1. The document describes an algorithm for recommending movies for two users to watch based on their ratings of movies. 2. It collects ratings data from users to create a ratings table and calculates a similarity matrix between movies based on the ratings. 3. It then takes the movies liked by each user, calculates their similarity to other movies, and recommends the movie with the highest combined similarity.

1. Find
movies
for
two
Allen
Sussman

9. Can we find a movie we’ll both actually like?

11. Each person enters movies they like and
2lu finds movies they’ll both like

12. Each person enters movies they like and
2lu finds movies they’ll both like

13. Algorithm: Collaborative Filtering
Ratings Table from
Movies->
Users->
1
2
3
4
5
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5

14. Algorithm: Collaborative Filtering
Ratings Table from
Movies->
Users->
1
2
3
4
5
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Movies Similarity Matrix
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1

15. Algorithm: Collaborative Filtering
Ratings Table from
Movies->
Users->
1
2
3
4
5
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Movies Similarity Matrix
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe

16. Algorithm: Collaborative Filtering
Ratings Table from
Movies->
Users->
1
2
3
4
5
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Movies Similarity Matrix
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1

17. Algorithm: Collaborative Filtering
Ratings Table from
Movies->
Users->
1
2
3
4
5
f(
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Clue
1
0.2
0.3
0.4
0.5
,
Babe
0.4
0.2
0.2
1
0.5
)=
Movies Similarity Matrix
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1

18. Algorithm: Collaborative Filtering
Ratings Table from
Movies Similarity Matrix
Movies->
Users->
1
2
3
4
5
f(
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Clue
1
0.2
0.3
0.4
0.5
,
Babe
0.4
0.2
0.2
1
0.5
)=
Clue
Kids
Jaws
Babe
Big
0.6
0.2
0.225
0.6
0.5
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1

19. Algorithm: Collaborative Filtering
Ratings Table from
Movies Similarity Matrix
Movies->
Users->
1
2
3
4
5
f(
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Clue
1
0.2
0.3
0.4
0.5
,
Babe
0.4
0.2
0.2
1
0.5
)=
Clue
Kids
Jaws
Babe
Big
0.6
0.2
0.225
0.6
0.5
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Largest number is for the movie Big. Users should watch it!

20. Algorithm: Collaborative Filtering
Ratings Table from
Movies Similarity Matrix
Movies->
Users->
1
2
3
4
5
f(
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Clue
1
0.2
0.3
0.4
0.5
,
Babe
0.4
0.2
0.2
1
0.5
)=
Clue
Kids
Jaws
Babe
Big
0.6
0.2
0.225
0.6
0.5
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Largest number is for the movie Big. Users should watch it!
Cross-validation: 90% of recommendations were given
a rating of 3 or above by both users

22. Allen Sussman, Ph.D.

23. Goodness-of-recommendation (GoR) function
Similarity of
movie to user 1
movie
Similarity of
movie to user 2
movie
GoR(movie)=mean(s1,s2) - 0.25diff(s1,s2)
If average similarity
to the input movies
is high, that’s good!
If movie is very
similar to user 1
movie but not
user 2 movie (or
vice versa), that’s
bad!

24. Algorithm
Ratings Table
Movies->
Users->
1
2
3
4
5
f(
Clue Kids Jaws Babe Big
5
3
4
5
None
None
5
1
5
None
3
None
1
4
3
1
5
1
4
3
2
4
1
4
5
Clue
1
0.2
0.3
0.4
0.5
,
Babe
0.4
0.2
0.2
1
0.5
)=
0.6
0.2
0.225
0.6
0.5
Movies Similarity Matrix
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Say User 1 likes Clue
User 2 likes Babe
Clue
Kids
Jaws
Babe
Big
Clue Kids Jaws Babe Big
1
0.2
0.3
0.4
0.5
0.2
1
0.3
0.2
0.3
0.3
0.3
1
0.2
0.3
0.4
0.2
0.2
1
0.5
0.5
0.3
0.3
0.5
1
Largest number is for the movie Big. Users should watch it!
f(s1,s2)=mean(s1,s2)-α*diff(s1,s2)
For multiple input movies,
f(s1,1,s1,2,…,s2,1,s2,2,…) = mean(s1,1,s1,2,…,s2,1,s2,2,…)α*std(s1,1,s1,2,…,s2,1,s2,2,…)-β*diff(mean(s1,1,s1,2,…),mean(s2,1,s2,2,…))

25. Cross-Validation
Movies Similarity Matrix
Ratings Table
Movies->
Users->
Training Set
Ground Truth
Clue Kids Jaws Babe Big
Test Set
Features
1
Consider two users in test set
Features
Test Set
1
5
2
4
5
1
5
2
My Recommendations
Clue Kids Jaws Babe Big
Ground
Truth
User 1
User 2
Use algorithm and similarity matrix on
then compare predictions and truth
3
2
Ground
Truth
4
to predict
Y
Y
Y