϐϡʔλωοτϫʔΫ
   ͳͲͷؔ܎΍ߏ଄Λ෼ੳ͢Δάϥϑཧ࿦Λϕʔεͱͨ͠෼ੳख๏
   (ग़య : https://www.slideshare.net/kashitan/tidygraphggraph) (https://www.amazon.co.jp/exec/obidos/ASIN/4320019288)
   ͜ΕͰษڧ͠·ͨ͠
   ࠷ۙͷTokyoRͩͱ

   @kashitan ͞Μ͕
   ൃදͨ͠Γͯͨ͠
   

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4. ωοτϫʔΫ෼ੳ
   Α͋͘Δͷ͸ωοτϫʔΫͷࢦඪͷࢉग़΍ߏ଄ͷநग़
   - த৺ੑ

   ͲͷΑ͏ͳਓ͕த৺తͳਓ෺͔
   - ίϛϡχςΟநग़

   ͲͷΑ͏ͳάϧʔϓʹ෼͔Ε͍ͯΔ͔
   - ૬ؔ܎਺

   ̎ͭͷωοτϫʔΫ͸ࣅ͍ͯΔ͔Ͳ͏͔
   - ίΞநग़

   ωοτϫʔΫͷີʹ݁߹ͨ͠த৺෦෼
   

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5. ωοτϫʔΫͷ͋Δ̎఺ͷ௖఺ؒ J K
   ͷล͸ɺ֬཰QJKͰ֬཰తʹൃੜ͢Δͱߟ͑Δ
   QJK͸ύϥϝʔλВΛ࣋ͭϩδεςΟοΫϞσϧͰදݱͰ͖Δ
   ௖఺J Kͱ௖఺K Lʹล͕ுΔ֬཰͸QJKºQKLͱදݱͰ͖Δ
   ౷ܭతωοτϫʔΫ෼ੳ
   K
   L J
   

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6. ࢦ਺ϥϯμϜάϥϑϞσϧ FYQPOFOUJBMSBOEPNHSBQINPEFM
   
   ɹϥϯμϜάϥϑ:ʹ͓͍ͯಛఆͷάϥϑߏ଄Z͕ಘΒΕΔ֬཰͸֤ล͕ுΔ֬཰ͷ

   ྦྷ৐ͰදݱͰ͖Δͱߟ͑ͨϞσϧ
   ౷ܭతωοτϫʔΫ෼ੳ
   yʹ͋Δลͷ਺
   ύϥϝʔλ
   ن֨Խఆ਺
   ωοτϫʔΫશମ
   ͷลͷൃੜ֬཰
   

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7. ࢦ਺ϥϯμϜάϥϑϞσϧɹQϞσϧ
   ɹϥϯμϜάϥϑ:ͷลͷൃੜ֬཰͸༷ʑͳཁૉʹΑΓ֬཰తʹܾ·ΔϞσϧ
   ౷ܭతωοτϫʔΫ෼ੳ
   ཁૉ
   ϊʔυͷಛ௃ྔɿ೥ྸɺॏΈɺ෦ॺʜ
   ลͷಛ௃ྔɿަࡍظؒɺ޷Έʜ
   ϊʔυؒͷؔ܎ͷಛ௃ɿ೥ྸࠩɺۈଓظؒࠩʜ
   ߏ଄తͳಛ௃ྔɿLελʔߏ଄ͷ਺ʜ
   ωοτϫʔΫͷߏ੒ཁ
   ཁૉͷ਺
   

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8. ద༻σʔλ
   

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9. ద༻σʔλ
   ೥ྸ
   ৬ۀ
   ࡱӨ৔ॴ
   ண༻ϒϥϯυ
   

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10. Ϟνϕʔγϣϯ
    ล͸ண༻ϒϥϯυͷ
    ڞ௨౓
    ϒϥϯυͷબ୒ͷੑ࣭Λ
    දݱͰ͖ͳ͍͔
    (͔ͳΓແཧ໼ཧ)
    

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11. σʔλऔಘ
    • ($1্Ͱ%PDLFSΛ༻͍ͯ3TUVEJP34FMFOJVN؀ڥΛ࡞੒
    • SWFTUQBDLBHFΛར༻ͯ͠εΫϨΠϐϯά
    • ϙΞιϯ෼෍ʹै͏ִؒͰϖʔδऔಘ ͳΜͱͳ͘
    
    • ໿Ұ೥෼ਓͷεφοϓσʔλΛऔಘ
    

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12. σʔλ֬ೝ
    ண༻ϒϥϯυϥϯΩϯά
    ண༻ϒϥϯυωοτϫʔΫ
    

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13. Ϟσϧ࡞੒(ྫ)
    ࢦ਺ϥϯμϜϞσϧ͸TUBUOFUQBDLBHFͰ࣮૷͕Ͱ͖·͢ɻ
    # ωοτϫʔΫΦϒδΣΫτͷ࡞੒

    network <- as.network(x = graph_matrix, directed = FALSE, loops = FALSE)
    # ֤Τοδʹઆ໌ม਺(೥ྸ)Λ௥Ճ
    network %v% "Age" <- Age
    # ֤Τοδͷ೥ྸͷࠩΛܭࢉ
    diff.age <- abs(sweep(matrix(snap_info$Age, nrow = 638, ncol = 638),
    2, snap_info$Age))
    # Ϟσϧ࡞੒

    model <- ergm( network ~ edges + edgecov(diff.age) + nodecov(“Age”) )

    

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14. Ϟσϧ࡞੒
    ࢦ਺ϥϯμϜϞσϧ͸TUBUOFUQBDLBHFͰ࣮૷͕Ͱ͖·͢ɻ
    # ετϦʔτεφοϓͷp*Ϟσϧੜ੒
    snap_net_model <- ergm(snap_net ~ 

    edges + # ลͷ਺
    nodecov(“Age")+ # ೥ྸࠩ
    edgecov(diff.age) + # ೥ྸ
    nodematch(“Occupation”) + # ৬ۀ
    nodematch("Point") ) # ࡱӨ৔ॴ

    

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15. ݁ՌΛݟͯΈΔ
    > summary(snap_net_model)
    < ུ >
    Monte Carlo MLE Results:
    Estimate Std. Error MCMC % z value Pr(>|z|)
    edges -5.2066393 0.2692526 0 -19.337 <1e-04 ***
    edgecov.diff.age -0.0015763 0.0094767 0 -0.166 0.8679
    nodecov.Age -0.0003136 0.0061215 0 -0.051 0.9591
    nodematch.Occupation -0.0453192 0.0842853 0 -0.538 0.5908
    nodematch.Point 0.1491330 0.0628610 0 2.372 0.0177 * 

    < ུ >
    AIC: 13485 BIC: 13536 (Smaller is better.)

    ࡱӨ৔ॴ͕ลͷൃੜʹ
    Өڹ͍ͯͦ͠͏
    AIC/BICͰม਺બ୒Մೳ
    

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16. ݁ՌΛݟͯΈΔ
    ϞσϧΛ༻͍ͯγϛϡϨʔγϣϯ
    ࣮ઢɿγϛϡϨʔγϣϯʹΑΔ஋

    ശͻ͛ਤɿ࣮σʔλͷ஋
    ౰ͯ͸·Γྑ͘ͳ͍ʜ
    

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17. ·ͱΊ
    • ࠓճͷεφοϓ৘ใͰ͸ɺண༻ϒϥϯυͷؔ܎ੑΛࢦ਺ϥϯμϜ
    άϥϑϞσϧͰ͏·͘දݱͰ͖·ͤΜͰͨ͠
    • ౷ܭతωοτϫʔΫ෼ੳ͸݁ߏ໘ന͍ͷͰɺษڧͯ͠ΈͯͶ
    • ࢲ΋౷ܭతωοτϫʔΫ෼ੳͷษڧଓ͚͍͖͍ͯͨͱࢥ͍·͢
    • ͳͷͰɺৄ͍͠ํ͸͝ڭतئ͍͠·͢
    

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18. • ڞཱग़൛ʮωοτϫʔΫ෼ੳୈ̎൛ʯླ໦౒ஶ

    IUUQTXXXBNB[PODPKQFYFDPCJEPT"4*/
    • \UJEZHSBQI^ͱ\HHSBQI^ʹΑΔϞμϯͳωοτϫʔΫ෼ੳ

    IUUQTXXXTMJEFTIBSFOFULBTIJUBOUJEZHSBQIHHSBQI
    • 3ʹΑΔωοτϫʔΫ෼ੳΛ·ͱΊ·ͨ͠ωοτϫʔΫͷࢦඪฤ

    IUUQTRJJUBDPNTBMUDPPLZJUFNTFEDFEGCDE
    • 3ʹΑΔωοτϫʔΫ෼ੳΛ·ͱΊ·ͨ͠౷ܭతωοτϫʔΫ෼ੳฤ

    IUUQTRJJUBDPNTBMUDPPLZJUFNTCBFGDFCGBDFBDCGD
    ࢀߟ
    

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