mining the network value of customers
DESCRIPTION
Mining the Network Value of Customers. Zhenwei He & Cen Zhe Qiao School of Informatics University of Edinburgh. Outline. Introduction Modeling Markets as Markov random field Mining from Collaborative Filtering System(CFS) Example: - the EachMovie collaborative filtering database - PowerPoint PPT PresentationTRANSCRIPT
Mining the Network Value of Customers
Zhenwei He & Cen Zhe QiaoSchool of Informatics
University of Edinburgh
Outline
• Introduction• Modeling Markets as Markov random field• Mining from Collaborative Filtering
System(CFS)• Example: - the EachMovie collaborative filtering database
• Future work• Conclusion
Introduction
• Mass Marketing• Direct Marketing: independent assumption• Viral Marketing: strongly dependent• Data mining: plays a key role
General framework Optimize the choice of which customers to market to Estimating what customer acquisition cost is justified for each
How to do that?
• Modeling markets as Social Network
• Mining the network from Collaborative Filtering Databases
Modeling Markets as Social Network
• Some mathematical notations:n - the number of customers - if customer i buys the product/ ith-customer - set of neighbors of - the customers whose value is know(unknown) - the number of unknown neighbors of - set of attributes of the product - the marketing action that is taken for customer iC - the cost of marketing to a customer
}1,0{iX},...,{ ,niiii xxN iX
)(, uk XXu
iui XNN
}{ ,...,1 mYYY iX
iM
Modeling Markets as Social Network
r0 - the revenue from selling the product to customer if NO marketing action is performed.
r1 - the revenue from selling the product to customer if marketing action is performed
- the result of setting to 1 and leaving the rest of M unchanged - similar
Where
)(1 Mfi iM)(0 Mfi
}{ ,...,1 nMMM
Modeling Markets as Social Network
• The customer’s network value = {the Customer’s TOTAL value} – {The customer’s INTRINSIC value}
• The total value of customer is measured byWhich is
• The intrinsic value of customer is
),,( MYXELP k
))(,,())(,,( 01 MfYXELPMfYXELP ik
ik
),,( MYXELP ki
Modeling Markets as Social Network
• The global lift in profit:
Where ri = r1 if Mi =1, ri = r0 otherwise, and |M| is the number of 1’s in M
• The expected lift in profit:
CMMYXXPrMYXXPrMYXELP n
ik
in
ik
iik ||),,|1(0),,|1(),,(
1 01
CMfYXXPrMfYXXPrMYXELP ik
iik
ik
i ))(,,|1(0))(,,|1(1),,( 01
Modeling Markets as Social Network
• Our goal: - to find the assignment of values to M that maximizes ELP
• Problem: - required trying all possible combinations of assignment!
• Solution: - approximate procedures
Single Pass Methods Greedy search
Hill-Climbing search
Modeling Markets as Social Network
• There may be another problem.• How do we compute ?
• L.Pelkwitz (1990), A continuous relaxation labeling for Markov Random fields
• can be approximate by its maximum entropy estimate given the marginal
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),,|,(
),,|(
ui
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jii
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MYXXPMYNXP
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uij
kj NforXMYXXP ),,,|(
Modeling Markets as Social Network
• expresses as a function of themselves • Can be iteratively to find them• Relaxation labeling : - guaranteed to converge to locally consistent values as long as the initial
assignment is sufficiently close to them.• Initialization: the network-less probability
• Problem: exponential in
• Solution: Gibbs Sampling / k-shortest-path algorithm
),,|( MYXXP ki
),|( MYXP i
uiN
m
k iiiiiii MYPXYPXMPXPMYXP1
),(/)|()|()(),|(
Modeling Markets as Social Network
• Recall:
• still don’t know!• From Naïve Bayes:
Where• Now can be computed by :
)(),,|(),,|(),,|( u
iuijNC NX
kjii
ki MYXXPMYNXPMYXXP
),,|( MYNXP ii
m
k ikii
iiiiii XyP
NMYPXMPNXPMYNXP
1)|(
)|,()|()|(),,|(
)|0()0|,()|1()1|,()|,( iiiiiiiiii NXPXMYPNXPXMYPNMYP
),,|( MYNXP ii
)|(),|(),(),|( ikiiiii XyPXMPXPNXP
Mining the network from Collaborative Filtering Databases
• : vary from application to application
• Collaborative Filtering System: Users rate a set of items (like: amazon.com) These ratings are then used to recommend other items the user might be
interested in
• But…how?
• The basic idea( given by GroupLens ): To predict a user’s rating of an item as a weighted average of the rating given by
similar users Then recommend items with high predicted ratings
)|( ii NXP
Mining the network from Collaborative Filtering Databases
• The Pearson correlation coefficient:
Where is user i’s rating of item k, is the mean of user i’s ratings , likewise for j;and the summations and means are computed over the item k that both i and j haverated.
• Given an item k that user I has not rated, the rating of k for the user is then predicted as:
Where is a normalization factor, and is the set of users most similar to I according to PCC
k k jjkiik
k jjkiikij
RRRR
RRRRW
22 )()(
))((
ikR iR
ij NX jjkjiiik RRWRR )(ˆ
ij NX ijW ||/1iN in
Mining the network from Collaborative Filtering Databases
• Thus we can compute :
Piecewise-linear model Obtained by dividing ‘s range into bins Compute Mean and for each bin Estimate by interpolating linearly between the two nearest
means
• Finally for the model:
))(ˆ|()|( iiiii NRXPNXP
)|( ii NXP
iR̂
iR̂ )ˆ|( ii RXP))(ˆ|( iii NRXP
)|(),|(),|(),(),ˆ|( YRPXYPXMPXPRXP iikiiiii
Example: the ‘EachMovie’ collaborative filtering database
• ‘EachMovie’---word of mouth ---Rating ---Movie Information• The Data• Model Accuracy• Network Value• Marketing Experiments
The Model
• Y={Y1,Y2,…,Y10} p(Y|Xi) • Pearson correlation coefficient for Wij (with
penalized value 0.05)• •
)|(),|(),|(),(),ˆ|( YRPXYPXMPXPRXP iikiiiii
}1),0|1(min{)1|1( iiii MXPMXP
Frame of the model
Empirical distribution
The Data
• Training set: all movies before Sep 1 1996 ---Sold before Jan 1996 ---Srecent Jan-Sep 1996• Test set: movies Sep-Dec 1996• Inactive people
Model Accuracy
• Set M=M0 • Estimate the p(Xi|Xk, Y, M)• No rating from inactive people---p(Xi|Y)=0• Correlation=p(Xi|Xk, Y, M)/actual Xi
• Not really satisfactory as the genre is the only input
Network Value
Weight ranking function
A good customer to market
• Likely to give high rating• Strong weight to influence• Has many neighbors who are easily be
influenced• High probability of purchasing
Marketing Experiments
• Traditional direct marketing• Network-based marketing ---single pass ---greedy search ---hill climbing• Scenarios: Free Movie, Discounted Movie,
Advertising
Profits and runtimes obtained using different marketing strategies
Related Work
• Regarding the Netwotk ---Email logs (Schwartz and Wood) ---ReferralWeb ---MRF classification of Web pages(Chak)• Regarding the Marketing ---impact on the customers’ closest friends
(Krackhardt)
Future Work
• Expect larger network to be mined• Mining a network from multiple sources of
relevant information• Mining the unknown networks• Towards more detailed node models and
multiple types of relations between nodes
Conclusion
• Data mining in viral marketing• Customers as nodes and impact on each other• social network from collaborative filtering
database• Optimize marketing decision