1. Non-linear Mining of Competing Local Activities
Yasuko Matsubara (Kumamoto University)
Yasushi Sakurai (Kumamoto University)
Christos Faloutsos (CMU)
WWW 2016
Y. Matsubara et al.

2. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
Global US CA AU ZA IT CN JP BR
WWW 2016
Y. Matsubara et al.

3. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
Global US CA AU ZA IT CN JP BR
Q. Any global/local trends?
WWW 2016
Y. Matsubara et al.

4. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
Global CA
Q. Any global/local trends?
WWW 2016
Y. Matsubara et al.

5. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
Global
Nexus
Kindle CA
WWW 2016
Y. Matsubara et al.

6. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
1. Exponential growth
Global
Nexus
Kindle CA
WWW 2016
Y. Matsubara et al.

7. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
VS.
2. Competition
Global
Nexus
Kindle
VS. CA
WWW 2016
Y. Matsubara et al.

8. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
New Year
3. Seasonality
Global
Xmas
Nexus
Kindle CA
WWW 2016
Y. Matsubara et al.

9. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
4. Deltas (outliers)
Global
(released)
Nexus
Kindle CA
WWW 2016
Y. Matsubara et al.

10. Given: local user activities
e.g., Google search volumes for
(for 236 countries, from 2004 to 2015)
Kindle, Nexus
4. Deltas (outliers)
Global
Goal: find global/local patterns,
fully automatically
Nexus
Kindle CA
WWW 2016
Y. Matsubara et al.

11. Data description X Time-stamped events: {activity, location, time}
Activity
Time (weekly)
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Y. Matsubara et al.

12. e.g., ‘Kindle’, ‘US’, ‘April 1-7, 2014’, ‘100’
Data description
Time-stamped events: {activity, location, time}
Location X
Activity x
e.g., ‘Kindle’, ‘US’, ‘April 1-7, 2014’, ‘100’
Time (weekly)
WWW 2016
Y. Matsubara et al.

13. Problem definition Given: Tensor X (activity x location x time) X
WWW 2016
Y. Matsubara et al.

14. Problem definition B C S D
Given: Tensor X (activity x location x time) Find: Compact description of X X
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

15. Problem definition B C S D
Given: Tensor X (activity x location x time) Find: Compact description of X X
Basics
Competition
Seasonality
Deltas
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

16. Problem definition Global Local & B C S D
Given: Tensor X (activity x location x time) Find: Compact description of X X
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

17. Problem definition B C S D NO magic numbers ! Parameter-free!
Given: Tensor X (activity x location x time) Find: Compact description of X
NO magic numbers !
Parameter-free! X
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

18. Roadmap ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions
WWW 2016
Y. Matsubara et al.

19. Modeling power of CompCube
Products
News sources
WWW 2016
Y. Matsubara et al.

20. Modeling power of CompCube
Products
News sources
WWW 2016
Y. Matsubara et al.

21. Modeling power of CompCube
VS.
Q. Any global/local
competition?
e.g., in
Nexus
Kindle
Products
News sources
WWW 2016
Y. Matsubara et al.

22. Modeling power of CompCube
e.g., Google search volumes for
Kindle, Nexus US CA JP CN BR AU ZA IT
Weak/Average/Strong
Local Competition strength
WWW 2016
Y. Matsubara et al.

23. Modeling power of CompCube
e.g., Google search volumes for
Kindle, Nexus US CA JP CN BR AU ZA IT
Weak/Average/Strong
Local Competition strength
WWW 2016
Y. Matsubara et al.

24. Modeling power of CompCube
e.g., Google search volumes for
Kindle, Nexus US CA JP CN BR AU ZA IT
Weak/Average/Strong
Local Competition strength
WWW 2016
Y. Matsubara et al.

25. Modeling power of CompCube
Products
News sources
WWW 2016
Y. Matsubara et al.

26. Modeling power of CompCube
Products
News sources
Q. Any seasonality? in
WWW 2016
Y. Matsubara et al.

27. Modeling power of CompCube
e.g., Local seasonality for
iPod
Component #1
Component #2
WWW 2016
Y. Matsubara et al.

28. Modeling power of CompCube
e.g., Local seasonality for
iPod
Dec.
Xmas
Component #1
Component #2
WWW 2016
Y. Matsubara et al.

29. Modeling power of CompCube
e.g., Local seasonality for
iPod
Feb.
Chinese New Year
Component #1
Component #2
WWW 2016
Y. Matsubara et al.

30. Modeling power of CompCube
Products
News sources
WWW 2016
Y. Matsubara et al.

31. Modeling power of CompCube
Products
News sources
Q. Any world-wide
events?
WWW 2016
Y. Matsubara et al.

32. Modeling power of CompCube
Fitting result for
News resources
WWW 2016
Y. Matsubara et al.

33. Modeling power of CompCube
Fitting result for
News resources
Detected!
US election
Nov. 2008
Wikipedia
WWW 2016
Y. Matsubara et al.

34. Modeling power of CompCube
Fitting result for
News resources
Detected!
US election
Nov. 2008
Q. Which countries are
interested in US politics?
Wikipedia
WWW 2016
Y. Matsubara et al.

35. Modeling power of CompCube
Fitting result for
News resources
Weak/Strong
Local attention to
US election
US election
Nov. 2008
Wikipedia
WWW 2016
Y. Matsubara et al.

36. Roadmap ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔
WWW 2016
Y. Matsubara et al.

37. Problem definition B C S D
Given: Tensor X (activity x location x time) Find: Compact description of X X
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

38. Problem definition B C S D
Given: Tensor X (activity x location x time) Find: Compact description of X X
Basics
Competition
Seasonality
Deltas
CompCube X B C S D
WWW 2016
Y. Matsubara et al.

39. Main ideas: MANT analysis
Main ideas: MANT analysis
MANT analysis
Multi-Aspect Non-linear Time-series
#1 Non-linear models
#2 Tensor analysis X
#3 Automatic mining
NO magic numbers!
WWW 2016
Y. Matsubara et al.
© 2015 Sakurai, Matsubara & Faloutsos

40. Main ideas: MANT analysis
Main ideas: MANT analysis
Idea #1: Non-linear modeling
Virtual ecosystem on the Web
Ecosystem in the Jungle
Ecosystem on the Web
Species
Activities
Food
VS.
User
VS.
share
share
Image courtesy of xura, criminalatt, David Castillo Dominici, happykanppy at FreeDigitalPhotos.net.
WWW 2016
Y. Matsubara et al.
© 2015 Sakurai, Matsubara & Faloutsos

41. Main ideas: MANT analysis
Main ideas: MANT analysis
Idea #1: Non-linear modeling
Virtual ecosystem on the Web
Ecosystem in the Jungle
Non-linear
dynamical system
Ecosystem on the Web
Species
Activities
Food
VS.
User
VS.
share
share
Image courtesy of xura, criminalatt, David Castillo Dominici, happykanppy at FreeDigitalPhotos.net.
WWW 2016
Y. Matsubara et al.
© 2015 Sakurai, Matsubara & Faloutsos

42. Main ideas: MANT analysis
Main ideas: MANT analysis X
Idea #2: Tensor analysis
CompCube X
Extract B C
Compress S D X
WWW 2016
Y. Matsubara et al.
© 2015 Sakurai, Matsubara & Faloutsos

43. Main ideas: MANT analysis
Idea #3: MDL for fitting: parameter-free
CompCube X B C S D
NO magic numbers
Parameter-free!
WWW 2016
Y. Matsubara et al.

44. Roadmap ✔ ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔ ✔
WWW 2016
Y. Matsubara et al.

45. Proposed model: CompCube
(a) CompCube-dense X
(b) CompCube B C S D
WWW 2016
Y. Matsubara et al.

46. Proposed model: CompCube
(a) CompCube-dense X
(b) CompCube B C S D
WWW 2016
Y. Matsubara et al.

47. CompCube-dense B C S D Given: Output: Basics Competition SeasonalityX B C S D
Basics
Competition
Seasonality
Deltas
WWW 2016
Y. Matsubara et al.

48. CompCube-dense B C S D Non-linear dynamical system Details X WWW 2016
Y. Matsubara et al.

49. CompCube-dense B C S D Non-linear dynamical system
Details
Non-linear dynamical system
P: latent popularity X B C S D
WWW 2016
Y. Matsubara et al.

50. CompCube-dense B C S D Non-linear dynamical system
Details
Non-linear dynamical system
P: latent popularity
V: estimated volume X B C S D
WWW 2016
Y. Matsubara et al.

51. CompCube-dense B C S D Non-linear dynamical system Details X WWW 2016
Y. Matsubara et al.

52. CompCube-dense B C S D Non-linear dynamical system Details X WWW 2016
Y. Matsubara et al.

53. CompCube-dense B C S D Non-linear dynamical system Basics Details X
WWW 2016
Y. Matsubara et al.

54. B G1: Basics + + t=0 t=1 t=2 Popularity size increases over time eat
Jungle +
Species
Foods
attract + +
Web +
Activities
Users
t=0
t=1
t=2
WWW 2016
Y. Matsubara et al.

55. B G1: Basics B + + t=0 t=1 t=2 Popularity size increases over time eat
(activity i, location l)
eat +
Jungle +
Species
Foods
attract + B +
Web
Initial condition (i.e., P(0) =p )
Growth rate, attractiveness
Carrying capacity (=available user resources) +
Activities
Users
t=0
t=1
t=2
WWW 2016
Y. Matsubara et al.

56. CompCube-dense B C S D Non-linear dynamical system Competition DetailsX B C S D
WWW 2016
Y. Matsubara et al.

57. C G1: Competition VS. VS. Interaction between multiple keywords
Species
Food
resources
VS.
Activities
User
resources
VS.
share
share
WWW 2016
Y. Matsubara et al.

58. C G1: Competition C VS. VS. Interaction between multiple keywords
(location l)
Species
Food
resources
VS.
Activities
User
resources
VS.
share C
share
Competition coefficient in location l
i.e., effect rate of activity j on i in l
WWW 2016
Y. Matsubara et al.

59. CompCube-dense B C S D Non-linear dynamical system Seasonality DetailsX B C S D
WWW 2016
Y. Matsubara et al.

60. S G1: Seasonality Season/Climate Seasonal events
“Hidden” seasonal activities
Season/Climate
Seasonal events
Image courtesy of xura, criminalatt, David Castillo Dominici, happykanppy at FreeDigitalPhotos.net.
WWW 2016
Y. Matsubara et al.

61. Users change their behavior according to local seasonal events!
G1: Seasonality S
“Hidden” seasonal activities
Users change their behavior according to local seasonal events!
Season/Climate
Seasonal events S
Image courtesy of xura, criminalatt, David Castillo Dominici, happykanppy at FreeDigitalPhotos.net.
WWW 2016
Y. Matsubara et al.

62. CompCube-dense B C S D Non-linear dynamical system Deltas Details X
WWW 2016
Y. Matsubara et al.

63. CompCube-dense B C S D Non-linear dynamical system Deltas Details
(activity i, location l, time t)
Deltas X B C S D
WWW 2016
Y. Matsubara et al.

64. Proposed model: CompCube
(a) CompCube-dense X
(b) CompCube B C S D
WWW 2016
Y. Matsubara et al.

65. Initial attempt: CompCube-dense
Given:
CompCube-dense X B C S D
Basics
Competition
Seasonality
Deltas
WWW 2016
Y. Matsubara et al.

66. Initial attempt: CompCube-dense
Given:
CompCube-dense X B C S D
Basics
Competition
Seasonality
Deltas
Dense,
Redundant,
Local ONLY
WWW 2016
Y. Matsubara et al.

67. Initial attempt: CompCube-dense
Given:
CompCube-dense X B C S D
Basics
Competition
Seasonality
Deltas
Dense,
Redundant,
Local ONLY
Ideal model:
Compact,
Powerful
WWW 2016
Y. Matsubara et al.

68. Final model: CompCube B C S D (a) CompCube-dense Compress Summarize &
(b) CompCube B C S D
WWW 2016
Y. Matsubara et al.

69. Final model: CompCube Global B C S D (a) CompCube-dense Compress
Summarize
&
Global
(b) CompCube B C S D
WWW 2016
Y. Matsubara et al.

70. Final model: CompCube Global Local B C S D (a) CompCube-dense Compress
Summarize
&
Global
(b) CompCube
Local B C S D
WWW 2016
Y. Matsubara et al.

71. Final model: CompCube Global Local B C S D (a) CompCube-dense Compress
Summarize
&
Dense
Sparse G L
&
Global
(b) CompCube
Local B C S D
WWW 2016
Y. Matsubara et al.

72. Roadmap ✔ ✔ ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔ ✔ ✔
WWW 2016
Y. Matsubara et al.

73. Challenges
Q1. How can we efficiently estimate parameters? Q2. How can we automatically find best parameter sets? X B C S D
WWW 2016
Y. Matsubara et al.

74. Challenges Idea (1) : TetraFit algorithm B C S D
Q1. How can we efficiently estimate parameters? Q2. How can we automatically find best parameter sets? X
Idea (1) : TetraFit algorithm B C S D
Idea (2): Model description cost
WWW 2016
Y. Matsubara et al.

75. Challenges Idea (1) : TetraFit algorithm B C S D
(Details in paper)
Q1. How can we efficiently estimate parameters? Q2. How can we automatically find best parameter sets? X
Idea (1) : TetraFit algorithm B C S D
Idea (2): Model description cost
WWW 2016
Y. Matsubara et al.

76. Roadmap ✔ ✔ ✔ ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔ ✔ ✔ ✔
WWW 2016
Y. Matsubara et al.

77. Experiments We answer the following questions… Q1. Effectiveness
How well does it explain important patterns?
Q2. Accuracy
How well does it fit real datasets?
Q3. Scalability
How does it scale in terms of computational time?
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Y. Matsubara et al.

78. Q1. Effectiveness 1. Products 2. News VS. VS. WWW 2016
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79. Q1. Effectiveness 1. Products 2. News Local competition VS. VS. VS.
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80. Q1. Effectiveness 1. Products 2. News Local seasonality Dec. Feb. VS.
Christmas
Chinese New Year
Dec.
Feb.
VS.
iPod
iPod
2. News
VS.
WWW 2016
Y. Matsubara et al.

81. Q1. Effectiveness 1. Products 2. News Local seasonality Nexus release
New Year sale
VS.
2. News
Nexus
Kindle
VS.
WWW 2016
Y. Matsubara et al.

82. Q1. Effectiveness 1. Products 2. News Deltas US election Nov. 2008
Weak/Strong
Wikipedia
VS.
2. News
VS.
WWW 2016
Y. Matsubara et al.

83. Q1. Effectiveness 3. Beers 4. Cocktails VS. VS. WWW 2016
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84. Q1. Effectiveness 3. Beers 4. Cocktails Local competition VS. VS. VS.
WWW 2016
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85. Q1. Effectiveness 3. Beers 4. Cocktails Local seasonality VS.
Summer spike
for Coors
VS.
WWW 2016
Y. Matsubara et al.

86. Q1. Effectiveness
5. Cars
6. SNS
WWW 2016
Y. Matsubara et al.

87. Q1. Effectiveness 5. Cars 6. SNS Deltas (“tesla”) Nikola Tesla
(Google Doodle)
6. SNS
WWW 2016
Y. Matsubara et al.

88. Q1. Effectiveness
7. Finance
8. Software
WWW 2016
Y. Matsubara et al.

89. Q1. Effectiveness 7. Finance 8. Software Local competition HTML VS.
WWW 2016
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90. New Year holiday for XML
Q1. Effectiveness
7. Finance
Local seasonality
XML
8. Software
New Year holiday for XML
WWW 2016
Y. Matsubara et al.

91. Q2. Accuracy RMSE between original and fitted volume WWW 2016
Y. Matsubara et al.

92. CompCube consistently wins!
Q2. Accuracy
RMSE between original and fitted volume
CompCube consistently wins!
WWW 2016
Y. Matsubara et al.

93. Q3. Scalability Wall clock time vs. activity , location , Time X X X
WWW 2016
Y. Matsubara et al.

94. Q3. Scalability Wall clock time vs. activity , location , TimeX X X
CompCube is linear w.r.t. data size : O(dmn)
WWW 2016
Y. Matsubara et al.

95. Roadmap ✔ ✔ ✔ ✔ ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔ ✔ ✔ ✔ ✔
WWW 2016
Y. Matsubara et al.

96. CompCube at work - forecasting
Forecasting future local activities
Location
Activity
Train:
2/3 sequences
Forecast:
1/3 following years X ?
Time (weekly)
WWW 2016
Y. Matsubara et al.

97. CompCube at work - forecasting
Forecasting results for #1 Products
1. Products
CompCube captures future activities very well
WWW 2016
Y. Matsubara et al.

98. CompCube at work - forecasting
Forecasting error (original vs. forecasts)
WWW 2016
Y. Matsubara et al.

99. CompCube at work - forecasting
Forecasting error (original vs. forecasts)
CompCube consistently wins!
WWW 2016
Y. Matsubara et al.

100. Roadmap ✔ ✔ ✔ ✔ ✔ ✔ ✔ Motivation Modeling power of CompCube Overview
Proposed model
Algorithm
Experiments
CompCube – at work
Conclusions ✔ ✔ ✔ ✔ ✔ ✔
WWW 2016
Y. Matsubara et al.

101. Conclusions ✔ ✔ ✔ B C S D ✔ CompCube has the following advantages
Effective
Finds important patterns
Practical
Long-range forecasting
Parameter-free
No parameter tuning
Scalable
It is linear ✔ ✔ ✔ X B C S D
CompCube ✔
WWW 2016
Y. Matsubara et al.

102. Thank you! Data & Code: http://www.cs.kumamoto-u.ac.jp/~yasuko CA ITUS CA JP CN BR AU ZA IT
Weak/Average/Strong
Data & Code:
WWW 2016
Y. Matsubara et al.

103. Non-linear Mining of Competing Local Activities
Yasuko Matsubara (Kumamoto University)
Yasushi Sakurai (Kumamoto University)
Christos Faloutsos (CMU)
WWW 2016
Y. Matsubara et al.