Summary

• Transportation data during Jan.-Oct., 2020 can be represented as a mixture of 12 basic patterns.
  • Each basic pattern is a combination of the following spacial and temporal patterns.
    • Spacial: “among neighbor prefectures” and “between metropolitan and nation-wide areas”.
    • Temporal: “weekday” and “holiday”.
• Correlation analysis between weekly average of effective reproduction number (Rt) and the 12 basic patterns after mid. of March tells:
  • Rt of Hokkaido has week correlation with 3 basic patterns.
    • Need simulation analysis to confirm dependency and controllability.

Procedure of Analysis

• Consider travel data among prefectures as a 3D tensor whose axes are origin, destination, and date.
  • Data source: Blogwatcher, Inc.
  • Inner-prefecture travel are not counted, because they include staying home.
  • The travel tensor is normalized as a probability tensor whose total is 1.
• Apply non-negative tensor factorization to the travel tensor and get a mixture of basic patterns.
  • Each basic pattern is a direct product of an inter-prefecture matrix (spacial factor) and a day vector (temporal pattern).

• Calculate correlation between changes of Rt and the day vector of each basic pattern.

BIC Analysis

• Try to calculate BIC in order to determine the suitable number of basic patterns.
  • BIC becomes minimum at 12 basic patterns.

Acquired Temporal Pattern of Each Basic Patterns (1)

• Plots of changes of probabilities of temporal patterns of 12 basic patterns (0th...11th).
  • The 0th pattern (among neighbor prefectures, weekday) is a major part of whole travel pattern.

Acquired Temporal Pattern of Each Basic Patterns (2)

• Details of 1st ... 11th basic patterns.
  • The 4th and 7th patterns are relatively large.
    • The 4th pattern: among neighbor prefecture, holiday.
    • The 7th pattern: between metropolis and nation-wide.

Each Temporal Patterns (0th ... 5th)

• types:
  • weekday: has narrow valleys at weekends.
  • holiday: has peeks at weekends.
  • pre-corona: Jan. and Feb. are larger than summer and autumn
  • post-corona: summer and autumn are larger than Jan. and Feb.
• horizontal axis: day
  • Jan. 1st -- Oct. 30th, 2020.
• vertical axis: prob.

Each Temporal Patterns (6th ... 11th)

• types:
  • weekday: has narrow valleys at weekends.
  • holiday: has peeks at weekends.
  • pre-corona: Jan. and Feb. are larger than summer and autumn
  • post-corona: summer and autumn are larger than Jan. and Feb.
• horizontal axis: day
  • Jan. 1st -- Oct. 30th, 2020.
• vertical axis: prob.

Each Spacial Pattern(0th-5th)

• lneighbor type: large at diagonal region.
• metropolis nation-wide: horizontal and vertical bands.
• nation-wide: spread widely.

• horizontal: from pref.
• vertical: to pref.
• color: prob.  (scaled for each pattern)

Each Spacial Pattern(6th-11th)

• lneighbor type: large at diagonal region.
• metropolis nation-wide: horizontal and vertical bands.
• nation-wide: spread widely.

• horizontal: from pref.
• vertical: to pref.
• color: prob.  (scaled for each pattern)

Prefectures

• 0: Hokkaido （representative of Hokkaido Area）
• 1: Aomori
• 2: Iwate
• 3: Miyagi （representative of Tohoku Area）
• 4: Akita
• 5: Yamagata
• 6: Fukushima
• 7: Ibaraki
• 8: Tochigi
• 9: Gunma
• 10: Saitama
• 11: Chiba
• 12: Tokyo （representative of Kanto Area）
• 13: Kanagawa
• 14: Yamanashi
• 15: Nagano
• 16: Niigata
• 17: Toyama
• 18: Ishikawa （representative of Hokuriku Area）
• 19: Fukui
• 20: Gifu
• 21: Shizuoka
• 22: Aichi （representative of Tokai Area）
• 23: Mie
• 24: Shiga
• 25: Kyoto
• 26: Osaka （representative of Kinki Area）
• 27: Hyogo
• 28: Nara
• 29: Wakayama
• 30: Tottori
• 31: Shimane
• 32: Okayama
• 33: Hiroshima（representative of Chugoku Area） 
• 34: Tokushima
• 35: Kagawa
• 36: Ehime （representative of Shikoku Area）
• 37: Kochi
• 38: Yamaguchi
• 39: Fukuoka （representative of North Kyushu Area）
• 40: Saga
• 41: Nagasaki
• 42: Kumamoto
• 43: Oita
• 44: Miyazaki
• 45: Kagoshima （representative of South Kyushu Area）
• 46: Okinawa （representative of Okinawa Area）

Correlation Matrix between Basic Patterns and Rt.

• Period: mid of Mar. 〜 Oct.
  • Use weekly average of Rt with 8 days delay.
• Rt of Hokkaido has week correlations with f03, f06 and f07 patterns.
  • Each pattern is between metropolis and nation-wide on weekday.

Scatter Plot

Scatter of f06(horizontal) and Rt(vertical)

Scatter of f07(horizontal) and Rt(vertical)

• Scatter Plots between Rt of Hokkaido and f06, f07
  • week correlations
  • colors indicate the number of week.
    • The correlation with f06 becomes weeker in later weeks.

(ref.) Correlation Matrix between Basic Patterns and Rt.

• using Rt on-time (no delay)
  • correlations are relatively low.