Kai Shu1,2, Ping Luo1
Li Wan2, Peifeng Yin
3, Linpeng Tang
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Deal or Deceit:
Detecting Cheating in Distribution Channels
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Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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Introduction
• Motivation
• Problem Formulation
• Detection Framework
• Experimental results
• Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Introduction
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Manufacturer
End user
Manufacturer
Partner
End user
√
Low
price
High
price
Price
Difference
Distribution channel Price difference
Manufacturer
Partner Partner
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Introduction
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×
Cheating seller Cheating buyer
Detect cheating in distribution channel
×
A typical cheating scenario
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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• Introduction
Motivation
• Problem Formulation
• Detection Framework
• Experimental results
• Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Motivation
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⋯
Time series of purchase quantities
?
Time series of purchase quantities for each partner
Data: from the perspective of manufactory
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Motivation (2)
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Purchase quantity
Month
𝑣1 𝑣2 𝑣1 𝑣2 𝑣1 𝑣2
×
×𝑣1 𝑣2
Negative
correlation
The purchase quantities of 𝑣1 and 𝑣2 change collectively
Observation
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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• Introduction
• Motivation
Problem Formulation
• Detection Framework
• Experimental results
• Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Problem Formulation
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⋯
𝑥1 𝑥2 𝑥𝑛
𝑣1 𝑣2 𝑣𝑛
Degree of cheating
Input Output
Audit staff
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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• Introduction
• Motivation
• Problem Formulation
Detection Framework
• Experimental results
• Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework
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all purchase
volume sequences
(𝑥𝑖|𝑖 = 1,2, … , 𝑛)
Building Partner
Correlation Graph (PCG)
Partitioning
Ranking the partners by
probabilistic modelRanking of
cheating partners
A ···
B ···
Step 2
Step 3
Step 1
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 1)
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0
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Purchase quantity
Month
𝑣1 𝑣2
• Tick-to-tick correspondence
Pearson correlation
• Symmetric measure
𝑣1
𝑣2 ?Cheating seller
Cheating buyer
Pearson 𝑣1, 𝑣2 = Pearson(𝑣2, 𝑣1)
No negative
correlation
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 1)
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Dynamic time warping
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Purchase quantity
Month
𝑣1 𝑣2 𝑣1 𝑣2 𝑣1 𝑣2
Learn the correspondence relationship of elements between two time
series to minimize the Pearson correlation.
Warping direction
Directed Pearson Correlation (DPC)
𝑟𝑑𝑝𝑐(𝑥1, 𝑥2) ≔ min{1
𝐿
𝑙=1
𝐿
(𝑥1 𝑖𝑙 − 𝑥1𝜎𝑥1
)(𝑥2 𝑗𝑙 − 𝑥2𝜎𝑥2
)}
Where (𝑖𝑙 , 𝑗𝑙) is the element of a warping path 𝑃 and 𝐿 = 𝑃 .
Cheating seller
Cheating buyer
𝑟𝑑𝑝𝑐(𝑥1, 𝑥2) ≠ 𝑟𝑑𝑝𝑐(𝑥2, 𝑥1)
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 1)
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𝑣𝑖 𝑣𝑗
𝑤𝑖𝑗 = −𝑟𝑑𝑝𝑐(𝑥𝑖 , 𝑥𝑗)
If 𝑤𝑖𝑗 ≥ 𝜂, keep the edge
×
If 𝑤𝑖𝑗 < 𝜂, remove the edge
all purchase
volume sequences
(𝑥𝑖|𝑖 = 1,2, … , 𝑛)
PCG
Step 1
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 2)
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Cheating Sellers
Cheating Buyers
PCG
Bipartite Graph
A ···
B ···
Cheating Seller Cheating Buyerand Not true
A partner can only be cheating seller or cheating buyer
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 2)
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Maximize 𝑤𝐴𝐵
Classical graph cut problem (MAX DICUT)
Cheating Sellers
Cheating Buyers
A ···
B ···
𝑤𝐴𝐵
𝑤𝐵𝐴
Maximize 3𝑤𝐴𝐵 −𝑤𝐵𝐴
New graph cut problem
We propose a greedy algorithm to solve this new NP-hard problem.
Solution algorithm
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 3)
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A ···
B ···
𝑣𝑖(𝛼𝑖 , 𝛽𝑖)
𝑣𝑗(𝛼𝑗 , 𝛽𝑗)
𝑤𝑖𝑗
𝑣𝑖(𝛼𝑖 , 𝛽𝑖)
𝑣𝑗(𝛼𝑗 , 𝛽𝑗)
𝑤𝑖𝑗
Generate the edges and the weights in resultant bipartite graph.
Probabilistic model
Maxmize log 𝑝 𝑤𝑖𝑗 , 𝜽 + 𝜆 ∙ 𝐶(𝜽)
𝜽 is the set of all parameters
Bipartite Graph
Probabilistic model
𝐵𝑒𝑡𝑎 𝑤𝑖𝑗; 𝛼𝑖 , 𝛽𝑗
𝛼𝑖 𝛽𝑗 𝑤𝑖𝑗𝛽𝑗 𝑤𝑖𝑗𝛼𝑖
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Detection Framework (Step 3)
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𝜋𝑖𝑗 =𝛼𝑖𝛼𝑖 + 𝛽𝑗
𝜋𝑖𝑗 is the expected value of beta distribution with parameters (𝛼𝑖 , 𝛽𝑗)
Probability weight 𝜋𝑖𝑗
Ranking score function
Bipartite Graph
A ···
B ···
Ranking of
cheating partners
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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• Introduction
• Motivation
• Problem Formulation
• Detection Framework
Experimental results
• Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results
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Dataset
Gold Silver All
# Total partners 104 424 528
# Cheating partners 17 85 102
Evaluation measure
For the top-k ranking list, giving a number 𝑘,we
count the number of hits in it.
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛@𝑘 =#hits in top−k list
𝑘
𝑅𝑒𝑐𝑎𝑙𝑙@𝑘 =#hits in top−k list
𝑀
𝐹1@𝑘 = 2 ∙𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛@𝑘 ∙ 𝑅𝑒𝑐𝑎𝑙𝑙@𝑘
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛@𝑘 + 𝑅𝑒𝑐𝑎𝑙𝑙@𝑘
Ground truth
k1 2 3 k-1
Precision
Recall
F1 score
k
evalu
ation
hits
AUC
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results (1)
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• DPC improves performance
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5
10
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35
40
AU
C_F1
Pearson_Rank Noncut_Rank Noncut_ProbRank Cut_Rank Cut_ProbRank
PCG Partition Ranking
Pearson correlation DPC No Yes Edge weight Probability
Noncut_Rank √ √ √
Noncut_ProbRank √ √ √
Cut_Rank √ √ √
Cut_ProbRank √ √ √
Pearson_Rank √ √ √
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results (2)
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• DPC improves performance
0
5
10
15
20
25
30
35
40
AU
C_F1
Pearson_Rank Noncut_Rank Noncut_ProbRank Cut_Rank Cut_ProbRank
PCG Partition Ranking
Pearson correlation DPC No Yes Edge weight Probability
Noncut_Rank √ √ √
Noncut_ProbRank √ √ √
Cut_Rank √ √ √
Cut_ProbRank √ √ √
Pearson_Rank √ √ √
Noncut_Rank Cut_RankNoncut_ProbRank Cut_ProbRank
• Partitioning improves
performance
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results (3)
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• DPC improves performance
0
5
10
15
20
25
30
35
40
AU
C_F1
Pearson_Rank Noncut_Rank Noncut_ProbRank Cut_Rank Cut_ProbRank
PCG Partition Ranking
Pearson correlation DPC No Yes Edge weight Probability
Noncut_Rank √ √ √
Noncut_ProbRank √ √ √
Cut_Rank √ √ √
Cut_ProbRank √ √ √
Pearson_Rank √ √ √
• Partitioning improves
performance
Noncut_Rank Noncut_ProbRank Cut_Rank Cut_ProbRank
• Probability ranking improves
performance
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results (4)
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• DPC improves performance
0
5
10
15
20
25
30
35
40
AU
C_F1
Pearson_Rank Noncut_Rank Noncut_ProbRank Cut_Rank Cut_ProbRank
PCG Partition Ranking
Pearson correlation DPC No Yes Edge weight Probability
Noncut_Rank √ √ √
Noncut_ProbRank √ √ √
Cut_Rank √ √ √
Cut_ProbRank √ √ √
Pearson_Rank √ √ √
• Partitioning improves
performance
Cut_ProbRank
• Probability ranking improves
performance
• Cut_ProbRank performs best
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Experimental results (5)
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Precision Recall F1 score
Cut_ProbRank always performs the best
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Outline
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• Introduction
• Motivation
• Problem Formulation
• Detection Framework
• Experimental results
Conclusion
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Conclusion
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The first quantitative work to detect cheating in distribution
channels.
• A new correlation method (i.e. DPC) by Introducing
dynamic time warping technique.
• A new graph cut problem for graph partitioning.
• A probability model for node ranking.
Kai Shu et al. Deal or Deceit: Detecting Cheating in Distribution Channels
Thanks
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