Learning with Green’s Function with Application to Semi-Supervised Learning and Recommender System...
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![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/1.jpg)
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.
![Page 2: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/2.jpg)
Outline Green’s Function Graph-Based Semi-supervised Learning
with Green’s Function Item-Based Recommendation Using
Green’s Function Extension
![Page 3: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/6.jpg)
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
![Page 7: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/9.jpg)
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
![Page 10: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/11.jpg)
Recommendation with Green’s Function
Results compared to traditional methods: MAE: Mean Absolute Error M0E: Mean Zero-one Error
![Page 12: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/12.jpg)
Extension
Combination between semi-supervised learning and recommendation?
Combine with other recommendation algorithms?
Improve graph-based semi-supervised learning with other algorithm?
![Page 13: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/13.jpg)
Discussion and Suggestion
![Page 14: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062600/5a4d1b4d7f8b9ab0599a603a/html5/thumbnails/14.jpg)
Thank You!