1. Collaborative Filtering for Streaming data
颜荣圻

2. Outline Introduction Matrix Factorization Distributed SGD
Spark & Spark Streaming
Our Work 2 2

3. Outline Introduction Matrix Factorization Distributed SGD
Spark & Spark Streaming
Our Work 3 3

4. Introduction
Movie Rating 4

5. Introduction
Netflix Prize 5

6. Introduction
Recommendtion 6

7. How to fill in the blanks?
Introduction
Collaborative Filtering
What do I recommend? =
How to fill in the blanks? 7

8. Introduction
Goal
Predict movies of interest to a user based on movies watched by user and others
Collectively filter the ratings of a large group of users
Data: a stream of incoming ratings 8

9. Outline Introduction Matrix Factorization Distributed SGD
Spark & Spark Streaming
Our Work 9 9

10. m: number of rows(users) n: number of columns(items)
Matrix Factorization
Model: Matrix Completion Problem
m: number of rows(users)
n: number of columns(items)
R: incomplement matrix of ratings
Rij : the rating user i assigns to item j 10

11. Matrix Factorization V k UT
Approach: Low-rank Matrix Factorization
Find a low-rank matrix factorization of the ratings matrix
U=[u1,u2,... ui ... um] V=[v1,v2,... vj ... vn] k UT V 11

12. Matrix Factorization Low-rank Matrix Factorization: action: yes
k: we assume that the ratings users assign to items are determined by k latent features.
vAve=[8, 7, 0, 1,...,2] T
fiction: yes
action: yes
romance: no
comedy: a little 12

13. Matrix Factorization Low-rank Matrix Factorization:
Each item j has k weights,
The rating user i assigns to item j: 13

14. Matrix Factorization Optimization problem:
Let denote the set of entries in R for which the rating is known
We wish to find matrixes and
which minimize the sum
min<Rij, R'ij> 14

15. Matrix Factorization Optimization problem:
To prevent overfitting, we introduce a regularization term with a penalty parameter
λ > 0.
denotes the Frobenius norm, 15

16. Matrix Factorization Optimization problem: is a given loss function
The regularized square loss:
non-convex 16

17. Outline Introduction Matirx Factorization Distributed SGD
Spark & Spark Streaming
Our Work 17 17

18. Distributed SGD Method: Stochastic Gradient Descent (SGD)
>0 is the step size 18

19. Distributed SGD 19

20. Distributed SGD
Algorithm Design: 20

21. Distributed SGD Distributed Matrix =>Parallelized SGD:
Divide the ratings matrix R into blocks and distribute the blocks to different processors.
For and : and 21

22. Distributed SGD Batch Streaming Algorithm:
We must distribute the blocks in a way that avoids conflicting updates. 22

23. Initialize Matrix R & U &V
Streaming DSGD
Batch Streaming Algorithm:
Join U &V, R=UTV
make perdiction
Divide Matrix
Select blocks
Initialize Matrix R & U &V
Worker
Driver
Make RDD
live data stream(i,j,R)
SGD
Block 3
Block 1
Block 2
Update u1 & v1
Update u2 & v2
Update u3 & v3 23

24. Outline Introduction Matrix Factorization Distributed SGD
Spark & Spark Streaming
Our Work 24 24