Discussion Paper No.J-7ࢯ࣮ࢩ࣓ࣕࣝࢹ࢕࢔ୖࡢࢸ࢟ࢫࢺ᝟ሗࢆ⪃៖ࡋࡓ
♫఍ࢿࢵࢺ࣮࣡ࢡศᯒࣔࢹࣝ

஬༑ᔒᮍ᮶ ↷஭ఙᙪ2020 ᖺ ᭶ Data Science and Service Research
Discussion Paper

Center for Data Science and Service Research
Graduate School of Economic and Management

Tohoku University27-1 Kawauchi, Aobaku

Sendai 980-8576, JAPANιʔγϟϧϝσΟΞ্ͷςΩετ৘ใΛߟྀͨࣾ͠ձωοτϫʔΫ෼ੳϞσϧ‫ेޒ‬ཛྷະདྷ *রҪ৳඙ 

2020 ೥ 5 ݄

Abstractۙ೥ɼࣾձωοτϫʔΫΛϞσϧԽͯ͠෼ੳ͢ΔࡍʹɼωοτϫʔΫ৘ใ͚ͩͰͳ͘ɼ
ਓʑ͕ιʔγϟϧϝσΟΞ্ͳͲͰੜ੒͢ΔςΩετ৘ใΛߟྀͯ͠ίϛϡχςΟߏ଄Λ
ଊ͑Δ͜ͱͷॏཁੑ͕૿͍ͯ͠ΔɽςΩετ৘ใΛߟྀ͢Δ͜ͱʹΑΓɼωοτϫʔΫ্ͰີʹΤοδ͕‫ܗ‬੒͞Ε͍ͯΔߏ଄ͷதʹɼਓʑ͕࣋ͭ‫ڵ‬ຯ΍ؔ৺ʹԠͨ͡ෳ਺ͷ·ͱ·Γ͕ଘࡏ͢Δͱ͍͏Α͏ͳෳࡶͳίϛϡχςΟߏ଄Λ࣋ͭࣾձωοτϫʔΫͷ෼ੳ͕ՄೳͱͳΔɽຊ‫Ͱڀݚ‬͸ɼ͜ΕΛϞσϧԽͨ͠ Igarashi and Terui (2020) ʹΑΔωο
τϫʔΫσʔλͱςΩετσʔλͷಉ࣌ར༻ϞσϧΛ֦ு͠ɼΤοδੜ੒֬཰Λؔ܎͢Δϊʔυ͝ͱʹҟͳΔΑ͏ʹఆࣜԽ͢Δ͜ͱͰɼϊʔυͷ࣍਺෼෍͕΂͖৐ଇʹै͏ͱ͍͏ࣾձωοτϫʔΫ͕࣋ͭҰൠతͳੑ࣭Λߟྀ͢ΔϞσϧΛఏҊ͍ͯ͠ΔɽTwitter Λ༻͍࣮ͨূ෼ੳͰ͸ɼఏҊϞσϧΛ༻͍࣮ͨσʔλ΁ͷԠ༻ྫΛࣔ͢ͱͱ΋ʹɼઌߦ‫ݚ‬‫͚͓ʹڀ‬Δ‫ط‬ଘϞσϧΑΓ΋༏Εͨ༧ଌੑೳΛ࣋ͭ͜ͱΛࣔ͢ɽ

Keywords: ࣾձωοτϫʔΫ෼ੳɾίϛϡχςΟ‫ݕ‬ग़ɾςΩετղੳɾτϐοΫϞσ
ϦϯάɾϕΠζਪఆɾϊʔυ࣍਺ͷҟ࣭ੑ* ౦๺େֶେֶӃ‫ڀݚֶࡁܦ‬Պɹത࢜‫ظޙ‬՝ఔɿ˟ 980-8576 ɹ‫ٶ‬৓‫ݝ‬ઋ୆ࢢ੨༿۠઒಺ 27 ʵ 1ʢE-mailɿ

mirai.igarashi.s7@dc.tohoku.ac.jpʣɽຊ‫ڀݚ‬͸ JSPS Պ‫ݚ‬අ 18J20698 ͷॿ੒Λड͚ͨ΋ͷͰ͢ɽ ౦๺େֶେֶӃ‫ڀݚֶࡁܦ‬Պɹ‫ڭ‬तʢE-mailɿterui@tohoku.ac.jpʣɽຊ‫ڀݚ‬͸ JSPS Պ‫ݚ‬අ (A) 17H01001
ͷॿ੒Λड͚ͨ΋ͷͰ͢ɽ

1

ং࿦

Social Networking Sites (SNS) ͷྲྀߦ΍ e-ίϚʔεαΠτͷ୆಄ͳͲʹΑΓɼফඅऀΛऔΓ‫ࣾ͘ר‬ձωοτϫʔΫΛ෼ੳ͠ɼͦͷߏ଄Λ೺Ѳ͢Δ͜ͱ͸ɼ‫ۀا‬ͷϚʔέςΟϯά‫׆‬ಈʹ͓͚ΔॏཁͳҐஔΛ઎ΊΔΑ͏ʹͳ͍ͬͯΔɽࣾձωοτϫʔΫ෼ੳͷख๏͸ɼ౷‫ֶܭ‬΍ࣾձֶͷ෼໺Λத৺ʹ௕೥‫͞ڀݚ‬Ε͓ͯΓɼωοτϫʔΫߏ଄Λଊ͑ΔͨΊͷ౷‫ܭ‬Ϟσϧ͕ଟ͘ఏҊ͞Ε͍ͯΔ (e.g., Snijders and Nowicki, 1997; Airoldi et al., 2008)ɽ͜ΕΒͷϞσϧͰ͸ɼωοτϫʔΫ্ͷϊʔυͱΤοδΛ‫؍‬ଌσʔλͱͯ͠ѻ͍ɼ͔ͦ͜ΒίϛϡχςΟߏ଄Λநग़͢Δ͜ͱΛ໨తͱ͍ͯ͠Δɽ·ͨɼࣾձωοτϫʔΫʹ͓͍ͯɼϊʔυ͸ਓʑͷ͜ͱΛද͓ͯ͠Γɼਓʑͷଐੑ΍ߦಈͱ͍ͬͨ෇ਵతͳσʔλΛߟྀ͢Δ͜ͱͰɼωοτϫʔΫϞσϧͷਫ਼៛ԽΛ໨ࢦ͢‫ڀݚ‬΋೤৺ʹऔΓ૊·Ε͍ͯΔ (e.g., Handcock et al., 2007)ɽதͰ
΋ɼۙ೥͸ɼιʔγϟϧϝσΟΞͷྲྀߦ΍‫ޱ‬ίϛ‫ػ‬ೳΛ౥ࡌͨ͠ e-ίϚʔεαΠτͷ୆಄ͳͲʹΑΓɼϢʔβʔੜ੒ίϯςϯπ (User-Generated-ContentsɼUGC)ɼಛʹςΩετ৘ใΛωοτϫʔΫͱ૊Έ߹ΘͤͨࣾձωοτϫʔΫ෼ੳϞσϧ͕ଟ͘ఏҊ͞Ε͍ͯΔ (e.g., Liuet al., 2009; Bouveyron et al., 2018)ɽ
ωοτϫʔΫ৘ใ͚ͩͰͳ͘ςΩετ৘ใ΋ߟྀͨ͠ϞσϧΛߏங͢Δ͜ͱͷར఺ͱͯ͠͸ɼҰํͷ৘ใ͚ͩͰ͸ଊ͑Δ͜ͱ͕೉͍͠ίϛϡχςΟߏ଄Λநग़Ͱ͖Δͱ͍͏఺͕‫ڍ‬͛ΒΕΔɽྫ͑͹ɼ͋Δֶߍͷಉ‫ڃ‬ੜͰߏ੒͞ΕΔίϛϡχςΟΛ૝ఆ͢Δɽͦ͜Ͱ͸ɼֶੜΒ͸‫ʹ͍ޓ‬ԿΒ͔ͷؔ܎ੑΛ࣋ͬͨີ౓ͷߴ͍ωοτϫʔΫ͕‫ܗ‬੒͞Ε͍ͯΔ͸ͣͰ͋Δɽ
͕ͨͬͯ͠ɼωοτϫʔΫ৘ใͷΈΛߟྀͨ͠ϞσϧΛ༻͍ΔͱɼͦͷΑ͏ͳωοτϫʔΫ্ʹ͸ɼҰͭͷίϛϡχςΟ͕ଘࡏ͍ͯ͠Δͱೝࣝ͞ΕΔɽ͔͠͠ɼͦΕͱಉ࣌ʹɼֶੜΒ͸Իָ΍ಡॻɼεϙʔπͱ͍༷ͬͨʑͳझຯΛ͍࣋ͬͯΔ͜ͱ͕ߟ͑ΒΕΔͨΊɼ‫ڞ‬௨ͷझຯΛֶ࣋ͬͨੜΒΛ·ͱΊͯෳ਺ͷίϛϡχςΟ͕ଘࡏ͢ΔͱΈͳ͢ํ͕ɼΑΓҙຯͷ͋ΔηάϝϯςʔγϣϯͱͳΔՄೳੑ͕͋ΔɽIgarashi and Terui (2020) Ͱ͸ɼͦͷΑ͏ͳίϛϡχςΟΛτϐοΫϕʔεɾίϛϡχςΟͱ໊෇͚ɼωοτϫʔΫͱςΩετΛߟྀͨ͠ϞσϧʹΑΔ‫ݕ‬ग़ΛఏҊ͍ͯ͠ΔɽιʔγϟϧϝσΟΞʹ୅ද͞ΕΔΦϯϥΠϯ্ͷࣾձωοτϫʔΫͰ͸ɼ‫ੈ࣮ݱ‬քʹ͓͚Δࣾձతͳͭͳ͕Γ͚ͩͰͳ͘ɼ‫ڵ‬ຯ΍ؔ৺ͳͲʹ‫͍ͭͨͮج‬ͳ͕Γɼͭ·ΓτϐοΫϕʔεɾίϛϡχςΟ͕఺ࡏ͍ͯ͠Δ͜ͱ͕ߟ͑ΒΕΔͨΊɼϝσΟ1Ξ্ʹੜ੒͞ΕͨςΩετίϯςϯπ͔ΒͦͷϢʔβʔͷ‫ڵ‬ຯ΍ؔ৺Λਪఆ͢Δ͜ͱͰɼࣾ
ձωοτϫʔΫ෼ੳϞσϧΛਫ਼៛Խͤ͞Δ͜ͱ͕Ͱ͖Δɽ
·ͨɼࣾձωοτϫʔΫ͕࣋ͭੑ࣭ͷҰͭͱͯ͠ɼ࣍਺෼෍͕΂͖৐ଇʹै͏ͱ͍͏ੑ
࣭͕͋Δɽ͜Ε͸ɼ͘͝গ਺ͷਓʑ͕ଟ͘ͷਓʑͱωοτϫʔΫ্Ͱؔ܎Λ࣋ͪɼͦͷଞେ੎ͷਓʑ͸ɼ͘͝গ਺ͷਓʑͱͷΈؔ܎ੑΛ࣋ͭ܏޲ʹ͋Δͱ͍͏ੑ࣭Ͱ͋ΔɽͦͷΑ͏ʹɼ‫࣮ݱ‬ͷࣾձωοτϫʔΫʹ͓͍ͯɼ࣍਺͸ϊʔυ͝ͱʹҟ࣭Ͱ͋Δ͕ɼ֬཰తϒϩοΫϞσϧ (Snijders and Nowicki, 1997) ͳͲ୅දతͳωοτϫʔΫϞσϧͷଟ͕ͦ͘͏Ͱ͋ΔΑ͏ʹɼIgarashi and Terui (2020) Ͱ͸ɼ࣍਺ͷҟ࣭ੑΛߟྀ͍ͯ͠ͳ͍ɽ
ຊ‫Ͱڀݚ‬͸ɼIgarashi and Terui (2020) ͷϞσϧΛ֦ு͠ɼϒϩοΫϞσϧʹଈͨ͠Τοδੜ੒֬཰Λϊʔυ͝ͱʹҟ࣭ͳΤοδ֬཰ͱ͠ɼ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ϞσϧΛఏҊ͢
Δɽຊ‫ڀݚ‬ͷ࣮ূ෼ੳͰ͸ɼ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ఏҊϞσϧΛɼҰൠతͳ֬཰ϒϩοΫϞσϧͱಉ༷ʹҟ࣭ੑΛߟྀ͠ͳ͍ࠩ෼Ϟσϧͱൺֱ͠ɼ֎૷༧ଌʹ͓͍ͯఏҊϞσϧͷํ͕༏Ε͍ͯΔ͜ͱΛࣔ͢ɽҎԼɼ2 અͰ͸ɼࣾձωοτϫʔΫ෼ੳʹؔ܎͢Δઌߦ‫ڀݚ‬Λ·ͱΊɼຊ‫ڀݚ‬ͷ໨తͱҐஔ͚ͮΛ໌֬ʹ͢Δɽ3 અͰ͸ɼఏҊϞσϧΛઆ໌͠ɼ4 અͰ͸ͦͷਪఆ๏Λಋग़͢Δɽଓ
͍ͯɼ5 અͰ͸ɼTwitter σʔλΛར༻࣮ͨ͠ূ‫ڀݚ‬Λใࠂ͠ɼ࠷‫ʹޙ‬ɼ6 અͰ݁࿦ͱࠓ‫ޙ‬ͷ՝୊Λड़΂Δɽ

2

ઌߦ‫ڀݚ‬

2.1

ࣾձωοτϫʔΫ෼ੳϞσϧͷਐల౷‫ֶܭ‬΍ࣾձֶͳͲΛத৺ͱͯ͠ɼ‫͔͘ݹ‬ΒࣾձωοτϫʔΫΛϞσϧԽ͠ɼͦͷߏ଄Λ೺Ѳ͢ΔͨΊͷ‫͕ڀݚ‬ଓ͍͍ͯΔɽதͰ΋୅දతͳ΋ͷ͕ɼ֬཰తϒϩοΫϞσϧ (Stochastic

Block Models, SBM, Wang and Wong, 1987; Snijders and Nowicki, 1997) Ͱ͋ΔɽSBM ͸ɼϊʔυ͕ K ‫ݸ‬ͷίϛϡχςΟͷ͏ͪҰ͚ͭͩʹଐ͢Δ͜ͱΛԾఆ͓ͯ͠Γɼϊʔυ i ͕ଐ͢ΔίϛϡχςΟΛ zi ∈ {1, . . . , K} ͱ͢Δͱɼϊʔυ i ͱ j ͷؒʹΤοδ͕ੜ੒͞ΕΔ֬཰͸ɼψzi zj Ͱද͞ΕΔɽ͜Ε͸ɼK × K ߦྻ Ψ ͷ (zi , zj ) ੒෼Ͱ͋ΓɼΤοδ֬཰Λද͢ύϥϝʔ2λͰ͋Δɽ

SBM ͸ɼϞσϧ͕ఏҊ͞ΕͯҎ߱ɼ༷ʑͳจ຺ͰϞσϧͷ֦ு͕औΓ૊·Ε͓ͯΓɼྫ͑͹ɼAiroldi et al. (2008) ͸ɼSBM ͷ֦ுϞσϧͱͯࠞ͠߹ϝϯόʔγοϓ֬཰తϒϩοΫϞσϧ (Mixed Membership Stochastic Blockmoldels, MMSB) ΛఏҊ͍ͯ͠ΔɽSBM ͕ɼϊʔυʹ୯ҰͷϝϯόʔγοϓΛԾఆ͍ͯͨ͠ͷʹର͠ɽMMSB Ͱ͸ɼ֤ϊʔυ͸ɼଞϊʔυͱͷؔ܎ੑຖʹෳ਺ͷίϛϡχςΟʹଐ͢Δ͜ͱ͕‫ڐ‬༰͞Ε͍ͯΔɽϊʔυ i ͔Β j ͷؔ܎ੑʹ͓͍ͯɼϊʔυ i ͕ଐ͢ΔίϛϡχςΟΛ sij ɼϊʔυ j ͕ଐ͢ΔίϛϡχςΟΛ rji ͱ͢Δͱɼ྆ऀͷؒʹΤοδ͕ੜ੒͞ΕΔ֬཰͸ɼψsij rji Ͱද͞ΕΔɽ͜ͷ֦ுʹΑΓɼMMSB
͸ίϛϡχςΟͷॏͳΓΛߟྀ͢Δ͜ͱ͕Ͱ͖ʢSBM Ͱ͸ίϛϡχςΟ͕ॏͳΔ͜ͱ͸ͳ͍ʣɼΑΓ‫ʹ࣮ݱ‬ଈͨ͠ϞσϦϯά͕Մೳͱͳ͍ͬͯΔɽ
·ͨɼࣾձֶͷจ຺Ͱ͸ɼϊʔυؒͷؔ܎ੑ͕ੑผ΍೥ྸͱ͍ͬͨϊʔυ‫ݻ‬༗ͷಛ௃ྔͷӨ‫ڹ‬Λड͚ܾͯ·Δ͜ͱ΋஌ΒΕ͍ͯΔ (Hoﬀ et al., 2002; Handcock et al., 2007; Krivitsky

et al., 2009)ɽ͔͠͠ɼຊ‫Ͱڀݚ‬͸ɼιʔγϟϧϝσΟΞʹ୅ද͞ΕΔΑ͏ͳΦϯϥΠϯ্ͷࣾձωοτϫʔΫʹண໨͍ͯ͠ΔͨΊɼͦͷΑ͏ͳಛ௃ྔ͸ߟྀ͠ͳ͍ɽTwitter ͷΑ͏ͳಗ໊‫ܕ‬ιʔγϟϧϝσΟΞͰ͸ɼϢʔβʔ͸೥ྸ΍ੑผͱ͍ͬͨ‫ݸ‬ਓ৘ใΛӅͨ͠ঢ়ଶͰΞΧ΢ϯτΛొ࿥͢Δ͜ͱ͕Ͱ͖ɼͦͷΑ͏ͳঢ়‫͍͓ͯʹگ‬ଞऀͱؔ܎Λ݁ͿࡍʹߟྀͰ͖Δ
৘ใ͸ɼ૬ख͕‫ܗ‬੒͍ͯ͠ΔωοτϫʔΫͱϝσΟΞ্ʹ౤ߘͨ͠ίϯςϯπͷΈͰ͋Δɽ
͜ΕΒͷσʔλ͕ར༻ՄೳͰ͋Ε͹ɼఏҊϞσϧʹऔΓࠐΉ͜ͱ͸༰қͰ͋Γɼࣾձֶతࢹ
఺͔Βͷ෼ੳ΋ՄೳͰ͋Δɽ

2.2

ωοτϫʔΫͱςΩετ৘ใͷಉ࣌ϞσϦϯάʹؔ͢Δ‫ڀݚ‬લઅͰ‫ࣾͨ͛ڍ‬ձωοτϫʔΫϞσϧʹؔ͢Δ‫Ͱڀݚ‬͸ɼωοτϫʔΫ৘ใͷΈʹண໨ͯ͠ϞσϧΛఏҊ͍ͯ͠Δ͕ɼۙ೥ɼTwitter ΍ Facebook ͱ͍ͬͨΦϯϥΠϯ্ͷࣾձωοτϫʔΫߏ଄ΛΑΓਂ͘ཧղ͢ΔͨΊʹɼωοτϫʔΫͱςΩετ৘ใΛͲͪΒ΋ߟྀ͢ΔϞσϧ͕੝Μʹ‫͞ڀݚ‬Ε͍ͯΔɽྫ͑͹ɼChang and Blei (2010) ͸ɼϊʔυʹ‫ݻ‬༗ͷςΩετ৘ใʹରͯ͠τϐοΫϞσϧΛద༻͠ɼϊʔυͷςΩετʹׂΓ౰ͯΒΕͨτϐοΫׂ߹ͷྨࣅ౓ʹԠͯ͡ϊʔυؒͷΤοδੜ੒֬཰͕ఆٛ͞ΕΔɼؔ܎τϐοΫϞσϧ (Relational

3

Topic Model, RTM) ΛఏҊ͍ͯ͠Δɽͨͩ͠ɼRTM ͷ໨త͕ɼωοτϫʔΫ৘ใΛՃຯͯ͠ςΩετ৘ใʹ͓͚ΔτϐοΫΛਪఆ͢Δ͜ͱͰ͋Δͷʹରͯ͠ɼຊ‫ڀݚ‬ͷ໨త͸ςΩετ৘ใΛߟྀͯ͠ωοτϫʔΫ্ͷίϛϡχςΟߏ଄Λ೺Ѳ͢Δ͜ͱͰ͋ΔΑ͏ʹରরతͳ΋ͷͰ͋Δɽ

Chang and Blei (2010) ͷΑ͏ʹςΩετ৘ใΛજࡏతσΟϦΫϨ഑෼๏ (latent Dirichlet
allocation, LDA, Blei et al., 2003) ΍ͦͷ֦ுϞσϧΛ༻͍ͯωοτϫʔΫϞσϧʹऔΓࠐΉͱ͍͏ํ๏͸ଞʹ΋͍͔ͭ͘ͷ‫ݟͰڀݚ‬ΒΕΔɽྫ͑͹ɼLiu et al. (2009) ͸ɼTopic-Link

LDA ΛఏҊ͓ͯ͠Γɼϊʔυ‫ݻ‬༗ͷςΩετ৘ใΛߟྀͯ͠ίϛϡχςΟߏ଄Λ‫ݕ‬ग़͢Δͱ
͍͏఺Ͱຊ‫ͱڀݚ‬ಉ͡໨తΛ͍࣋ͬͯΔɽͨͩ͠ɼSBM ͱಉ༷ʹɼϊʔυ͕୯Ұͷίϛϡχ
ςΟʹଐ͢Δ͜ͱΛԾఆ͍ͯ͠Δ෦෼͸ຊ‫ͱڀݚ‬ҟͳΔ఺Ͱ͋Δɽ·ͨɼLiu et al. (2009)Ͱ͸ɼΤοδੜ੒֬཰͕ɼϊʔυ‫ݻ‬༗ͷτϐοΫ‫ͼٴ‬ίϛϡχςΟׂ߹ͷྨࣅ౓ʹΑͬͯఆٛ͞Ε͍ͯΔͨΊɼର৅ͱ͢ΔωοτϫʔΫΛແ޲άϥϑͱͯ͠ѻ͏͜ͱΛ૝ఆ͍ͯ͠Δͷʹର͠ɼຊ‫ڀݚ‬Λ‫ؚ‬ΊͨϒϩοΫϞσϧʹ͓͍ͯ͸ɼK × K ߦྻͷΤοδ֬཰ύϥϝʔλΛ༻͍ͨωοτϫʔΫϞσϦϯάʹΑΓɼάϥϑͷํ޲ੑʹ͔͔ΘΒͣϞσϧΛద༻ՄೳͰ͋
Δɽଞʹ΋ɼBouveyron et al. (2018) ͸ɼSBM ʹςΩετ৘ใͷϞσϧΛՃ͑Δ͜ͱͰ֦ு
ͨ͠ɼStochastic Topic Block Model (STBM) ΛఏҊ͍ͯ͠Δɽ͜ΕΒ͸୯ҰͷϝϯόʔγοϓΛԾఆͨ͠ SBM ͷ֦ுϞσϧͰ͋Δ͕ɼZhu et al. (2013)͸ɼϊʔυͷࠞ߹ϝϯόʔγοϓΛԾఆ͠ɼςΩετͱωοτϫʔΫ৘ใͷ྆ऀΛߟྀ͢Δ
ωοτϫʔΫ෼ੳϞσϧΛఏҊ͍ͯ͠Δɽ͜ͷ఺ʹ͓͍ͯຊ‫͚͓ʹڀݚ‬ΔఏҊϞσϧͱ΋ࣅͨߏ଄Λ༗͍ͯ͠Δ͕ɼओͳ૬ҧ఺͸ɼΤοδʹׂΓ౰ͯΒΕΔίϛϡχςΟͱ୯‫ׂʹޠ‬Γ౰ͯΒΕΔτϐοΫ͕ಉҰͷ෼෍ʹै͍ͬͯΔͱ͍͏఺Ͱ͋Δɽ‫͑׵͍ݴ‬Ε͹ɼZhu et al.

(2013) ͸ίϛϡχςΟͱτϐοΫͷ࣍‫ݩ‬ΛಉҰͷ΋ͷͱͯ͠ѻ͍ͬͯΔͱ͍͑Δɽ͔͠͠ɼ‫ݱ‬࣮ͷࣾձωοτϫʔΫͰ͸ɼίϛϡχςΟͱτϐοΫ͕ඞͣ͠΋‫ʹ͍ޓ‬ରԠ͍ͯ͠Δͱ͸‫ݶ‬Βͳ͍ɽྫ͑͹ɼԻָͱεϙʔπʹ‫ڵ‬ຯͷ͋Δϝϯόʔ͕ີͳϦϯΫߏ଄Λ͍࣋ͬͯΔωοτϫʔΫΛߟ͑Δɽ͜ͷΑ͏ͳίϛϡχςΟΛ Zhu et al. (2013) ͷϞσϧͰ‫ݕ‬ग़ͨ͠ͱ͢
ΔͱɼҰͭͷίϛϡχςΟʹରͯ͠ɼԻָͱεϙʔπͱ͍͏ෳ਺ͷҙຯత·ͱ·ΓΛ΋ͭτϐοΫ͕ରԠͯ͠͠·͍ɼτϐοΫͷղऍੑʹ͚ܽΔɽҰํͰɼຊ‫Ͱڀݚ‬͸ɼίϛϡχςΟ

4ͱτϐοΫ͕ͦΕͧΕҟͳΔ෼෍ʹै͏͜ͱΛԾఆ͓ͯ͠Γɼ্‫ه‬ͷΑ͏ͳωοτϫʔΫʹରͯ͠΋ɼҰͭͷίϛϡχςΟͱɼԻָτϐοΫ‫ͼٴ‬εϙʔπτϐοΫͷΑ͏ʹผʑʹෳ਺τϐοΫΛରԠͤ͞Δ͜ͱ͕Ͱ͖Δɽ3 અͰ͸ɼͦͷৄࡉͳఆࣜԽΛઆ໌͢Δɽ͜ΕΒͷ‫ط‬ଘϞσϧΛ౿·͑ͯɼIgarashi and Terui (2020) Ͱ͸ɼϊʔυͷࠞ߹ϝϯόʔγοϓΛԾఆͨ͠ωοτϫʔΫͱςΩετͷಉ࣌ϞσϦϯάΛఏҊ͍ͯ͠Δɽຊ‫Ͱڀݚ‬͸ɼ͜ͷϞσϧΛ֦ு͠ɼΤοδ֬཰Λϊʔυ͝ͱʹҟ࣭ͳύϥϝʔλͱ͢ΔϞσϧΛ‫ݕ‬౼͢Δɽ͜ΕʹΑΓɼࣾձωοτϫʔΫ͕Ұൠతʹ༗͢Δ࣍਺෼෍ͷҟ࣭ੑΛߟྀͨ͠ϞσϦϯά͕
ՄೳͱͳΔɽઌߦ‫͍͓ͯʹڀݚ‬͸ɼKarrer and Newman (2011) ͕ɼSBM Ͱఆٛ͞ΕΔΑ͏ͳϊʔυʹ͍ͭͯಉ࣭తͳΤοδੜ੒֬཰Λద༻͢ΔͷͰ͸ͳ͘ɼϊʔυ͝ͱͷ‫ظ‬଴࣍਺Λύϥϝʔλͱͯ͠ಋೖ͠ɼؔ܎͢ΔϊʔυʹԠͯ͡Τοδੜ੒֬཰͕ҟ࣭ͱͳΔΑ͏ͳิਖ਼Λߦ͏ϞσϧΛఏҊ͍ͯ͠Δɽຊ‫͚͓ʹڀݚ‬ΔఆࣜԽͰ͸ɼΤοδੜ੒֬཰ࣗମΛϊʔυ͝ͱʹҟ࣭ͳύϥϝʔλͱͯ͠ఆ͓ٛͯ͠ΓɼKarrer and Newman (2011) ͱ΋ҟͳΔΞϓϩʔνΛͱ͍ͬͯΔɽ
ද 1 Ͱ͸ɼ͜͜·Ͱʹٞ࿦ͨ͠ຊ‫ͱڀݚ‬ઌߦ‫ͱڀݚ‬ͷൺֱΛ·ͱΊ͍ͯΔɽ·ͣɼωοτϫʔΫ΍ςΩετͲͪΒ͔ͷΈΛ‫؍‬ଌσʔλͱͯ͠ѻ͏Ϟσϧͱൺֱ͢Δͱɼຊ‫Ͱڀݚ‬ఏҊ͢ΔϞσϧ͸ɼͦͷ྆ऀΛߟྀͯࣾ͠ձωοτϫʔΫ෼ੳΛߦ͏΋ͷͰ͋Γɼલड़ͨ͠Α͏ʹͲͪΒ͔Ұํͷ৘ใ͚ͩͰ͸ัଊ͢Δ͜ͱ͕೉͍͠ωοτϫʔΫߏ଄Λ໌Β͔ʹग़དྷΔՄ
ೳੑ͕͋Δɽ·ͨɼͦͷ྆৘ใΛѻ͏‫ط‬ଘϞσϧͱൺֱ͢Δͱɼϊʔυʹࠞ߹ϝϯόʔγοϓΛ‫ڐ‬༰͍ͯ͠Δ఺ɼάϥϑͷ༗޲ແ޲ʹ͔͔ΘΒͣద༻Մೳͳ఺ɼͦͯࣾ͠ձωοτϫʔΫʹ͓͚Δ࣍਺ͷҟ࣭ੑΛߟྀͨ͠ϞσϦϯάΛߦ͍ͬͯΔ఺͕ຊ‫ڀݚ‬ͷಛ৭ͱ‫͑ݴ‬Δɽ͜
ΕΒͷൺֱΛ௨ͯ͠ɼ5 અͰ͸ɼఏҊϞσϧ͔Β࣍਺ͷҟ࣭ੑͷߟྀΛআ͍ͨϞσϧʹ͋ͨ
Δ Igarashi and Terui (2020)ɼ‫ͼٴ‬ςΩετ৘ใΛߟྀ͠ͳ͍Ϟσϧʹ૬౰͢Δ Airoldi et al.

(2008) ΛൺֱϞσϧͱͯͦ͠ΕΒͷ༧ଌੑೳΛ‫͍ͯ͠ূݕ‬Δɽ

5

3

Ϟσϧ

ຊઅͰ͸ɼ·ͣఏҊϞσϧͷ‫ͳͱૅج‬Δ Igarashi and Terui (2020) ͷϞσϧΛ঺հ͠ɼ࣍ʹͦͷࠩҟΛ໌Β͔ʹ͠ͳ͕Βຊ‫͢༻࢖Ͱڀݚ‬ΔϞσϧͷઆ໌Λߦ͏ɽ·ͨɼ྆ϞσϧͰ‫ڞ‬௨ͯ͠ɼ‫؍‬ଌ͞ΕΔσʔλ͸ɼωοτϫʔΫ৘ใΛද͢ྡ઀ߦྻ Aɼ‫ͼٴ‬ϊʔυʹ‫ݻ‬༗ͷςΩετ৘ใΛද͢୯‫ޠ‬ͷ Bag-of-Words ू߹ W ͷೋͭͰ͋Δɽ
·ͣɼD ‫ݸ‬ͷϊʔυΛ࣋ͭ༗޲άϥϑΛߟ͑Δͱɼͦͷྡ઀ߦྻ A ͸ɼD × D ߦྻͰ͋Γɼߦྻͷ֤ཁૉ͸ϊʔυؒͷؔ܎ੑΛࣔ͢ೋ஋ม਺Ͱ͋Δɽͭ·Γɼaij = 0 ͸Τοδ͕ଘࡏ͠ͳ͍͜ͱΛද͠ɼaij = 1 ͸ଘࡏ͢Δ͜ͱΛද͢ɽ·ͨɼࣗ‫ݾ‬ϧʔϓ͸ߟ͑ͳ͍͜ͱ
ͱ͠ɼશͯͷ i ʹ͍ͭͯ aii = 0 Ͱ͋ΔɽIgarashi and Terui (2020) Ͱ͸ɼϊʔυ i ͔Β j ΁ͷؔ܎ੑʹ͓͍ͯɼͦͷૹΓख i ͕જࡏతͳίϛϡχςΟsij ∈ {1, . . . , K}ʢK ͸ίϛϡχ
ςΟ਺ʣʹଐ͠ɼड͚ख j ͸જࡏίϛϡχςΟrji ∈ {1, . . . , K} ʹଐ͢Δ͜ͱΛԾఆ͢Δɽ·ͨɼ͜ΕΒજࡏίϛϡχςΟͷߦྻද‫ݱ‬Λ S = (sij ), R = (rji ) ͱ͢ΔɽϞσϧͷੜ੒աఔʹ͓͍ͯɼૹΓख‫ͼٴ‬ड͚खͷίϛϡχςΟ͸ΧςΰϦΧϧ෼෍ɼsij | ηi ∼ Categorical (ηi )ɼ

rji | ηj ∼ Categorical (ηj ) ʹै͏ɽͨͩ͠ɼηi = (ηi1 , . . . , ηiK ) ͸ϊʔυ i ͷίϛϡχςΟॴଐׂ߹Λද͢ύϥϝʔλͰ͋Γɼ k ηik = 1 Λຬͨ͢ɽ͜ͷίϛϡχςΟ෼෍ͷߦྻද‫ݱ‬͸
H = (η1 , . . . , ηD ) Ͱද͞ΕΔɽH ͷࣄલ෼෍͸σΟϦΫϨ෼෍ ηi | γ ∼ Dirichlet(γ) ʹै͏͜ͱΛԾఆ͓ͯ͠Γɼγ = (γ1 , . . . , γK ) ͸ਪఆʹ͋ͨͬͯௐ੔͕ඞཁͳϋΠύʔύϥϝʔλͰ͋Δɽϊʔυ i ͱ j ؒͷؔ܎ੑ aij ͸ɼsij ͱ rji ͕ॴ༩ͷ࣌ɼϕϧψʔΠ෼෍ɼaij | sij = k, rji =k  , Ψ ∼ Bernoulli (ψkk ) ʹै͏͜ͱΛԾఆ͢Δɽͨͩ͠ɼψkk ͸ɼૹΓखͷίϛϡχςΟ͕ k ɼड͚खͷίϛϡχςΟ͕ k  ͷ࣌ʹΤοδ͕ੜ੒͞ΕΔ֬཰Λࣔ͢ɽ·ͨɼΤοδ֬཰
ͷ K × K ߦྻද‫ݱ‬͸ Ψ = (ψkk ) Ͱද͞Εɼߦྻͷ֤ཁૉ͸ɼࣄલ෼෍ͱͯ͠ϕʔλ෼෍ɼψkk | δkk , kk ∼ Beta(δkk , kk ) Λ࣋ͭɽ͜ͷͱ͖ɼδ,  ͸ Ψ ͱಉ࣍͡‫ݩ‬Λ࣋ͭϋΠύʔύϥϝʔλͰ͋ΔɽैͬͯɼίϛϡχςΟ෼෍ H Λॴ༩ͱͨ͠ͱ͖ͷωοτϫʔΫσʔλʹର͢Δ৚݅෇໬6౓͸ҎԼͰఆٛ͞ΕΔɽ

p(A, S, R, Ψ | H)
= p(A | S, R, Ψ)p(S | H)p(R | H)p(Ψ | δ, )
 K K
 D
D



=
{p(aij | sij , rji , Ψ)p(sij | ηi )p(rji | ηj )}p(ψkk | δkk , kk ).
i=1

(1)

k=1 k =1

j=1,j=iଓ͍ͯɼϊʔυ‫ݻ‬༗ͷςΩετίϯςϯπʹ͍ͭͯߟ͑Δɽ͜͜Ͱ͸ɼϊʔυ i ͕ੜ੒ͨ͠ςΩετʹ͍ͭͯɼจষ಺ͷ୯‫ޠ‬ͷॱ൪Λແࢹͯ͠ɼͭ·Γ Bag-of-Words ͷ‫Ͱࣜܗ‬อଘͨ͠ Mi ‫ݸ‬ͷ୯‫ޠ‬Λ‫؍‬ଌσʔλͱ͢Δɽϊʔυ i ʹؔ͢Δ m ൪໨ͷ୯‫ ޠ‬wim ͸જࡏతͳίϛϡχςΟxim ∈ {1, . . . , K} ‫ͼٴ‬τϐοΫ zim ∈ {1, . . . , L}ʢL ͸τϐοΫ਺ʣΛ࣋ͭ͜ͱΛԾఆ͢Δɽ୯‫ޠ‬ίϛϡχςΟͱ୯‫ޠ‬τϐοΫͷ഑ྻද‫ݱ‬͸ͦΕͧΕ X ͱ Z Ͱද͞Εɼ֤഑ྻͷཁૉ͸ Mi ࣍‫ݩ‬ͷϕΫτϧͰ͋ΔɽϞσϧͷੜ੒աఔʹ͓͍ͯɼ୯‫ޠ‬ίϛϡχςΟxim ͸ΧςΰϦ
Χϧ෼෍ xim | ηi ∼ Categorical(ηi ) ʹै͏ɽ͜͜Ͱɼηi ͕୯‫ޠ‬ίϛϡχςΟxim ͚ͩͰͳ͘ɼ
ϊʔυίϛϡχςΟsij , rji Λੜ੒͢ΔύϥϝʔλͰ͋ͬͨ͜ͱΛࢥ͍ग़͢ͱɼηi ͸ωοτϫʔΫσʔλͱςΩετσʔλͷϞσϧʹ‫ڞ‬௨͢ΔύϥϝʔλͰ͋Γɼ྆ऀͷ৘ใΛͭͳ͛Δ໾ׂΛՌ͍ͨͯ͠ΔɽҰํɼ୯‫ޠ‬τϐοΫ͸୯‫ޠ‬ίϛϡχςΟ͕ॴ༩ͷঢ়ଶͰΧςΰϦΧϧ෼෍ zim | xim = k, Θ ∼ Categorical(θk ) ʹै͏ɽ͜ͷͱ͖ɼθk = (θk1 , . . . , θkL ) ͸ɼίϛϡχςΟk ʹؔ͢ΔτϐοΫׂ߹Λࣔ͢ύϥϝʔλͰ͋Γɼ l θkl = 1 Λຬͨ͢ɽ͜ͷτϐοΫ
෼෍ͷߦྻද‫ݱ‬͸ Θ = (θ1 , . . . , θk ) Ͱ͋Γɼࣄલ෼෍͸σΟϦΫϨ෼෍ θk | α ∼ Dirichlet(α)ʹै͏ɽ୯‫ޠ‬τϐοΫ zim Λॴ༩ͱͯ͠ɼͦΕʹରԠ͢Δ୯‫ ޠ‬wim ∈ {1, . . . , V }ʢV ͸૯୯‫਺ޠ‬ʣ͸ɼ୯‫ޠ‬τϐοΫʹରԠ͢ΔΧςΰϦΧϧ෼෍ wim | zim = l, Φ ∼ Categorical(φl ) ʹै͏ɽͨͩ͠ɼφl = (φl1 , . . . , φlV ) ͸ɼͦͷτϐοΫʹ͓͍ͯ୯‫͕ޠ‬ੜ੒͞ΕΔ֬཰Λද͢୯‫ޠ‬෼෍Ͱ͋Γɼ v φlv = 1 Λຬͨ͢ɽ୯‫ޠ‬෼෍ͷߦྻද‫ݱ‬͸ Φ = (φ1 , . . . , φL ) Ͱ͋Γɼͦͷࣄલ෼෍͸σΟϦΫϨ෼෍ φl ∼ Dirichlet(β) ʹै͏ɽैͬͯɼςΩετσʔλʹର͢Δ৚݅෇໬౓͸ɼಉ͘͡ίϛϡχςΟ෼෍ H Λॴ༩ͱ͠7ͯɼҎԼͰఆٛ͞ΕΔɽ

p(W, X, Z, Θ, Φ | H)
= p(W | Z, Φ)p(Z | X, Θ)p(X | H)p(Θ | α)p(Φ | β)
 K
M
D
L

i


=
{p(wim | zim , Φ)p(zim | xim , Θ)p(xim | ηi )}p(θk | α)p(φl | β).
i=1

m=1

k=1

(2)

l=1

ίϛϡχςΟ෼෍ H Λॴ༩ͱ͢Δ͜ͱͰɼࣜʢ1ʣ‫ͼٴ‬ʢ2ʣͷ৚݅෇໬౓͕ಠཱͱͳΔԾఆ
Λஔ͍͍ͯΔͨΊɼIgarashi and Terui (2020) ͷ݁߹෼෍͸ɼࣜʢ1ʣͱʢ2ʣ‫ ͼٴ‬H ͷີ౓Λֻ͚߹ΘͤΔ͜ͱͰҎԼͷΑ͏ʹಘΒΕΔɽ

p(A, W, S, R, X, Z, H, Ψ, Θ, Φ)

 D
Mi
D



{p(aij | sij , rji , Ψ)p(sij | ηi )p(rji | ηj )}{p(wim | zim , Φ)P (zim | xim , Θ)p(xim | ηi )} ×
=
i=1
D

i=1

m=1

j=1,j=ip(ηi | γ)KK p(ψkk | δkk , kk )k=1 k =1K

p(θk | α)

k=1

L


p(φl | β).

(3)

l=1

Igarashi and Terui (2020) ͷϞσϧͰ͸ɼϢʔβʔ͕ੜ੒ͨ͠ςΩετίϯςϯπΛߟྀ͠ͳ͕ΒωοτϫʔΫ্ͷίϛϡχςΟߏ଄Λ೺Ѳ͢Δɼͭ·ΓτϐοΫϕʔεɾίϛϡχςΟΛ‫͚ͭݟ‬Δ͜ͱΛ໨తͱ͍ͯ͠Δɽ͜ͷͱ͖ɼϊʔυؒʹΤοδ͕ੜ੒͞ΕΔ֬཰Λɼ

aij = 1 | sij = k, rji = k  ∼ Bernoulli(ψkk ) ͱͯ͠શͯͷϊʔυʹରͯ͠ಉ࣭తͰ͋Δ͜ͱ
ΛԾఆ͍ͯ͠Δɽ͔͠͠ɼલઅͰ΋આ໌ͨ͠Α͏ʹɼ‫࣮ݱ‬ͷࣾձωοτϫʔΫʹ͓͍ͯ͸ɼ࣍਺͕ϊʔυʹΑͬͯେ͖͘ҟͳΔ͜ͱ͕ҰൠతͰ͋ΓɼIgarashi and Terui (2020) Ͱ͸ɼ͜ͷੑ࣭ΛߟྀͰ͖͍ͯͳ͍ͨΊɼ‫࣮ݱ‬ͷωοτϫʔΫσʔλʹରͯ͠े෼ʹϑΟοςΟϯά
Ͱ͖ͳ͍Մೳੑ͕͋Δɽຊ‫Ͱڀݚ‬͸ɼ͜ͷ໰୊Λղܾ͢ΔͨΊʹɼΤοδੜ੒֬཰ͷ෦෼Λ aij = 1 | sij = k, rji =k  ∼ Bernoulli(ψjkk ) ͱͯ͠ϞσϧΛ֦ு͢Δɽ͜ͷͱ͖ɼψjkk ͸ɼૹΓखͷίϛϡχςΟ͕ k Ͱɼड͚खͷίϛϡχςΟ͕ k  ͷ࣌ʹΤοδ͕ੜ੒͞ΕΔ֬཰Λࣔ͠ɼड͚खͷϊʔυj ʹґଘ͢Δҟ࣭ͳύϥϝʔλͰ͋Δɽ͜ͷఆࣜԽʹΑΓɼྫ͑͹ɼड͚ख j ͕ίϛϡχςΟ

8k ͷதͰଟ͘ͷΤοδΛूΊΔɼ͍ΘΏΔϋϒϊʔυͰ͋Δ৔߹ʹɼψjkk ͕େ͖ͳ஋ΛऔΔ
͜ͱͰͦΕΛද‫͢ݱ‬Δɽ͜ΕʹΑΓɼఏҊϞσϧ͸ɼࣾձωοτϫʔΫʹ͓͚Δ࣍਺෼෍ͷҟ࣭ੑΛ൓ө͠ɼϊʔυ͝ͱͷ࣍਺ͷଟՉʹԠͯ͡Τοδ֬཰ύϥϝʔλΛҟ࣭తʹਪఆ͢
Δ͜ͱͰɼΑΓ‫࣮ݱ‬ͷࣾձωοτϫʔΫʹଈͨ͠ϞσϦϯά͕ՄೳͱͳΔɽ·ͨɼΤοδ֬཰ͷ K × K ߦྻද‫ݱ‬͸ Ψi = (ψikk ) Ͱද͞Εɼߦྻͷ֤ཁૉ͸ɼࣄલ෼෍ͱͯ͠ϕʔλ෼෍ɼψikk | δkk  , kk  ∼ Beta(δkk , kk ) ʹै͏͜ͱΛԾఆ͢Δɽຊ‫͍༻Ͱڀݚ‬ΔϞσϧ͸ɼ্ड़ͨ͠఺Ҏ֎͸ Igarashi and Terui (2020) ͱಉ͡ఆࣜԽΛԾఆ͍ͯ͠ΔͨΊɼίϛϡχςΟ෼෍ H Λॴ༩ͱͨ͠ͱ͖ͷωοτϫʔΫσʔλʹର͢Δ໬౓ɼࣜ (1) ͕ҎԼͷΑ͏ʹมߋ͞ΕΔɽ

p(A, S, R, Ψ | H)
= p(A | S, R, Ψ)p(S | H)p(R | H)p(Ψ | δ, )

 D
K
D
K 



=
{p(aij | sij , rji , Ψj )p(sij | ηi )p(rji | ηj )}p(ψikk | δkk , kk ) .
i=1

4

(4)

k=1 k =1

j=1,j=i৚݅෇͖ࣄ‫ޙ‬෼෍ͱύϥϝʔλਪఆઌߦ‫͍͓ͯʹڀݚ‬ɼτϐοΫϞσϧΛਪఆ͢ΔͨΊͷख๏͸ɼม෼ϕΠζ๏΍ஞֶ࣍श๏ͳ
Ͳଟ͘ఏҊ͞Ε͍ͯΔɽͦͷதͰ΋࠷΋޿͘࢖ΘΕ͍ͯΔ΋ͷͷҰ͕ͭɼ่յ‫ܕ‬Ϊϒεαϯ
ϓϦϯά (collapsed Gibbs sampling, CGS, Griﬃths and Steyvers, 2004) Ͱ͋Δɽ͜Ε͸ɼજࡏม਺ͷࣄ‫ޙ‬෼෍Λಋग़͢ΔաఔͰϞσϧύϥϝʔλΛੵ෼ফ‫͠ڈ‬ɼαϯϓϦϯάΛޮ཰తʹߦ͏ख๏Ͱ͋ΔɽҎԼͰ͸ɼຊ‫ڀݚ‬ͷఏҊϞσϧʹର͢Δ CGS ͷͷͨΊͷ৚݅෇͖ࣄ
‫ޙ‬෼෍Λಋग़͢ΔɽఏҊϞσϧʹ͓͚ΔɼίϛϡχςΟ෼෍ H ɼΤοδ֬཰ ΨɼτϐοΫ෼෍ Θɼ୯‫ޠ‬෼෍ Φ
ͷ 4 ͭͷύϥϝʔλʹ͍ͭͯ͸ɼࣄલ෼෍ͱͷ‫ڞ‬໾ੑʹ‫͖ͮج‬ɼ৚݅෇͖ࣄ‫ޙ‬෼෍Λ‫ط‬஌ͷ෼෍ͱͯ͠ಋग़͢Δ͜ͱ͕Ͱ͖Δɽͨͩ͠ɼͦͷৄࡉͳಋग़աఔ͸ Appendix A ʹৡΔɽ·ͨɼͦΕҎ֎ͷજࡏม਺ͱͯ͠ɼૹΓख‫ͼٴ‬ड͚खͷજࡏίϛϡχςΟS, Rɼ୯‫ޠ‬ͷજࡏίϛϡχςΟX ‫ͼٴ‬જࡏτϐοΫ Z ͷ 4 ͕ͭ͋Δ͕ɼ͜ΕΒͷ৚݅෇͖ࣄ‫ޙ‬෼෍͸ɼAppendix

9A Ͱಋग़ͨ͠ࣄ‫ޙ‬෼෍Λ༻͍ͯҎԼͷΑ͏ʹಋग़͞ΕΔɽ
p(sij = k, rji = k  | aij , A\ij , S\ij , R\ji , X, γ, δ, ) ∝p(sij = k | ηi )p(rji = k  | ηj )p(xi | ηi )p(xj | ηj )p(ηi | S\ij , R\ji , X, γ)p(ηj | S\ij , R\ji , X, γ)dηi dηj × p(aij | ψjkk )p(ψjkk | A\ij , S\ij , R\ji , δ, )dψjkk
N  \ji + Mjk + γk
Nik\ij + Mik + γk
 ×  jk×= t Nit\ij + Mit + γtt Njt\ji + Mjt + γt(+)

njkk \ij + δkk(+)

I(aij =1)(−)

njkk \ij + kkI(aij =0),(−)

njkk \ij + njkk \ij + δkk + kk

(5)p(xim = k, zim = l | W, S, R, X\im , Z\im , α, β, γ)∝ p(si , ri | ηi )p(xim = k | ηi )p(ηi | S, R, X\im , γ)dηi × p(zim = l | θk )
p(θk | X\im , Z\,im , α)dθk × p(wim = v | φl )p(φl | W\im , Z\im , β)dφlMMNik + Mik\im + γk
+ αl
+ βv
 ×   kl\im ×   lv\im.
= t Nit + Mit\im + γt
q Mkq\im + αq
u Mlu\im + βu(6)ͨͩ͠ɼࣜʢ5ʣʹ͓͚Δ Nik ͸ɼϊʔυ i ͕࣋ͭ D − 1 ‫ݸ‬ͷؔ܎ੑʹ͓͍ͯɼૹΓख‫ͼٴ‬ड͚खͷજࡏίϛϡχςΟͱͯ͠ k ׂ͕Γ౰ͯΒΕͨճ਺Λද͠ɼMik ͸ɼϊʔυ i ͷ୯‫ޠ‬ί(+)ϛϡχςΟʹ k ׂ͕Γ౰ͯΒΕͨճ਺Λද͢ɽnikk ͸ɼϊʔυ i ʹؔ͢Δ D − 1 ‫ݸ‬ͷؔ܎ੑ(−)ͷ͏ͪɼίϛϡχςΟk, k  ׂ͕Γ౰ͯΒΕͨΤοδ͕ੜ੒͞Ε͍ͯΔؔ܎ੑͷ਺ɼnikk ͸ɼΤοδ͕ੜ੒͞Ε͍ͯͳ͍ؔ܎ੑͷ਺Λද͢ɽࣜʢ6ʣʹ͓͚Δ Mkl ͸ɼίϛϡχςΟk ׂ͕Γ౰ͯΒΕͨ୯‫ޠ‬ͷ͏ͪτϐοΫ l ׂ͕Γ౰ͯΒΕͨճ਺ɼMlv ͸ɼ‫ޠ‬ኮ v ʹτϐοΫ l ׂ͕Γ౰ͯΒΕͨճ਺Λද͢ɽ·ͨɼఴ͑ࣈͷ \ ͸͜ΕΒͷΧ΢ϯτ͔Βɼ౰֘σʔλΛআ͘͜ͱΛҙຯ͢ΔɽCGS Ͱ͸ɼࣜʢ5ʣ‫ͼٴ‬ʢ6ʣʹैͬͯɼ֤ؔ܎ੑ‫ͼٴ‬୯‫ʹޠ‬ରͯ͠જࡏίϛϡχςΟͱτϐοΫΛ‫܁‬Γฦ͠αϯϓϦϯά͢Δɽ࠷ऴతʹɼॳ‫ظ‬஋ʹґଘ͢ΔՔಇ‫ؒظ‬Λআ͍ͨαϯϓϧΛ༻͍ͯɼੵ෼ফ‫ ͍ͨͯ͠ڈ‬4 ͭͷύϥϝʔλͷ‫ظ‬଴஋Λ‫͢ࢉܭ‬Δ͜ͱͰਪఆ஋ΛಘΔɽ

10

5

࣮ূ෼ੳ

5.1

࢖༻σʔλ

͜͜Ͱ͸ɼ‫࣮ݱ‬ͷΦϯϥΠϯࣾձωοτϫʔΫʹରͯ͠ɼఏҊϞσϧΛ༻͍ͨ෼ੳ͕༗ӹͰ
͋Δ͜ͱΛࣔͨ͢ΊʹɼTwitter σʔλΛ࢖࣮ͬͨূ෼ੳΛߦ͏ɽຊઅͰ͸ɼ·ͣ෼ੳʹ༻͍ͨσʔληοτͷ֓ཁͱલॲཧʹ͍ͭͯઆ໌͢Δɽຊ‫Ͱڀݚ‬͸ɼ೚ఱಊ‫ࣜג‬ձ͕ࣾ Twitter্Ͱอ͍࣋ͯ͠Δӳ‫ޠ‬൛ެࣜΞΧ΢ϯτΛத৺ͱ͢ΔωοτϫʔΫΛର৅ͱͯ͠ɼҎԼͷखॱͰσʔλΛऩू‫ͼٴ‬Ճ޻ͨ͠ɽ
·ͣɼ2018 ೥ 5 ݄ 1 ೔࣌఺ͰͷϑΥϩʔؔ܎ʹैͬͯɼ೚ఱಊͷΞΧ΢ϯτΛϑΥϩʔ͍ͯ͠ΔϢʔβʔ͔ΒϥϯμϜʹαϯϓϦϯάΛߦͬͨɽଓ͍ͯɼαϯϓϧ͞ΕͨϢʔβʔΛϑΥϩʔ͍ͯ͠ΔผͷϢʔβʔ͔Β΋ϥϯμϜʹαϯϓϦϯάΛߦͬͨɽͦͯ͠ɼͦΕΒͷϢʔβʔͰ‫ܗ‬੒͞ΕΔωοτϫʔΫʹ͓͍ͯɼೖ࣍਺ͱग़࣍਺ͷฏ‫ ͕ۉ‬3 ҎԼͷϢʔβʔΛ֎Ε஋ͱΈͳͯ͠σʔληοτ͔Βআ֎ͨ͠ɽ݁Ռͱͯ͠ɼ3,500 ਓͷϢʔβʔ͕࢒ΓɼωοτϫʔΫ಺ʹ͓͚ΔΤοδͷ૯਺͸ 68,949 ຊͰ͋ͬͨɽ͜ΕΒͷϢʔβʔͰ‫ܗ‬੒͞ΕΔ༗޲
άϥϑΛωοτϫʔΫ৘ใͱͯ͠࢖༻͢Δɽ࣍ʹɼςΩετσʔλͷ࡞੒ํ๏Λઆ໌͢Δɽ·ͣɼ্Ͱαϯϓϧ͞Εͨ 3,500 ਓ෼ͷΞΧ΢ϯτʹରͯ͠ɼ2017 ೥ 9 ݄ 1 ೔͔Β 2018 ೥ͷ 2 ݄ 28 ೔1 ·Ͱʹ౤ߘͨ͠౤ߘ಺༰͔ΒςΩετ෦෼Λશͯൈ͖ग़ͨ͠ɽ͜ΕΒͷςΩετσʔλʹରͯ͠ɼจষ͔Β୯‫΁߹ूޠ‬ͷ෼ղɼখจࣈ΁ͷ౷Ұɼ਺ࣈɼ‫߸ه‬ɼ‫ͼٴ‬ओཁͳετοϓϫʔυʢaɼtheɼI ͳͲʣͷ࡟আɼ‫͔ܗ༻׆‬Β‫΁װޠ‬ͷ౷ҰʢstemmingʣͷॱʹલॲཧΛߦͬͨɽ͞ΒʹɼॲཧࡁΈͷςΩετ
σʔλͷ͏ͪɼίʔύε಺Ͱͷස౓͕ 20 ҎԼɼ͋Δ͍͸ 20 ਓҎԼͷϢʔβʔʹ͔͠࢖ΘΕ͍ͯͳ͍௿ස౓ͷ୯‫ͱޠ‬ɼ50 ਓҎ্ͷϢʔβʔʹ࢖ΘΕ͍ͯΔߴස౓ͷ୯‫ޠ‬ΛɼτϐοΫਪఆ΁ͷѱӨ‫ڹ‬Λආ͚ΔͨΊʹσʔληοτ͔Βআ͍ͨɽ݁Ռͱͯ͠ɼίʔύε಺ʹ͸ 9,001छྨͷ୯‫࢒͕ޠ‬Γɼϊʔυ͝ͱͷฏ‫ۉ‬୯‫਺ޠ‬͸ 98.2 Ͱ͋ͬͨɽ࣍અͰ͸ɼఏҊϞσϧʹ͓͚ΔίϛϡχςΟ਺ɼτϐοΫ਺ͷܾఆํ๏Λઆ໌ͨ͠ͷͪɼ࡞੒ͨ͠σʔληοτʹର͢Δ
1ςΩετσʔλͷલॲཧͷஈ֊Ͱɼେ൒ͷϢʔβʔ͕ɼ2018 ೥ 3 ݄ʹ։͔Εͨ Nintendo Direct ͱ͍͏৽঎඼ൃදΠϕϯτʹؔ͢Δ౤ߘΛߦ͍ͬͯΔ͜ͱ͕൑໌ͨ͠ɽ͕ͨͬͯ͠ɼຊ‫Ͱڀݚ‬͸ɼ͜ͷΑ͏ͳଟ͘ͷϢʔβʔͰ‫ڞ‬௨͢ΔಉҰͷࣄ৅ʹର͢Δ౤ߘ͕τϐοΫͷਪఆʹ༩͑ΔӨ‫ڹ‬Λආ͚ΔͨΊɼςΩετσʔλͷ‫؍‬ଌ‫ؒظ‬Λ 2018 ೥ 2 ݄ 28 ೔·Ͱͱͨ͠ɽ

11ఏҊϞσϧͷਪఆ݁Ռʹ͍ͭͯٞ࿦͢Δɽ

5.2

෼ੳ݁Ռ

ఏҊϞσϧΛ‫ؚ‬ΊͯɼҰൠʹϒϩοΫϞσϧΛ༻͍ͯ෼ੳ͢Δࡍʹ͸ɼࣄલʹίϛϡχςΟ
਺ʢ‫ͼٴ‬ຊ‫Ͱڀݚ‬͸ͦΕʹՃ͑ͯτϐοΫ਺ʣΛܾΊΔඞཁ͕͋Δɽઌߦ‫Ͱڀݚ‬͸ɼίϛϡχςΟ਺ͷܾఆΛ৘ใྔ‫ج‬४Λ༻͍ͨϞσϧൺֱͱͯ͠ଊ͑ɼBIC ʹΑΔํ๏ (Handcock et al.,2007; Saldaña et al., 2017)ɼintegrated completed likelihood ʹΑΔํ๏ (Daudin et al., 2008;
Bouveyron et al., 2018)ɼม෼ϕΠζʹΑΔํ๏ (Latouche et al., 2012) ͳͲ༷ʑͳख๏͕
ఏҊ͞Ε͍ͯΔɽ͔͠͠ɼຊ‫Ͱڀݚ‬͸ɼۙ೥৽ͨͳ৘ใྔ‫ج‬४ͱͯ͠ఏҊ͞Εɼ‫Ͱࡏݱ‬͸਺ଟ͘ͷྖҬͰ࢖ΘΕ͍ͯΔ޿͘࢖͑Δ৘ใྔ‫ج‬४ (widely applecable information criterion,

WAIC, Watanabe, 2010) ΛϞσϧൺֱͷ‫ج‬४ͱͯ͠࠾༻ͨ͠ɽఏҊϞσϧʹର͢Δ WAICͷৄࡉ͸ Appendix B ʹৡΔɽද 2 ͸ɼίϛϡχςΟ਺‫ͼٴ‬τϐοΫ਺Λ 5 ͔Β 10 ͷൣғͰઃఆ͠ɼ5.1 અͰ࡞੒ͨ͠σʔληοτʹରͯ͠ WAIC Λ‫݁ͨ͠ࢉܭ‬ՌͰ͋Δɽͨͩ͠ɼ͜ͷ࣌ͷ‫܁‬Γฦ͠਺͸ 5,000 ճͰ͋Γɼͦͷ͏ͪ 2,000 ճΛॳ‫ظ‬஋ʹґଘ͢ΔՔಇ‫ͯ͠ͱؒظ‬আ͍
ͨɽ·ͨɼϋΠύʔύϥϝʔλͷઃఆ͸ɼͦΕͧΕɼαl = 0.1, ∀lɼβv = 0.1, ∀v ɼγk = 1.0, ∀k ɼ

δkk = kk = 0.1, ∀k, k  Ͱ͋Δɽͦͷ݁ՌɼίϛϡχςΟ਺ 7ɼτϐοΫ਺ 7 ͷϞσϧ͕બ͹ΕͨͨΊɼҎ߱Ͱ͸͜ͷϞσϧΛ༻͍ͨ Twitter σʔλͷ෼ੳ݁ՌΛٞ࿦͢Δɽ·ͣɼϊʔυʹґଘ͠ͳ͍άϩʔόϧύϥϝʔλΛ‫ݟ‬Δ͜ͱͰɼਓʑ͕‫ݕ‬ग़͞ΕͨίϛϡχςΟ಺ͰͲͷΑ͏ͳ͜ͱʹؔ৺Λ͍࣋ͬͯΔͷ͔͕෼͔Δɽਤ 2 ͸ɼਪఆ͞Εͨ୯‫ޠ‬෼෍ͷ஋͕࠷΋ߴ্͍Ґ 10 ‫ݸ‬ͷ୯‫ޠ‬ΛτϐοΫຖʹฒ΂ͨ΋ͷͰ͋Γɼ͜ΕʹΑͬͯτϐοΫͷҙຯΛղऍ͢Δ͜ͱ͕Ͱ͖Δɽ֤τϐοΫͷҙຯͱ୅දతͳ୯‫ޠ‬͸ҎԼͷ௨ΓͰ͋Δɽ
τϐοΫ 1 ͸Ξχϝʔγϣϯʹؔ͢ΔτϐοΫʢ୅දతͳ୯‫ޠ‬͸ blackclovɼhunterxhuntɼ

jojosbizarreadventur ͳͲʣɼτϐοΫ 2 ͸ετϦʔϛϯά഑৴શൠʹؔ͢ΔτϐοΫʢ୅දతͳ୯‫ޠ‬͸ teamemmmmsiɼtwitchkittenɼroku ͳͲʣɼτϐοΫ 3 ͸Իָʹؔ͢ΔτϐοΫ
ʢ୅දతͳ୯‫ޠ‬͸ vevoɼsprinrilla ͳͲʣɼτϐοΫ 4 ͸ήʔϜετϦʔϛϯά഑৴ʹؔ͢Δτ
ϐοΫʢ୅දతͳ୯‫ޠ‬͸ critical roleɼzeldathon ͳͲʣɼτϐοΫ 5 ͸ಡॻʹؔ͢ΔτϐοΫ
ʢ୅දతͳ୯‫ޠ‬͸ amreadɼbookreviewɼkindleunlimit ͳͲʣɼτϐοΫ 6 ͸Ϗδωεʹؔ͢12ΔτϐοΫʢ୅දతͳ୯‫ޠ‬͸ digitalmarketɼsmmɼcontentmarket ͳͲʣɼͦͯ͠τϐοΫ

7 ͸εϙʔπʹؔ͢ΔτϐοΫʢ୅දతͳ୯‫ޠ‬͸ oilerɼtfc ͳͲʣͱ‫͑ݴ‬Δɽ·ͨɼਤ 3 ͸ɼਪఆ͞Ε֤ͨίϛϡχςΟͷτϐοΫ෼෍Ͱ͋Γɼ֤ίϛϡχςΟ಺ʹ͓͚ΔτϐοΫͷׂ߹Λ֬ೝ͢Δ͜ͱ͕Ͱ͖Δɽ࣍ʹɼ֤ϊʔυʹ͍ͭͯҟ࣭ͳϩʔΧϧύϥϝʔλͷਪఆ݁ՌΛ֬ೝ͢Δɽਤ 4 ‫ ͼٴ‬5͸ɼϊʔυ൪߸ 1 ൪ͱ 237 ൪ʹؔ͢ΔΤοδ֬཰ͱίϛϡχςΟ෼෍ͷਪఆ݁ՌͰ͋Δɽ·ͨɼϊʔυ 1 ͷೖ࣍਺͸ 6ɼग़࣍਺͸ 0 Ͱ͋Γɼϊʔυ 237 ͷೖ࣍਺͸ 657ɼग़࣍਺͸ 37 Ͱ
͋Δɽਪఆ݁Ռ͸ɼ͜ͷ྆ϊʔυͷ࣍਺த৺ੑͷҧ͍Λ೗࣮ʹද͓ͯ͠Γɼϊʔυ 1 ͕ओʹଐ͢ΔίϛϡχςΟʢίϛϡχςΟ1 ͱ 6ʣʹؔ͢ΔΤοδ֬཰͸௿͍஋Ͱਪఆ͞Ε͍ͯΔͷʹରͯ͠ɼϊʔυ 237 ͕ओʹଐ͢ΔίϛϡχςΟʢίϛϡχςΟ1 ͱ 5ʣʹؔ͢ΔΤοδ֬཰͸ߴ͍஋Ͱਪఆ͞Ε͍ͯΔɽ͜ͷΑ͏ʹɼΤοδ֬཰ͷύϥϝʔλ͕Τοδͷ‫͕ܨ‬Γ΍͢͞ʹؔ͢Δҟ࣭ੑΛଊ͑ΒΕΔΑ͏ͳԾఆΛಋೖ͢Δ͜ͱͰɼΑΓॊೈʹωοτϫʔΫϞσϧΛද‫͖Ͱݱ‬ΔΑ͏ʹͳΓɼςετσʔλʹର͢Δ༧ଌੑೳ΋޲্͢Δ͜ͱ͕‫ظ‬଴͞ΕΔɽ࣍
અͰ͸ɼ͜ΕΛ‫͢ূݕ‬ΔͨΊʹɼઌߦ‫͚͓ʹڀݚ‬Δ‫ط‬ଘϞσϧͱ‫ʹڞ‬ൺֱ࣮‫ݧ‬Λߦ͏ɽ

5.3

༧ଌੑೳͷ‫ূݕ‬ຊઅͰ͸ɼఏҊϞσϧͷςετσʔλʹର͢Δ༧ଌੑೳΛɼൺֱϞσϧͱ‫͢ূݕʹڞ‬Δɽൺ
ֱϞσϧͱͯ͠ɼઌߦ‫͚͓ʹڀݚ‬Δ‫ط‬ଘϞσϧ͔ΒɼAiroldi et al. (2008) ͱ Igarashi andTerui (2020) ΛબΜͩɽAiroldi et al. (2008) ͷϞσϧ͸ɼIgarashi and Terui (2020) ͷϞσϧ͔ΒςΩετ৘ใͷߟྀΛআ͍ͨϞσϧʹ૬౰͢ΔͨΊɼ͜ΕΒΛൺֱ͢Δ͜ͱͰɼςΩετ৘ใΛߟྀ͢Δ͜ͱʹΑΔ༧ଌੑೳ΁ͷӨ‫ڹ‬Λ‫ݟ‬Δ͜ͱ͕Ͱ͖Δɽ͞ΒʹɼIgarashi andTerui (2020) ͷϞσϧ͸ɼຊ‫ڀݚ‬ͷϞσϧ͔ΒΤοδ֬཰ͷҟ࣭ੑΛআ͍ͨಉ࣭ϞσϧͰ͋Γɼҟ࣭ੑͷߏ଄͕༧ଌੑೳ΁༩͑ΔӨ‫ڹ‬Λ‫ݟ‬Δ͜ͱ͕Ͱ͖Δɽ

5.2 અͰ͸ɼશͯͷωοτϫʔΫɼςΩετσʔλΛֶशσʔλͱͯ͠ϞσϧͷਪఆΛߦ͕ͬͨɼ͜͜Ͱ͸ɼ֤ϊʔυ͕࣋ͭ D − 1 ‫ݸ‬ͷؔ܎ੑͷ͏ͪɼ90%Λֶशσʔλͱͯ͠Ϟσϧͷਪఆʹ࢖͍ɼ࢒Γͷ 10%Λςετσʔλͱͨ͠͠ɽςΩετσʔλʹ͍ͭͯ͸ɼલઅಉ༷
શͯͷσʔλΛֶशσʔλͱͯ͠༻͍ͨɽ·ͨɼ‫܁‬Γฦ͠਺΍ϋΠύʔύϥϝʔλͷઃఆ΋

13લઅͱಉ͡৚݅Ͱਪఆ͍ͯ͠Δɽ͜ΕΒͷ৚݅ͷԼͰֶशσʔλʹର͢ΔਪఆΛߦ͍ɼ֤ύϥϝʔλͷਪఆ஋Λಘͨɽਪఆ͞ΕͨίϛϡχςΟ෼෍ͱΤοδ֬཰Λ Ĥ, Ψ̂ ͱද͢ͱɼྫ
͑͹ఏҊϞσϧʹ͍ͭͯ͸ɼςετσʔλ aij ∈ Atest ʹର͢Δ༧ଌ֬཰͸ҎԼͰ‫͖Ͱࢉܭ‬Δɽ
K

K

η̂ik η̂jk ψ̂jkk

p(aij = 1) =(7)

k=1 k =1

Airoldi et al. (2008) ͱ Igarashi and Terui (2020) ͷϞσϧʹ͍ͭͯ΋ಉ༷ʹɼίϛϡχςΟ
෼෍ͱΤοδ֬཰ͷੵʹΑͬͯ༧ଌ֬཰Λ‫͖Ͱࢉܭ‬Δɽ
ද 3 ͸ɼίϛϡχςΟ਺ͱτϐοΫ਺ΛͦΕͧΕ 5 ͔Β 10 ·ͰมԽͤͨ͞ͱ͖ͷ֤Ϟσ
ϧͷ Area Under the CurveʢAUCʣͷ஋Ͱ͋Δɽ͜ΕΛ‫ݟ‬Δͱɼ΄΅શͯͷ૊Έ߹Θͤʹ͍ͭͯఏҊϞσϧʢද಺Ͱ͸ Heteroʣ͕ൺֱϞσϧͰ͋Δ Igarashi and Terui (2020)ʢද಺Ͱ
͸ HomoʣΑΓ΋༏Ε͍ͯΔ͜ͱ͕෼͔ΔɽΑͬͯɼࣾձωοτϫʔΫʹҰൠతʹΈΒΕΔ
࣍਺ͷҟ࣭ੑΛߟྀ͠ɼΤοδ͕ੜ੒͞ΕΔ֬཰͸ϊʔυ͝ͱʹಉ࣭తͰ͸ͳ͍ͱ͍͏Ծఆ
Λஔ͍ͨϞσϧͷํ͕༧ଌੑೳ͕༏ΕͨϞσϧͰ͋Δͱ͍͑Δɽ·ͨɼAiroldi et al. (2008)ʢද಺Ͱ͸ MMSBʣͱ Igarashi and Terui (2020) Λൺֱ͢ΔͱɼίϛϡχςΟͷ਺͕গͳ͍
ͱ͖ʢK = 5, 6ʣʹ͸ Airoldi et al. (2008) ͷํ͕ AUC ͕શମతʹߴ͘ɼίϛϡχςΟͷ਺͕ଟ͍ͱ͖ʢK = 8, 9, 10ʣ͸ Igarashi and Terui (2020) ͷํ͕શମతʹ AUC ͕ߴ͍ͱ͍͏݁
ՌͰ͋ͬͨɽ͜ͷ݁Ռ͔Βɼຊ‫ ͍ͨ༻Ͱڀݚ‬Twitter ωοτϫʔΫ͸ɼେ·͔ʹίϛϡχςΟ
Λ෼͚Δࡍʹ͸ωοτϫʔΫ৘ใͷΈΛߟྀ͢Δ͚ͩͰॆ෼Ͱ͋Δ͕ɼΑΓࡉ͔ͳίϛϡχςΟʹ෼͚Δ৔߹ʹ͸ɼςΩετ৘ใΛ༻͍ͯτϐοΫͷ·ͱ·ΓΛߟྀ͠ͳ͕Β෼͚ͨํ͕ΑΓྑ͍ΫϥελϦϯάͱͳΔωοτϫʔΫͰ͋Δͱ͍͑Δɽͭ·Γɼ1 અͰ΋ड़΂ͨΑ͏ʹɼֶߍ΍ಉ‫ڃ‬ੜͱ͍ͬͨେ͖ͳ·ͱ·ΓͷίϛϡχςΟͷத͔ΒɼԻָ΍εϙʔπͷΑ͏ʹझຯ΍ؔ৺ࣄ͕‫ڞ‬௨͍ͯ͠Δ·ͱ·ΓɼτϐοΫϕʔεɾίϛϡχςΟΛ‫͍͚ͯͭ͘ݟ‬ϞσϦϯά͕ɼΑΓਫ਼៛ͳωοτϫʔΫ෼ੳͷͨΊʹ͸༗ӹͰ͋Δͱ͍͏͕ࣔࠦಘΒΕͨɽ

14

6

݁࿦

ຊ‫Ͱڀݚ‬͸ɼࣾձωοτϫʔΫ෼ੳΛΑΓ‫ʹ࣮ݱ‬ଈͨ͠༗ҙٛͳ෼ੳͱ͢ΔͨΊʹɼωοτϫʔΫ৘ใ͚ͩͰͳ͘ɼਓʑͷ‫ڵ‬ຯ΍ؔ৺Λද͢ιʔγϟϧϝσΟΞ্ͷςΩετ৘ใΛߟྀ͠ɼ͞ΒʹɼࣾձωοτϫʔΫʹಛ༗ͷ࣍਺ͷҟ࣭ੑΛՃຯͨ͠ϞσϧΛఏҊͨ͠ɽઌߦ
‫͚͓ʹڀݚ‬Δ‫ط‬ଘϞσϧͱൺֱͨ͠ͱ͖ɼຊ‫Ͱڀݚ‬ఏҊ͢ΔϞσϧͷಛ৭ͱͯ͠͸ɼωοτϫʔΫ্ͷ֤ϊʔυ͕࣋ͭςΩετ৘ใΛར༻͍ͯ͠Δ఺ɼϊʔυ͕ͦΕͧΕͷؔ܎ੑʹԊͬͯෳ਺ͷίϛϡχςΟʹଐ͢Δ͜ͱΛ‫ڐ‬༰͍ͯ͠Δ఺ɼແ޲άϥϑ͔༗޲άϥϑʹ͔͔ΘΒͣద༻Ͱ͖Δ఺ɼͦͯ࣍͠਺ͷҟ࣭ੑΛߟྀ͠ɼΤοδ֬཰ͷύϥϝʔλ͕ϊʔυ͝ͱʹҟ࣭Ͱ͋Δ͜ͱΛԾఆ͍ͯ͠Δ఺͕‫͛ڍ‬ΒΕΔɽ͜ΕʹΑͬͯɼ࣍਺͕ϊʔυʹΑͬͯେ͖͘ҟͳΔҰൠతͳࣾձωοτϫʔΫʹରͯ͠΋े෼ͳϑΟοςΟϯάੑೳΛ༗͠ͳ͕ΒɼΤοδ͕ີʹू·͓ͬͯΓɼ͔ͭੜ੒͞ΕͨςΩετͷτϐοΫ͕ಉҰͷ෼෍͔Βੜ੒͞ΕΔɼτϐοΫϕʔεɾίϛϡχςΟͷ‫ݕ‬ग़͕ՄೳͱͳΔɽ
࣮ূ෼ੳͷ݁Ռɼ่յ‫ܕ‬ΪϒεαϯϓϦϯάʹΑͬͯਪఆ͞ΕΔఏҊϞσϧ͸ɼ‫࣮ݱ‬ͷ

Twitter σʔλʹରͯ͠ɼҙຯͷ͋ΔίϛϡχςΟ‫ͼٴ‬τϐοΫߏ଄Λଊ͑Δ͚ͩͰͳ͘ɼͲ
ͷΑ͏ͳίϛϡχςΟ਺ɼτϐοΫ਺ͷ૊Έ߹ΘͤͰ͋ͬͯ΋‫ط‬ଘϞσϧΑΓ΋༏Εͨ༧ଌੑೳΛ͓࣋ͬͯΓɼ࣍਺ͷҟ࣭ੑΛߟྀͯ͠Τοδ֬཰Λਪఆ͢ΔϞσϦϯά͸ɼ༧ଌੑೳ
ʹ͓͍ͯ༏Ε͍ͯΔ͜ͱ͕ࣔ͞Εͨɽ͞Βʹɼ͜ͷ݁Ռ͔ΒɼΦϯϥΠϯͷࣾձωοτϫʔΫ෼ੳʹ͓͍ͯɼωοτϫʔΫ্ͷେ·͔ͳίϛϡχςΟߏ଄Λ௒͑ͯɼ͞Βʹࡉ͔͘ΫϥελʔΛ෼ੳ͍ͯ͘͠৔߹͸ɼ֤ϊʔυ͕࣋ͭςΩετ৘ใΛՃຯͯ͠τϐοΫϕʔεɾίϛϡχςΟΛ‫͍͚ͯͭ͘ݟ‬ϞσϦϯά͕༗ӹͰ͋ΔͱͷࣔࠦΛಘΔ͜ͱ͕Ͱ͖ͨɽ
ຊ‫Ͱڀݚ‬͸ɼΦϯϥΠϯ্ͷࣾձωοτϫʔΫʹண໨ͨͨ͠Ίɼਓʑ͕ଞͱωοτϫʔΫΛ‫ܗ‬੒͢Δࡍʹ͸ɼ૬खͷωοτϫʔΫ৘ใͱςΩετ৘ใͷΈΛߟྀ͢Δͱ͍͏ԾఆΛஔ͖ɼ૬खͷ೥ྸ΍ੑผͱ͍ͬͨଐੑ৘ใɼ͋Δ͍͸ߦಈ΍ଶ౓ͱ͍ͬͨ৘ใ͸ɼ͜ΕΒͷσʔλ͕ར༻Ͱ͖ͳ͍͜ͱ͔ΒఏҊϞσϧͷߟྀ͔Β֎͍ͯͨ͠ɽҰํͰɼࣾձωοτϫʔΫ෼ੳʹؔ͢Δઌߦ‫ڀݚ‬ͷจ຺Ͱ͸ɼͦͷΑ͏ͳϊʔυ‫ݻ‬༗ͷʢ͋Δ͍͸ೋ߲ɼࡾ߲ؒͷʣಛ௃ྔ͕ωοτϫʔΫ‫ܗ‬੒ʹӨ‫͍ͯ͠ڹ‬Δ͜ͱ͕ଟ͘ͷ‫ࣔ͞Ͱڀݚ‬Ε͍ͯΔ (Hoﬀ et al., 2002;

Handcock et al., 2007)ɽຊ‫Ͱڀݚ‬͸ɼΤοδ‫ܗ‬੒ͷؔ਺͕ɼؔ܎ੑΛ݁Ϳ྆ऀͷίϛϡχςΟ
15෼෍ɼ‫܎ؔͼٴ‬ੑΛड͚औΔଆͷΤοδ֬཰Ͱߏ੒͞Ε͍͕ͯͨɼઌߦ‫ڀݚ‬Λࢀর͢Δͱɼ͜͜ʹଐੑ΍ߦಈ৘ใͱ͍ͬͨϊʔυ‫ݻ‬༗ͷಛ௃ྔΛ૊ΈࠐΉ֦ு͸༗ҙٛͰ͋Γɼ͜ΕΒͷ৘ใΛϞσϧʹऔΓࠐΉ͜ͱ͸௚઀తʹՄೳͰ͋Δɽσʔλͷར༻Մೳੑͱ߹Θͤͯࠓ‫ޙ‬ͷ՝୊ͱ͍ͨ͠ɽ

References
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Bouveyron, C., Latouche, P., and Zreik, R. The stochastic topic block model for the clustering of vertices in networks with textual edges. Statistics and Computing, 28(1):11–31,
2018.
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Hoﬀ, P. D., Raftery, A. E., and Handcock, M. S. Latent space approaches to social network
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Igarashi, M. and Terui, N. Characterization of Topic-based Online Communities by Combining Network Data and User Generated Content. Statistics and Computing, 2020. (forthcoming).
Karrer, B. and Newman, M. E. Stochastic blockmodels and community structure in networks.
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16

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17

Tablesද 1: ఏҊϞσϧͱ‫ط‬ଘϞσϧͷൺֱ

Blei et al. (2003)
Snijders and Nowicki (1997)‫؍‬ଌσʔλϝϯόʔγοϓ

άϥϑͷํ޲ੑ

࣍਺ͷҟ࣭ੑ

ςΩετͷΈ

ࠞ߹--ωοτϫʔΫͷΈ

୯Ұ

྆ํՄೳ

ߟྀͤͣ

ωοτϫʔΫͷΈ

ࠞ߹

྆ํՄೳ

ߟྀͤͣ

Chang and Blei (2010)ωοτϫʔΫʗςΩετࠞ߹ແ޲άϥϑͷΈ

ߟྀͤͣLiu et al. (2009)ωοτϫʔΫʗςΩετ୯Ұແ޲άϥϑͷΈ

ߟྀͤͣ

Bouveyron et al. (2018)ωοτϫʔΫʗςΩετ

୯Ұ

྆ํՄೳ

ߟྀͤͣ

Zhu et al. (2013)ωοτϫʔΫʗςΩετ

ࠞ߹

྆ํՄೳ

ߟྀͤͣ

Igarashi and Terui (2020)ωοτϫʔΫʗςΩετ

ࠞ߹

྆ํՄೳ

ߟྀͤͣ

ωοτϫʔΫͷΈ୯Ұ྆ํՄೳϊʔυ͝ͱͷ‫ظ‬଴࣍਺ύϥϝʔλΛಋೖωοτϫʔΫʗςΩετ

ࠞ߹

྆ํՄೳ

Τοδ֬཰Λҟ࣭ύϥϝʔλͱͯ͠ఆٛ

Airoldi et al. (2008)

Karrer and Newman (2011)
ຊ‫ڀݚ‬

18

ද 2: WAIC ʹΑΔϞσϧൺֱɿK ͸ίϛϡχςΟ਺ΛɼL ͸τϐοΫ਺Λද͠ɼଠࣈ͸࠷খͷ஋Λҙຯ͢Δɽ

K=5
K=6
K=7
K=8
K=9
K=10

L=5
4422206.32
4333313.32
4313265.58
4320416.87
4429170.84
4361219.83

L=6
L=7
L=8
4340879.93
4321068.95 4333535.35
4333488.66
4351008.38 4309479.01
4285253.01 4272682.48 4346780.91
4282485.37
4326300.05 4324393.23
4329997.66
4439594.82 4407656.85
4342899.53
4282056.30 4306509.44

19

L=94354814.11
4302773.27
4301005.75
4321806.29
4296128.61
4306244.12

L=104553144.83
4280703.13
4414800.13
4426226.19
4301655.85
4406655.34

ද 3: AUC ʹΑΔ༧ଌੑೳͷൺֱʀ֤Ϟσϧͷ໊લ͸ͦΕͧΕɼMMSB ͕ Airoldi et al.
(2008)ɼHomo ͕ Igarashi and Terui (2020)ɼHetoro ͕ຊ‫ڀݚ‬ͷϞσϧΛࢦ͠ɼଠࣈ͸֤ίϛϡχςΟ਺ʢK ʣɼτϐοΫ਺ʢLʣͷ૊Έ߹Θͤʹ͓͚Δ࠷େͷ AUC Λද͢ɽL
5
K=5
MMSB 0.897
Homo
0.896
Hetero 0.917
K=6
MMSB 0.913
Homo
0.904
Hetero 0.925
K=7
MMSB 0.907
Homo
0.920
Hetero 0.929
K=8
MMSB 0.904
Homo
0.925
Hetero 0.928
K=9
MMSB 0.912
Homo
0.920
Hetero 0.922
K=10
MMSB 0.906
Homo
0.923
Hetero 0.923

6

7

0.897
0.900
0.920

0.897
0.890
0.924

0.897 0.897
0.883 0.905
0.921 0.923

0.897
0.890
0.924

0.913
0.908
0.930

0.913
0.910
0.922

0.913 0.913
0.909 0.908
0.930 0.923

0.913
0.906
0.921

0.907
0.900
0.926

0.907
0.895
0.929

0.907 0.907
0.900 0.903
0.930 0.929

0.907
0.911
0.931

0.904
0.918
0.930

0.904
0.916
0.927

0.904 0.904
0.921 0.897
0.930 0.929

0.904
0.916
0.928

0.912
0.922
0.923

0.912
0.918
0.925

0.912 0.912
0.917 0.922
0.927 0.927

0.912
0.920
0.922

0.906
0.926
0.921

0.906
0.923
0.926

0.906 0.906 0.906
0.925 0.920 0.917
0.925 0.923 0.930

20

8

9

10

Figures

δ



θ

γ

Dir

α

∀k ∈ K

Dir

η

Multi

Multi

S

Beta

ψ

Multi

R

β
X

Multi

BernoulliZMulti∀k, k ∈ K

Dir

φ∀l ∈ LA

W∀j ∈ D, j = i

∀1 ≤ n ≤ Mi∀i ∈ Dਤ 1: ఏҊϞσϧͷάϥϑΟΧϧද‫ݱ‬21

nonfollow

teamemmmmsi

trapadrcriticalrol

iartg

growthhacksavvi

blackclov

dokkanvevo

zeldathonamreaddigitalmarket

lube

hunterxhunt

twitchkitten

ddriveorton

erotica

gdpr

foodpornjojosbizarreadventur

vgc

leed

fursuitfriday

asmsg

smm

oiler

mkleosaga

roku

spinrilla

dramaalert

momlifcontentmarket

austria

wnf

wizebot

ifb

sdlivehemp

gamedesign

tfc

hori

ryzen

gainwithpyewaw

htgawmwriterslif

podernfamili

crowdfirmdva

freebiefriday

gainwithxtiandela

sml

bookreview

socialmediamarket

tranc

hyrulesaga

streamersconnect

horfordrobloxdev

kindleunlimit

bigdata

tock

nyxl

nbalivsuav

yoongibookboostemailmarket

thexfil

Topic 1

Topic 2

Topic 3Topic 4

Topic 5Topic 6

Topic 7

ਤ 2: ਪఆ͞Εͨ୯‫ޠ‬෼෍ʹ͓͍ͯ࠷΋ߴ͍஋Λ্࣋ͭҐ 10 ‫ݸ‬ͷ୯‫ޠ‬

22Community 1

Community 2

Community 3

Community 5

Community 6

Community 7

Community 4

1.00

0.75

0.50

Topic distribution

0.25

0.00
1

1.00

0.75

0.50

0.25

0.00
1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

Topic

ਤ 3: ֤ίϛϡχςΟͷτϐοΫ෼෍ʹؔ͢Δਪఆ݁Ռ

23

2

3

4

5

6

7

Edge Probability

0.25 0.50 0.75

7Sender Community

6

5

4

3

2

1

1

2

3

4

5

6

7

6

7

Receiver Community

Community Distribution

0.6

0.4

0.2

0.0
1

2

3

4

5

Communityਤ 4: ϊʔυ 1 ͷΤοδ֬཰ͱίϛϡχςΟ෼෍ʹؔ͢Δਪఆ݁Ռ

24

Edge Probability

0.25 0.50 0.75

7Sender Community

6

5

4

3

2

1

1

2

3

4

5

6

7

6

7

Community Distribution

Receiver Community

0.6

0.4

0.2

0.0
1

2

3

4

5

Communityਤ 5: ϊʔυ 237 ͷΤοδ֬཰ͱίϛϡχςΟ෼෍ʹؔ͢Δਪఆ݁Ռ

25

Appendices৚݅෇͖ࣄ‫ޙ‬෼෍ͷಋग़

A??અͰ͸ɼજࡏίϛϡχςΟ‫ͼٴ‬જࡏτϐοΫͷ৚݅෇͖ࣄ‫ޙ‬෼෍Λಋग़ͨ͠ʢࣜ 5ɼ6ʣɽ͜ΕΒͷࣄ‫ޙ‬෼෍ΛಘΔͨΊʹ͸ɼ·ͣɼίϛϡχςΟ෼෍ɼΤοδ֬཰ɼτϐοΫ෼෍ɼ୯‫ޠ‬෼෍ͷ 4 ͭͷύϥϝʔλʹ͍ͭͯɼ৚݅෇͖ࣄ‫ޙ‬෼෍Λಋग़͢Δඞཁ͕͋Δɽࣄલ෼෍ͱ
ͷ‫ڞ‬໾ੑʹ‫͍ͯͮج‬ɼ͜ΕΒͷࣄ‫ޙ‬෼෍͸ҎԼͷΑ͏ʹಋग़͞ΕΔɽ
p(ηi | S, R, X, γ) =Γ(k Nik + Mik + γk )(8)k Γ(Nik + Mik + γk ) k=1(+)

p(ψikk | A, S, R, δ, ) =KNik +Mik +γk
ηik

(−)

Γ(nikk + nikk + δkk + kk )(+)(−)Γ(nikk + δkk )Γ(nikk + kk )LΓ ( l Mkl + αl )  Mkl +αlθp(θk | X, Z, α) =Πl Γ(Mkl + αl ) l=1 klVΓ ( v Mlv + βv )  Mlv +βvp(φl | W, Z, β) =φ,Πv Γ(Mlv + βv ) v=1 lv

I(a =1)

× ψikkij

(1 − ψikk )I(aij =0)

(9)
(10)

(11)

ఏҊϞσϧʹର͢Δ WAIC ͷఆٛࣜBఏҊϞσϧʹର͢Δ WAIC ͷఆٛࣜ͸ҎԼͷ௨ΓͰ͋Δɽ

lpd

(i)

= log

Mi
D
G 



1
(g)
(g)
p aij | H , Ψjp wim | H (g) , Θ(g) , Φ(g)G g=b+1 j=1
m=1

G
(i)
pwaic =
G−1

G1
G g=b+1G−

1
G g=b+1D(g)

log p aij | H (g) , Ψj

2

Mi

+



(g)

log p aij | H (g) , Ψj

Mi

+

(12)

log p wim | H (g) , Θ(g) , Φ

m=1

j=1

D





log p wim | H (g) , Θ(g) , Φ(g)


(g) 2



2 ⎞
⎠

m=1

j=1

(13)

D

(i)

lpd(i) − pwaic ,W AIC = −2
i=1

26

(14)

(g)

ͨͩ͠ɼp aij | H (g) , Ψj
ͱ p wim | H (g) , Θ(g) , Φ(g) ͸ɼCGS ʹΑΔαϯϓϧͷ͏ͪ g ճ໨ͷ‫܁‬Γฦ͠ʹ͓͚ΔαϯϓϧͰਪఆͨ͠ύϥϝʔλΛ༻͍ͯ‫͞ࢉܭ‬ΕΔ໬౓Ͱ͋ΓɼҎԼͰఆٛ͞Ε͍ͯΔɽ

p aij | H

(g)

(g)
, Ψj

K

K



p wim | H (g) , Θ(g) , Φ(g) =(g)(g)I(a =1)

(g)

(g)

ηik · ηjk · ψjkk ij=
k=1 k =1LK

k=1 l=1(g)

ηik · θkl · φlwim .

27· (1 − ψjkk )(g)I(aij =0)(15)(16)