Social Recommendation

1. Social Recommender System
2015/4/10 1Middleware, CCNT, ZJU
Yueshen Xu
Middleware, CCNT, ZJU
xyshzjucs@zju.edu.cn
xyshzjucs@gmail.com
Knowledge
Engineering
&
E-Commerce

2. Outline
2015/4/10 2Middleware, CCNT, ZJU
 Where from?
 How to recommend?
 What to recommend?
 What’s the problem?
 ML & DM
 Related Topics
 Trends
What’s your
perspective?
Basic, Generalized, Comprehensible

3. Introduction
 Social Overload
Facebook  largest social network site
– 600,000,000 users
YouTube  largest video sharing site
– 2,000,000,000
Twitter  largest microblogging site
– 65,000,000 tweets per day
Sina microblog  largest microblogging site in
China
– 400,000,000 users
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4. Introduction
 The Recommender Systems is an augmentation
of the social process
 Any CF system has social characteristics
 Social Media and Recommender Systems can
mutually benefit each other
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5. Introduction
2015/4/10 Middleware, CCNT, ZJU 5
Real-world examples
Why?
Different man,
Different news
Pioneer
‘....based on
recommendatio
n algorithms....’
Multi-Media

6. Fundamental Recommendation Approaches
 Collaborative filtering based Recommendation
Aggregate ratings of objects from users and generate
recommendation based on inter-user/inter-item
similarity
 Demographic Recommendation
Age,gender,income…
 Content-based Recommendation
Music gene
 Hybrid Methods
Mixed
2015/4/10 Middleware, CCNT, ZJU 6
Your imagination

7. Fundamental Recommendation Approaches
 In the real world, we seek advices from our
trusted people
 CF automate the process of ‘word-of-mouth’
Select a subset of the users(neighbors) to use as
recommenders
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Collaborative Filtering

8. Fundamental Recommendation Approaches
 Shall we recommend Superman for John?
Jon’s taste is similar to both Chris and Alice tastes 
Do not recommend Superman to him
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User based CF algorithm

9. Fundamental Recommendation Approaches
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User based CF algorithm
vi - the mean vote for user i
k - a normalization factor
pij – the predicitive vote
w(i,j ) – the similarity between ui and uk !
Cose based similarity Pearson Based similarity

10. Fundamental Recommendation Approaches
 The transpose of the user-based algorithms
Bob dislike Snow-white(which is similar to Shrek) 
Do not recommend
2015/4/10 Middleware, CCNT, ZJU 10
Item based CF algorithm
W(k,j) is a measure of item similarity – usually the cosine measure

11. Matrix Factorization
 Matrix Decomposition
Tri-angle
LU
QR
Spectral
SVD
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 Matrix Factorization
SVD-like
Non-negative
PMF
BPMF
pLSA, LDA
Matrix
Theory
Machine
Learning
Discriminative Model
Generative Model
Unsupervised
Learning

12. Matrix Factorization
---SVD : the ancestor
 Rudiment---Singular Value Decomposition
For an arbitrary matrix A there exists a factorization
named SVD, as follows:
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13. Matrix Factorization
---Latent Semantic Analysis  PTM  LDA
 Low-rank matrix factorization
Why factorizing?
– One is about the interpretation
– You prefer Lost in Thailand ‘cause it’s a drama, and X, and
Y, and Z, and ......
– X, Y & Z are named as latent factors
So matrix factorization can be come across as
another type of LSA(Latent Semantic Analysis)
2015/4/10 Middleware, CCNT, ZJU 13
Share us
sth
corssing
your mind
Probabilistic
Topic Model !

14. Matrix Factorization
---SVD-Like : low-rank matrix factorization
 Latent Factor Model  Generative Model
Low-rank matrix factorization  Latent Factor Space
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QPRR T


QPRR T


QPRR T


QPRR T


QPRR T


QPRR T


Rating
Matrix
Approximate
Rating Matrix User Latent
Factor Matrix
Item Latent
Factor Matrix
 

ff
ifufui fiQfuPqpriuR ),(),(),(
Predicted value ),( jiR

 

kk
ikuk kiQkuPqpjirjiR ),(),(),(),(
k-rank
factors
Basic Form

15. Matrix Factorization
---SVD-Like : low-rank matrix factorization
 Minimize the sum-squared errors
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Skip
Details
 

m
i
n
j
j
T
iij
QP
QPR
1 1
2
, 2
1
min  

m
i
n
j
j
T
iijij
QP
QPRI
1 1
2
,
)(
2
1
min
Frobenius Form
Just like Quadratic regression
I : the indicator function
 Regularization
Avoid overfitting  Why?  Sparsity/Sample
Shortage
2221
1 1
2
, 22
)(
2
1
min FF
m
i
n
j
j
T
iijij
QP
QPQPRI

 
 Solution
Stochastic Gradient Descent

16. Matrix Factorization
---PMF : the production of Bayesian Theory
 SVD-Like is not perfect  Why?
Subject & Object  the victim of formalism
 Maximum Posterior Probability(MAP) 
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)()(),|()|,( VpUpVURpRVUp 
   

m
i
n
j
I
Rj
T
iij
R
ij
VUrNVURp
1 1
2
,|),|( 


m
i
UiU IUNUp
1
22
),0|()|(  

n
j
ViV IVNVp
1
22
),0|()|( 
Gaussian
Noise
     

n
j
Vi
m
i
Ui
m
i
n
j
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T
iij IVNIUNVUrNRVUp
R
ij
1
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1
2
1 1
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),0|(),0|(,|)|,( 
Zero-mean spherical Gaussian prior

17. Surroundings
 Topics related
Non-negative Matrix Factorization
– Deng Cai etc.
Boltzmann Machines
– Discarded
Heterogeneous networks
– Prof. Han
– Link Prediction & Community Discovery
Transfer Learning & Online Learning
– Qiang Yang etc.
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Excavate
Structures
Neural
Network
‘Graph
Regularized
NMF for.....’
Different
Certain
Networks
Online
Algorithms
Others 
• Semantic
Web
• Ranking
• Computing
Ads
• Network
Marketing
• Clustering
• NLP
• TM
• Sociology
• Etc.

18. Trends
---Horizontal Expansion
 More Relationship  More Matrix
Social Network
– Turn to your friends for suggestion
Trust Network
– Turn to who you trust for suggestion
Clarify the connection
– What’s the relationship?
– Why does it work?
2015/4/10 Middleware, CCNT, ZJU 18
Weight &
Relationship
Social/Trust
Network
 Etc.
Structure of Networks

19. Trends
---Vertical Expansion
 3-4-5- Dimensions  Tensor
A tensor can be represented as a multi-dimensional
array of numerical values.
– 1-dimensional tensor : Vector
– 2-dimensional tensor : Matrix
Tensor Decomposition & Tensor Factorization
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observed
value
3th, Latent factor,
Time or Tag
1th Latent factor
one, User
2thLatent factor ,
Item


20. 2015/4/10 20Middleware, CCNT, ZJU
Social Recommender System