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DEIM2023 大規模Webデータにおけるキーワード・地域ごとの拡散パターン抽出

DEIM2023 大規模Webデータにおけるキーワード・地域ごとの拡散パターン抽出

taichi_murayama

March 13, 2023
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  1. 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? ?
  2. 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.
  3. 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
  4. 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
  5. 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౓
  6. 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.
  7. 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
  8. 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
  9. 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
  10. 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
  11. 17 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit

    Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&
  12. 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
  13. 19 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ Reaction term: FLUXCUBE Facebook Twitter Youtube

    Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&
  14. 20 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit

    Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&
  15. 21 ൓Ԡ߲: ΞΠσΞ ϩτΧɾϘϧςϥํఔࣜ ൓Ԡ߲: FLUXCUBE Facebook Twitter Youtube Reddit

    Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏&
  16. 22 ൓Ԡ߲: ΞΠσΞ Lotka-Volterra Equation Λ൓Ԡ߲ͱͯ͠ར༻ ൓Ԡ߲: FLUXCUBE 𝒇 𝑥$%&

    |𝝌𝒕,𝒊,: = 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥$%&+ 𝑏& 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE:
  17. 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
  18. 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
  19. 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
  20. 27 ֦ࢄ߲: FLUXCUBE ℊ 𝑥$%& |𝝌𝒕 , 𝒕 = 8

    𝑅𝑁𝑁(1: 𝑡) ⊙ 𝝌𝒕 𝜕𝑥$%& 𝜕𝑡 = 𝒇 𝑥$%& |𝝌𝒕,𝒊,: + ℊ 𝑥$%& |𝝌𝒕 , 𝒕 FLUXCUBE: l ૬ޓ࡞༻ͷਪఆʹRecurrent Neural NetworkΛར༻ l ॱ໰୊: ํఔࣜͷۙࣅղ l ٯ໰୊: ؍ଌσʔλ͔ΒύϥϝʔλΛਪఆ l ਺ཧϞσϧͷҰ෦ʹχϡʔϥϧωοτϫʔΫΛ׆༻͢Δ͜ͱ ͰॊೈͳϞσϦϯάͱߴ͍આ໌ੑΛཱ྆
  21. 28 RNNͷग़ྗ஋ʹΑͬͯɺ֤Ωʔϫʔυͷ֦ࢄͷӨڹΛදݱ ֦ࢄ߲: FLUXCUBE ℊ 𝑥$%& |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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 37 ࣮ݧઃఆ l 13, 26, 52 िؒઌͷ༧ଌ஋ͷਫ਼౓ΛධՁ l ධՁࢦඪ l

    RMSE, MAE: খ͍͞஋Ͱ͋Δ΄Ͳߴ͍ਫ਼౓ σʔληοτ l Google Trend͔ΒऔಘՄೳͳ10೥ؒ ͷ1िؒ͝ͱͷݕࡧ਺ (7छྨ) ࣮ݧ
  29. 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
  30. 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
  31. 43 Case study1: Vod Case Study AppleTV / ESPN /

    HBO / Hulu / Netflix Sling / Vudu / Youtube Keyword List
  32. 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