Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System...
-
Upload
clifford-fleming -
Category
Documents
-
view
219 -
download
0
description
Transcript of Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System...
Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System
----Chris Ding, R. Jin, T. Li and H.D. Simon. A Learning Framework using Green’s Function and Kernel Regularization with Application to Recommender System. KDD’07.
Outline Green’s Function Graph-Based Semi-supervised Learning
with Green’s Function Item-Based Recommendation Using
Green’s Function Extension
Green’s Function Green’s Function
Given a weighted graph G=(V,E),
W=
D=
The Graph Laplacian matrix L= D-W.
1 2
43
5
0.2
0.25
0.40.6
0.50.8
0.1
1 0.2 0.8 0.5 00.2 1 0.25 0.1 00.8 0.25 1 0 0.40.5 0.1 0 1 0.60 0 0.4 0.6 1
2.5 0 0 0 00 1.55 0 0 00 0 2.45 0 00 0 0 2.2 00 0 0 0 2
Green’s Function Green’s Function
Defined as the inverse of L = D-W with zero-mode discarded.
discard
* 1
2
1( )
Tni i
i i
v vG L
D W
,k k kLv v 1 20 ... n
1 0
Semi-Supervised with Green’s Function
Green’s Function Interpreted as an electric resistor network
1 2
3
5
4
: 1voltage 23w
1/ij ij ijw I r
1
( ) ( ),
( )(0,...,0,1,0,...,0)
Tij i j i j
i
r e e G e e
G D We
Viewed as a similarity metric on a graph
Semi-Supervised with Green’s Function
Label Propagation Labeled data & , unlabeled data
labeled data unlabeled data
For 2-class problems: For k-class problems:
1{ }li ix 1{ }li iy 1{ }ni i lx
1
,l
j ji ii
y sign G y l j n
Label Propagation
1
1, argmax,
0,
l
k ji ikijk
k G yy l j n
otherwise
Semi-Supervised with Green’s Function
Compared to Harmonic Function Harmonic Function is an iterative procedure Outperforms Harmonic Function 7 datasets, 10% as labeled data
Recommendation with Green’s Function
Item-based Recommendation To calculate unknown rating by averaging
rating of similar items by test users User-item matrix R, : rates Item Graph G=(V,E) typical similarity: cosine similarity, conditional
probability…
M N
pqR pu qi
Recommendation with Green’s Function
Recommendation with Green’s Function
0
2 3 8 5 0 1 01 0 0 5 0 0 20 2 7 4 7 3 02 4 6 6 8 0 00 1 5 0 5 0 83 2 7 9 0 0 03 6 0 0 0 4 04 5 6 0 0 5 8
R
12 3
456
7 1( )
GD W
0T TR GR
Recommendation with Green’s Function
Experiments: Dataset: Movielens : 943 users; 1682 movies; ratings from 1 to 5 Training set: 90,570 records Test set: 9,430 records
Recommendation with Green’s Function
Results compared to traditional methods: MAE: Mean Absolute Error M0E: Mean Zero-one Error
Extension
Combination between semi-supervised learning and recommendation?
Combine with other recommendation algorithms?
Improve graph-based semi-supervised learning with other algorithm?
Discussion and Suggestion
Thank You!