taichi_murayama
March 13, 2023
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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

March 13, 2023

## Transcript

3. ### 3 Google Flu എܠ

Twitter Instagram Q: Ωʔϫʔυؒͷؔ܎͸ʁ Q: 国同⼠の関係は？ ？

6. ### 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. ### 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

9. ### 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. ### 10 ໰୊ఆٛ GivenΦϯϥΠϯ׆ಈσʔλ Goal 1 ஍Ҭؒͷ֦ࢄύλʔϯ Goal 2 Ωʔϫʔυؒͷؔ܎ Goal

3 قઅੑ Goal 4ߴ͍༧ଌਫ਼౓
11. ### 11 ໰୊ఆٛ Our solution: FLUXCUBE 拡散反応⽅程式 + ニューラルネットワーク GivenΦϯϥΠϯ׆ಈσʔλ Goal

1 ஍Ҭؒͷ֦ࢄύλʔϯ Goal 2 Ωʔϫʔυؒͷؔ܎ Goal 3 قઅੑ Goal 4ߴ͍༧ଌਫ਼౓
12. ### 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. ### 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. ### 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. ### 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. ### 16 ൓Ԡ߲: ΞΠσΞ ΞΠςϜͷؔ܎͸δϟϯάϧͷಈ෺ͷؔ܎ͱྨࣅ (Matsubara, 2015) ൓Ԡ߲: FLUXCUBE Spider monkeys

Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥\$%&+ 𝑏&

Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥\$%&+ 𝑏& 𝒄𝒋𝒋 : ΩʔϫʔυKͱΩʔϫʔυK` ؒͷ૬ޓ࡞༻ͷڧ͞

Reddit Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥\$%&+ 𝑏&

Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥\$%&+ 𝑏&

Kids Teens Adults 𝑎& 𝝌𝒕,𝒊,𝒋 1 − ∑&+ 𝑐&&+ 𝑥\$%&+ 𝑏&
22. ### 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. ### 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. ### 24 ֦ࢄ߲: ΞΠσΞ l Ωʔϫʔυؒͷ૬ޓ࡞༻͸֎෦ཁҼͳͲʹΑΓ ҰఆͰ͸ͳ͍ l ෳࡶͳݱ৅΍ٸܹͳมԽͳͲʹΑͬͯੜ͡Δɼ ࣌ؒมԽ͢Δ૬ޓ࡞༻Λଊ͑Δඞཁ ֦ࢄ߲:

FLUXCUBE Washington State Amazon Target ebay Craigslist
25. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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

૬ޓ࡞༻ ಉ͡άϧʔϓ
35. ### 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. ### 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. ### 37 ࣮ݧઃఆ l 13, 26, 52 िؒઌͷ༧ଌ஋ͷਫ਼౓ΛධՁ l ධՁࢦඪ l

RMSE, MAE: খ͍͞஋Ͱ͋Δ΄Ͳߴ͍ਫ਼౓ σʔληοτ l Google Trend͔ΒऔಘՄೳͳ10೥ؒ ͷ1िؒ͝ͱͷݕࡧ਺ (7छྨ) ࣮ݧ

41. ### 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. ### 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. ### 43 Case study1: Vod Case Study AppleTV / ESPN /

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

49. ### 49 l FLUXCUBE: ൓Ԡ֦ࢄํఔࣜͱੜଶܥΛදݱ͢Δ਺ཧϞσϧ -PULB 7PMUFSB NPEFM ʹجͮ͘ϞσϦϯάख๏ɽೖྗ͞Εͨσʔλʹજࡏత ʹଘࡏ͢Δقઅੑ΍૬ޓ࡞༻ͳͲͷྗֶతͳؔ܎Λநग़ l

(PPHMF5SFOEΛ༻͍ͨσʔλΛ༻͍ͯɼఏҊϞσϧͷ༗ޮੑΛఏࣔ l ؍ଌσʔλͷഎޙʹଘࡏ͢Δજࡏతͳ૬ޓ࡞༻΍ӨڹͷྲྀΕΛɼਓؒ ͕ղऍՄೳͳܗΛఏڙ ࠓޙͷల๬ l ࣗಈతʹؔ܎ͷ͋ΔΩʔϫʔυͱؔ܎ͷͳ͍ΩʔϫʔυΛ۠ผ͢Δ͜ ͱΛݕ౼ ·ͱΊ