1. Thesis presentation
Online recommendations
using matrix factorisation
Marcus Ljungblad
marcus@tuenti.com
Royal Institute of Technology, Stockholm, Sweden
Instituto Superior Técnico, Lisbon, Portugal
Universitat Politécnica de Catalunya, Barcelona, Spain

2. 40+ million videos
13+ million users
500 requests/second
y ea rs
0 6

3. 3 reasons:
- find good content
- improve user experience
- increase revenue
great!

5. 3 problems

6. 1: the data

7. 2: the model

8. 2: the model

9. 3: the system
hy so little
W esearch?
syste ms r

10. 3: the system

11. 3 1 problem

12. Question:
How do you serve
recommendations
from millions of items
to millions of users?

14. Video ratings
2 4 4 ? 1
3 5 ? ? 1
Users
? 4 2 1 ?
1 ? 1 3 3

15. def matrix_factorization(MatrixToFactorise, UsersPreferences, MoviesFeatures,
NumberOfLatentFeatures, MaxSteps=5000,
LearningRate=0.0002, RegularizationConstant=0.02):
MoviesFeatures = MoviesFeatures.T
for step in xrange(MaxSteps):
for user in xrange(len(MatrixToFactorise)):
for movie in xrange(len(MatrixToFactorise[user])):
if MatrixToFactorise[user][movie] > 0:
estimatedUserMovieFactors = MatrixToFactorise[user][movie] -
numpy.dot(UsersPreferences[user,:], MoviesFeatures[:,movie])
for feature in xrange(NumberOfLatentFeatures):
UsersPreferences[user][feature] = UsersPreferences[user][feature] +
LearningRate * (2 * estimatedUserMovieFactors *
MoviesFeatures[feature][movie] -
RegularizationConstant * UsersPreferences[user][feature])
MoviesFeatures[feature][movie] = MoviesFeatures[feature][movie] +
LearningRate * (2 * estimatedUserMovieFactors *
UsersPreferences[user][feature] -
RegularizationConstant * MoviesFeatures[feature][movie])
# if approximation is good enough, stop iterating
ApproximationError = calculate_mean_squared_error_of_estimate(MatrixToFactorise,
UsersPreferences,
MoviesFeatures,
out
NumberOfLatentFeatures,
ab
RegularizationConstant)
orry
if ApproximationError < 0.001:
break
S
the slide

16. [ 0.38 0.91 0.32 0.36 1.22]
[ 1.52 -0.07 0.66 0.76 0.79]
[ 0.72 0.98 0.98 1.28 1.75]
[ 0.79 0.63 0.08 0.9 1.46]
[ 1.54 -0.19 0.81 0.61 0.72]
[ 0.56 0.58 0.16 0.43 1.28]
[ 0.22 0.61 0.95 1.18 -0.09]
[-0.15 0.7 0.87 1.45 -0.3]
[-0.13 0.76 0.97 1.04 -0.26]

17. [ 2.05 3.97 3.96 2.12 1.01]
[ 2.93 5.02 3.21 1.61 0.98]
[ 2.15 3.95 2.01 1.05 1.1 ]
[ 1. 4.29 1.01 2.96 2.98]

18. [ 2.05 3.97 3.96 2.12 1.01]
[ 2.93 5.02 3.21 1.61 0.98]
[ 2.15 3.95 2.01 1.05 1.1 ]
[ 1. 4.29 1.01 2.96 2.98]
2 4 4 ? 1
3 5 ? ? 1
? 4 2 1 ?
1 ? 1 3 3

19. [ 2.05 3.97 3.96 2.12 1.01]
[ 2.93 5.02 3.21 1.61 0.98]
[ 2.15 3.95 2.01 1.05 1.1 ]
[ 1. 4.29 1.01 2.96 2.98]

20. 1 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5
6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65
6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2
34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1
13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111
23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6
34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6
14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34
13x40
51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13
3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4
2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2
24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1
2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24
43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6
23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42
34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5
6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4
million ratings
61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43
21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23
3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5
234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9
65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6
2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1
123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45
23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234
5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65
3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2
1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1
123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234 5 2 24 1 13 3 56 6 23 3 45
23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65 3 2 111 23 4 2 42 34 5 234
5 2 24 1 13 3 56 6 23 3 45 23 6 6 2 34 51 24 43 21 1 1 123 4 65 6 14 1 2 4 61 24 6 2 1 34 5 6 34 2 24 5 6 8 9 65
3 2 11

21. r in g
l us te
C

22. Millions of items
1
2
3

23. 1
2
3

24. Recommendation
Request
1
2
3

25. Recommendation
Request
1
2
3

26. Compass = last video

27. Interface Delegate Router Workers
Workers
Workers
request
start
route
compute
reply top N
merge
/ sort
top N to json
start

28. Did it work?

29. Results
- ~600 requests per second
- latency below 30 ms
- quality is ok

30. Results: Throughput

31. Results: Throughput
h uh?

32. Interface Delegate Router Workers
Workers
Workers
request
start
route
compute
reply top N
merge
/ sort
top N to json
start

33. Results: Quality
Queries Non-zero MAP
1 41 23%
2 87 25%
3 116 36%
4 165 58%
5 196 74%

34. Summary
- clustering is data
- balanced clusters needed
- scale is ok

36. Photos and imagery used in the presentation (except graphs and logos).
Amazon recommendations: http://pleated-jeans.com/2010/08/06/amazon-recommendations-for-characters-from-the-office/
Pile of books: http://www.paper-pills.com/category/gewgaws/page/2/
Function: http://en.wikipedia.org/wiki/File:Graph_of_example_function.svg
Server: http://arstechnica.com/gadgets/2007/08/windows-home-server-system-specs-prices-and-launch-date-leaked/
Tick: http://ia.wikipedia.org/wiki/File:Tick_green_modern.svg
Phone: http://www.foxbusiness.com/technology/2012/05/22/are-carrier-subsidies-hurting-innovation-and-driving-up-mobile-
phone-costs/
Man in front of computer: http://honesttogawd.blogspot.com.es/