େن໛Webσʔλʹ͓͚Δ Ωʔϫʔυɾ஍Ҭ͝ͱͷ֦ࢄύλʔϯநग़ ଜࢁଠҰ, দݪ༃ࢠ, ᓎҪอࢤ େࡕେֶ, ࢈ۀՊֶݚڀॴ DEIM 2023

2 ιʔγϟϧηϯαʔͷ໾ׂ എܠ ιʔγϟϧηϯαʔ ࣮ࡍͷࣾձ ౤ߘݕࡧ ϑΟʔυόοΫ

3 Google Flu എܠ

4 ݕࡧΫΤϦ͔Βજࡏతͳؔ܎Λଊ͑ΒΕΔ͔ʁ Ϟνϕʔγϣϯ U.S. Japan Italy Facebook Twitter Instagram Facebook Twitter Instagram Q: Ωʔϫʔυؒͷؔ܎͸ʁ Q: 国同⼠の関係は？ ？

5 ໰୊ఆٛ (JWFO ΦϯϥΠϯ׆ಈσʔλ e.g., άʔάϧݕࡧ

6 ໰୊ఆٛ (PBM ஍Ҭؒͷ֦ࢄύλʔϯ e.g., άʔάϧݕࡧ taylor swift lady gaga beyonce katy perry maroon 5 stevie wonder Group A: Russia, Mexico, Spain, Vietnam, etc. Group B: United Kingdom, Germany, France, etc. Group C: United States, Canada, Australia, etc. Group D: Iran, Pakistan, Brazil, Argentina, etc. Group E: China, Japan, Vietnam, South Africa, etc.

7 ໰୊ఆٛ (PBM Ωʔϫʔυؒͷؔ܎ e.g., άʔάϧݕࡧ United States lady gaga maroon 5 stevie wonder beyonce katy perry taylor swift Japan lady gaga maroon 5 stevie wonder beyonce katy perry taylor swift

8 ໰୊ఆٛ (PBM قઅੑ e.g., άʔάϧݕࡧ

9 ໰୊ఆٛ (PBM ߴ͍༧ଌਫ਼౓ e.g., άʔάϧݕࡧ 2012 2014 2016 2018 Time Keywords Countries Russia Mexico Colombia Modeling Forecasting beyonce katy perry stevie wonder taylor swift lady gaga maroon 5

10 ໰୊ఆٛ GivenΦϯϥΠϯ׆ಈσʔλ Goal 1 ஍Ҭؒͷ֦ࢄύλʔϯ Goal 2 Ωʔϫʔυؒͷؔ܎ Goal 3 قઅੑ Goal 4ߴ͍༧ଌਫ਼౓

11 ໰୊ఆٛ Our solution: FLUXCUBE 拡散反応⽅程式 + ニューラルネットワーク GivenΦϯϥΠϯ׆ಈσʔλ Goal 1 ஍Ҭؒͷ֦ࢄύλʔϯ Goal 2 Ωʔϫʔυؒͷؔ܎ Goal 3 قઅੑ Goal 4ߴ͍༧ଌਫ਼౓

12 ൓Ԡ֦ࢄํఔࣜ Our model: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 Main Equation ൓Ԡ߲ ෼ࢄ߲ Reaction-Diffusion System is utilized is a mathematical model corresponding for physical phenomena.

13 Our model: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 Main Equation ෼ࢄ߲ Amazon BestBuy ebay Target ڝ߹ؔ܎ ૬ޓؔ܎ Macy’s Washington State Amazon Target ebay Craigslist قઅ߲ ϒϥοΫϑϥΠσʔ + × ൓Ԡ֦ࢄํఔࣜ ൓Ԡ߲

14 Our model: FLUXCUBE ೖྗ: 𝝌 = 𝒙𝒕𝒊𝒋 λΠϜεςοϓ U ஍Ҭ J ΞΠςϜ K 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 反応拡散⽅程式 FLUXCUBE 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& ൓Ԡ߲ ֦ࢄ߲ قઅ߲

15 Our model: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 反応拡散⽅程式 FLUXCUBE 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& ൓Ԡ߲ Amazon BestBuy ebay Target Competitive relationship Mutualistic relationship Macy’s

16 ൓Ԡ߲: ΞΠσΞ ΞΠςϜͷؔ܎͸δϟϯάϧͷಈ෺ͷؔ܎ͱྨࣅ (Matsubara, 2015) ൓Ԡ߲: FLUXCUBE Spider monkeys Capybaras Squirrel monkeys Macaws Fruits Nuts Grass Facebook Twitter Youtube Reddit Kids Teens Adults 類似

17 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&

18 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏& 𝒄𝒋𝒋 : ΩʔϫʔυKͱΩʔϫʔυK` ؒͷ૬ޓ࡞༻ͷڧ͞

19 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ Reaction term: FLUXCUBE Facebook Twitter Youtube Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&

20 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&

21 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&

22 ൓Ԡ߲: ΞΠσΞ Lotka-Volterra Equation Λ൓Ԡ߲ͱͯ͠ར༻ ൓Ԡ߲: FLUXCUBE 𝒇 𝑥$%& |𝝌𝒕,𝒊,: = 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏& 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE:

23 ֦ࢄ߲: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 反応拡散⽅程式 FLUXCUBE 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& Seasonal term ֦ࢄ߲ Washington State Amazon Target ebay Craigslist

24 ֦ࢄ߲: ΞΠσΞ l Ωʔϫʔυؒͷ૬ޓ࡞༻͸֎෦ཁҼͳͲʹΑΓ ҰఆͰ͸ͳ͍ l ෳࡶͳݱ৅΍ٸܹͳมԽͳͲʹΑͬͯੜ͡Δɼ ࣌ؒมԽ͢Δ૬ޓ࡞༻Λଊ͑Δඞཁ ֦ࢄ߲: FLUXCUBE Washington State Amazon Target ebay Craigslist

25 ֦ࢄ߲: ΞΠσΞ l Ωʔϫʔυؒͷ૬ޓ࡞༻͸֎෦ཁҼͳͲʹΑΓ ҰఆͰ͸ͳ͍ l ෳࡶͳݱ৅΍ٸܹͳมԽͳͲʹΑͬͯੜ͡Δɼ ࣌ؒมԽ͢Δ૬ޓ࡞༻Λଊ͑Δඞཁ ֦ࢄ߲: FLUXCUBE Washington State Amazon Target ebay Craigslist 相互作⽤はPhysics-informed neural networksのアイデアを活⽤して RNNを利⽤

26 Physics-informed neural Network (PINN) l ෺ཧϞσϧͷؔ਺͸ਂ૚ֶशͰۙࣅՄೳ l ॱ໰୊: ํఔࣜͷۙࣅղ l ٯ໰୊: ؍ଌσʔλ͔ΒύϥϝʔλΛਪఆ l ༩͑ΒΕֶͨशσʔλͱɺٻΊ͍ͨύϥϝʔλ͕ํఔࣜΛຬ ͨ͢Α͏ʹղۭؒΛ੍ݶ͢Δ͜ͱͰద੾ͳύϥϝʔλΛਪఆ ֦ࢄ߲: FLUXCUBE ภඍ෼ํఔࣜͰ͋Δ֦ࢄ൓Ԡํఔࣜͷ ύϥϝʔλͷҰ෦Λ/FVSBM/FUXPSL ͰॊೈʹදݱΛࢼΈΔ

27 ֦ࢄ߲: FLUXCUBE ℊ 𝑥$%& |𝝌𝒕 , 𝒕 = 8 𝑅𝑁𝑁(1: 𝑡) ⊙ 𝝌𝒕 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE: l ૬ޓ࡞༻ͷਪఆʹRecurrent Neural NetworkΛར༻ l ॱ໰୊: ํఔࣜͷۙࣅղ l ٯ໰୊: ؍ଌσʔλ͔ΒύϥϝʔλΛਪఆ l ਺ཧϞσϧͷҰ෦ʹχϡʔϥϧωοτϫʔΫΛ׆༻͢Δ͜ͱ ͰॊೈͳϞσϦϯάͱߴ͍આ໌ੑΛཱ྆

28 RNNͷग़ྗ஋ʹΑͬͯɺ֤Ωʔϫʔυͷ֦ࢄͷӨڹΛදݱ ֦ࢄ߲: FLUXCUBE ℊ 𝑥$%& |𝝌𝒕 , 𝒕 = 8 𝑅𝑁𝑁(1: 𝑡) ⊙ 𝝌𝒕 𝑹𝑵𝑵(𝟏: 𝒕) Time カナダからフランスへ の各キーワードの影響 の流れ

29 قઅ߲: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 拡散反応⽅程式 FLUXCUBE 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& قઅ߲ Washington State Amazon Target ebay Craigslist

30 ΦϯϥΠϯσʔλ͸ΫϦεϚε΍ϒϥοΫϑϥΠσʔͳͲ ͷقઅΠϕϯτʹԠͯ͡มԽ قઅ੒෼ͷநग़ قઅ߲: FLUXCUBE 𝑥$)*%& = 𝐹 ,-!"# ,$ + 𝑥$%& = 1 + 𝑺$ ./0 1 %& ⊙ ,-!"# ,$ + 𝑥$%& 季節性の周期 e.g., p = 52週間 ϒϥοΫϑϥΠσʔ

31 Our model: FLUXCUBE 𝜕𝒖 𝜕𝑡 = 𝒇 𝒖, 𝑡 + 𝒟Δ𝑢 反応拡散⽅程式 FLUXCUBE 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& ೖྗ: 𝝌 = 𝒙𝒕𝒊𝒋 λΠϜεςοϓ U ஍Ҭ J ΞΠςϜ K ൓Ԡ߲ ֦ࢄ߲ قઅ߲

32 Fitting: FLUXCUBE Loss Function 𝝌𝒄 − @ 𝝌 𝟐 + 𝛼 8 𝐷 4 + 𝛽 8 𝑆 4 ճؼ߲ εύʔε߲ 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& λΠϜεςοϓ U ஍Ҭ J ΞΠςϜ K ೖྗ: 𝝌 = 𝒙𝒕𝒊𝒋

33 l ଟ͘ͷ஍Ҭؒͷ૬ޓ࡞༻Λਪ࿦͢Δ͜ͱ͸ɺܭࢉίετ͕ߴ͍ ஍ҬͷάϧʔϓΠϯά

34 l ଟ͘ͷ஍Ҭؒͷ૬ޓ࡞༻Λਪ࿦͢Δ͜ͱ͸ɺܭࢉίετ͕ߴ͍ ஍ҬͷάϧʔϓΫϥελϦϯά 解決策: 学習前に似た地域を １つのグループとして扱う ΞϝϦΧ ೔ຊ ࣅͨ ૬ޓ࡞༻ ಉ͡άϧʔϓ

35 ஍ҬͷάϧʔϓΫϥελϦϯά 𝒇 𝑥$%& |𝝌𝒕,𝒊,: = 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏& 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE: 𝑔*, … 𝑔5$ =K-means UMAP 𝒂𝒊, 𝒃𝒊, 𝑪𝒊 , 𝑖 = [1, … , 𝐿] 各グループ を推定 各地域の反応項のパラメータ 地域の数 ൓Ԡ߲

36 ஍ҬͷάϧʔϓΫϥελϦϯά 𝒇 𝑥$%& |𝝌𝒕,𝒊,: = 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏& 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE: 𝑔*, … 𝑔5$ =K-means UMAP 𝒂𝒊, 𝒃𝒊, 𝑪𝒊 , 𝑖 = [1, … , 𝐿] Reaction term taylor swift lady gaga beyonce katy perry maroon 5 stevie wonder Group A: Russia, Mexico, Spain, Vietnam, etc. Group B: United Kingdom, Germany, France, etc. Group C: United States, Canada, Australia, etc. Group D: Iran, Pakistan, Brazil, Argentina, etc. Group E: China, Japan, Vietnam, South Africa, etc. 最適なグループ数 (𝑑!)を Model Description Cost (MDL) を⽤いて探索 各グループ を推定 各地域の反応項のパラメータ 地域の数

37 ࣮ݧઃఆ l 13, 26, 52 िؒઌͷ༧ଌ஋ͷਫ਼౓ΛධՁ l ධՁࢦඪ l RMSE, MAE: খ͍͞஋Ͱ͋Δ΄Ͳߴ͍ਫ਼౓ σʔληοτ l Google Trend͔ΒऔಘՄೳͳ10೥ؒ ͷ1िؒ͝ͱͷݕࡧ਺ (7छྨ) ࣮ݧ

38 ࣮ݧ݁Ռ ࣮ݧ

39 ࣮ݧ݁Ռ ࣮ݧ

40 ࣮ݧ݁Ռ ࣮ݧ

41 Ablation Study ࣮ݧ 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& قઅ߲Λ࡟আ ֦ࢄ߲Λ࡟আ ֦ࢄ߲Λఆ਺ʹஔ͖׵͑ ఏҊϞσϧ

42 Ablation Study ࣮ݧ 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 𝑥$)*%& = 𝐹 𝜕𝑥$%& 𝜕𝑡 + 𝑥$%& ℊ 𝑥)*+|𝝌𝒕 , 𝒕 = + 𝑅𝑁𝑁(1: 𝑡) ⊙ 𝝌𝒕 𝜶 ⊙ 𝝌𝒕 قઅ߲Λ࡟আ ֦ࢄ߲Λ࡟আ ֦ࢄ߲Λఆ਺ʹஔ͖׵͑ ఏҊϞσϧ

43 Case study1: Vod Case Study AppleTV / ESPN / HBO / Hulu / Netflix Sling / Vudu / Youtube Keyword List

44 Case study1: Vod Case Study ૬ޓ࡞༻

45 Case study1: Vod Case Study 影響の流れ

46 Case study2: SNS Case Study Line/facebook/slack/snapchat/ twitter/viber/whatsapp Keyword List

47 Case study2: SNS Case Study ૬ޓ࡞༻

48 Case study2: SNS Case Study 影響の流れ

49 l FLUXCUBE: ൓Ԡ֦ࢄํఔࣜͱੜଶܥΛදݱ͢Δ਺ཧϞσϧ -PULB 7PMUFSB NPEFM ʹجͮ͘ϞσϦϯάख๏ɽೖྗ͞Εͨσʔλʹજࡏత ʹଘࡏ͢Δقઅੑ΍૬ޓ࡞༻ͳͲͷྗֶతͳؔ܎Λநग़ l (PPHMF5SFOEΛ༻͍ͨσʔλΛ༻͍ͯɼఏҊϞσϧͷ༗ޮੑΛఏࣔ l ؍ଌσʔλͷഎޙʹଘࡏ͢Δજࡏతͳ૬ޓ࡞༻΍ӨڹͷྲྀΕΛɼਓؒ ͕ղऍՄೳͳܗΛఏڙ ࠓޙͷల๬ l ࣗಈతʹؔ܎ͷ͋ΔΩʔϫʔυͱؔ܎ͷͳ͍ΩʔϫʔυΛ۠ผ͢Δ͜ ͱΛݕ౼ ·ͱΊ