![Graph visualization
The data can be visualized as a (bipartite) graph.
Code : R
Library : igraph
JohnMike Dan Lea
Rock PopElectro R&B
1 l i b r a r y ( i g r a p h )
d = read . csv ( ” data . csv ” ) # Load Data
3 g = graph . data . frame ( d ) # Load Data i n t o graph
5 V( g ) $ type <− V( g ) $name %i n% d$ Item # Set graph as b i p a r t i t e
p l o t (g , l a y o u t=l a y o u t . b i p a r t i t e , v e r t e x . c o l o r=c ( ” green ” , ” cyan ” ) [V( g ) $ type +1])](https://image.slidesharecdn.com/introductiontorecommendersystems-171011212155/85/Introduction-to-recommender-systems-14-320.jpg)
![Incidence matrices
... or by two matrices:
Atrain =
Rock Pop Electro R&B
John : 1 0 0 0
Mike : 0 1 1 0
Dan : 1 1 0 1
Atest =
Rock Pop Electro R&B
Lea : 0 1 0 0
1 A t r a i n = A[ which ( rownames (A) != ”Lea” ) , ]
A t e s t = A[ which ( rownames (A) == ”Lea” ) , ]](https://image.slidesharecdn.com/introductiontorecommendersystems-171011212155/85/Introduction-to-recommender-systems-16-320.jpg)
![R code
Collaborative filtering in 10 lines of code.
1 l i b r a r y ( i g r a p h ) # Load graph l i b r a r y
2 g = graph . data . frame ( read . csv ( ” data . csv ” ) ) # Read and con vert data i n t o graph
V( g ) $ type <− V( g ) $name %i n% d$ Item # Set graph as b i p a r t i t e
4 A = get . i n c i d e n c e (g , s p a r s e=TRUE) # Compute I n c i d e n c e Matrix
5 A t r a i n = A[ which ( rownames (A) != ”Lea” ) , ]
A t e s t = A[ which ( rownames (A) == ”Lea” ) , ]
N t r a i n = 1/ s q r t (A t r a i n % ∗ % rep (1 , ncol (A) ) )
8 M norm = diag ( as . v e c t o r (N t r a i n ) )
sim matrix norm = M norm % ∗ % (A t r a i n % ∗ % A t e s t )
10 s c o r e M a t r i x = t ( as . matrix ( sim matrix norm ) ) % ∗ % A t r a i n](https://image.slidesharecdn.com/introductiontorecommendersystems-171011212155/85/Introduction-to-recommender-systems-27-320.jpg)
Introduction to recommender systems
- 1. An introduction to recommendation algorithms Collaborative filtering: how does it work? Arnaud de Myttenaere
- 2. About me Data Scientist, PhD Founder of Uchidata Consultant at Octo Technology, Sydney Several projects on recommendation algorithms (Viadeo social network, e-commerce, news website, . . . )
- 3. How do recommendation algorithms work?
- 4. Context Available data Personal information Historical behavior Objective → If a young man is a fan of Daft Punk, what’s the best artist we could recommend to him?
- 5. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 6. Model Based approach 1. Build a dataset which summarizes the data UserId Like Gender Age Artist Style Country 1 1 M 25 Daft Punk Electro France 1 0 M 25 Lady Gaga Pop USA 2 1 F 20 The Beatles Rock UK target user information item information 2. Learn a model to predict the target variable using your favorite algorithm: Linear Regression, Random Forest, XGBoost, . . . 3. For each new customer, apply the model on a set of artists and recommend the ones with the highest scores.
- 7. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 8. Memory Based approach How to recommend items to a particular customer or user? For each new customer: Search for similar customers in historical data Recommend popular items among similar customers Example: Collaborative Filtering.
- 10. Collaborative filtering: why? Collaborative Filtering algorithms1 .. are intuitive are simple to implement scales relatively well captures many implicit signals are hard to beat 1 Criteo Product Recommendation Beyond Collaborative Filtering - welcome to the Twilight Zone!, Olivier Koch RecSys Meetup London - Sept 20, 2017
- 11. But Collaborative Filtering algorithms also have some limitations2 : does not scales that well in practice does not capture temporal signals does not solve cold start does not address exploration in the long tail 2 Criteo Product Recommendation Beyond Collaborative Filtering - welcome to the Twilight Zone!, Olivier Koch RecSys Meetup London - Sept 20, 2017
- 12. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 13. Context Let us consider the following example: John likes Rock Mike likes Pop and Electro Dan likes Pop, R&B and Rock Lea likes Pop This information can be loaded in the folowing dataset: Customer Item John Rock Mike Pop Mike Electro Dan Pop Dan R&B Dan Rock Lea Pop Objective: find the best recommendation for Lea.
- 14. Graph visualization The data can be visualized as a (bipartite) graph. Code : R Library : igraph JohnMike Dan Lea Rock PopElectro R&B 1 l i b r a r y ( i g r a p h ) d = read . csv ( ” data . csv ” ) # Load Data 3 g = graph . data . frame ( d ) # Load Data i n t o graph 5 V( g ) $ type <− V( g ) $name %i n% d$ Item # Set graph as b i p a r t i t e p l o t (g , l a y o u t=l a y o u t . b i p a r t i t e , v e r t e x . c o l o r=c ( ” green ” , ” cyan ” ) [V( g ) $ type +1])
- 15. Incidence matrix This graph can be represented by a matrix... Rock Pop Electro R&B John : 1 0 0 0 Mike : 0 1 1 0 Dan : 1 1 0 1 Lea : 0 1 0 0 A = get . i n c i d e n c e (g , s p a r s e=TRUE)
- 16. Incidence matrices ... or by two matrices: Atrain = Rock Pop Electro R&B John : 1 0 0 0 Mike : 0 1 1 0 Dan : 1 1 0 1 Atest = Rock Pop Electro R&B Lea : 0 1 0 0 1 A t r a i n = A[ which ( rownames (A) != ”Lea” ) , ] A t e s t = A[ which ( rownames (A) == ”Lea” ) , ]
- 17. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 18. If similarity is the number of items in common (1/2) The similarity vector is given by: SimMatrix = Atrain ⊗ t(Atest) i.e. SimMatrix = 1 0 0 0 0 1 1 0 1 1 0 1 ⊗ 0 1 0 0 = 0 1 1 John Mike Dan Indeed Lea does not have any item in common with John, but has 1 item in common with Mike and Dan (Pop). sim matrix = A t r a i n % ∗ % A t e s t
- 19. If similarity is the number of items in common (2/2) Then the recommendation scores are given by scoreMatrix = t(SimMatrix) ⊗ Atrain i.e. scoreMatrix = 0 1 1 ⊗ 1 0 0 0 0 1 1 0 1 1 0 1 So scoreMatrix = Rock Pop Electro R&B (1 2 1 1) 1 s c o r e M a t r i x = t ( as . matrix ( sim matrix ) ) % ∗ % A t r a i n
- 20. Comments If similarity is the number of items in common... → not optimal since users with a lot of items will be very similar to (almost) every user. → hard to use because leads to a lot of items with the same recommendation score. Better similarity metric: cosine similarity → Idea: normalize the similarity using the number of items associated to each users.
- 21. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 22. Cosine similarity (1/3) Using the same data: Atrain = Rock Pop Electro R&B John : 1 0 0 0 Mike : 0 1 1 0 Dan : 1 1 0 1 The normalization vector is: Ntrain = 1 1/ √ 2 1/ √ 3 John is associated to 1 item (Rock) Mike is associated to 2 items (Pop, Electro) Dan is associated to 3 items
- 23. Cosine similarity (1/3) Then the normalized similarity matrix is given by: SimMatrixnorm = 1 . . . 1√ 2 . . . 1√ 3 ⊗ 0 1 1 = 0 1/ √ 2 1/ √ 3 0 0.71 0.58 John Mike Dan →Lea is more similar to Mike than Dan, because she has an item in common with both but Mike is associated to less items than Dan, so the link with Mike is stronger. 1 N t r a i n = 1/ s q r t (A t r a i n % ∗ % rep (1 , ncol (A) ) ) M norm = diag ( as . v e c t o r (N t r a i n ) )
- 24. Cosine similarity (3/3) The matrix of scores is given by: scoreMatrix = t(SimMatrixnorm) ⊗ Atrain i.e. scoreMatrix = 0 0.71 0.58 ⊗ 1 0 0 0 0 1 1 0 1 1 0 1 So scoreMatrix = Rock Pop Electro R&B (0.58 1.29 0.71 0.58) s c o r e M a t r i x = t ( as . matrix ( sim matrix norm ) ) % ∗ % A t r a i n
- 25. Comments For Atest = Rock Pop Electro R&B Lea : 0 1 0 0 Recommendation scores are scoreMatrix = Rock Pop Electro R&B (0.58 1.29 0.71 0.58) 1. Pop is the best recommendation for Lea, but she is already associated to Pop. 2. If the objective is to recommend new items, Electro is the best recommendation for Lea. 3. Rock and R&B have the same score and can be ordered by frequencies or randomly.
- 26. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 27. R code Collaborative filtering in 10 lines of code. 1 l i b r a r y ( i g r a p h ) # Load graph l i b r a r y 2 g = graph . data . frame ( read . csv ( ” data . csv ” ) ) # Read and con vert data i n t o graph V( g ) $ type <− V( g ) $name %i n% d$ Item # Set graph as b i p a r t i t e 4 A = get . i n c i d e n c e (g , s p a r s e=TRUE) # Compute I n c i d e n c e Matrix 5 A t r a i n = A[ which ( rownames (A) != ”Lea” ) , ] A t e s t = A[ which ( rownames (A) == ”Lea” ) , ] N t r a i n = 1/ s q r t (A t r a i n % ∗ % rep (1 , ncol (A) ) ) 8 M norm = diag ( as . v e c t o r (N t r a i n ) ) sim matrix norm = M norm % ∗ % (A t r a i n % ∗ % A t e s t ) 10 s c o r e M a t r i x = t ( as . matrix ( sim matrix norm ) ) % ∗ % A t r a i n
- 28. In practice Can be precomputed and do not need to be updated in real time : Atrain and Mnorm Must be computed in real time : Atest and scoreMatrix (matrix calculation) Optimal number of users : too small → bad performance, too big → too slow (unless computation is parallelized).
- 29. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 30. Collaborative Filtering Notations Let Iu(t) be the vector of items associated to a user u at time t: Iu(t) = (0, 0, . . . , 1, . . . , 0) where the kth coefficient is equal to 1 if item k is associated to user u at time t, and 0 else. Example: in music recommendation an ”item” could be an artist (or a song), and coefficient k is equal to 1 if the user u likes the artist (or song) k.
- 31. Collaborative Filtering Then, for t > t, the collaborative filtering algorithm estimates Iu(t ) (the future vector of items associated to the user u) by: Iu(t ) = v=u sim(v, u) · Iv (t) where sim(v, u) represents the similarity between users u and v. → The most relevant items for the user u are the ones with the highest score.
- 32. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 33. Similarity function The similarity between two users can be defined as the number of items in common. Then sim(u, v) = Iu|Iv where ·|· is the classical scalar product. → not optimal since users with a lot of items will be very similar to every user.
- 34. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 35. Cosine similarity Cosine similarity One can normalize the similarity by the number of items associated to users u and v. sim(u, v) = Iu|Iv Iu · Iv However, as Iu(t ) = v=u Iu|Iv Iu · Iv · Iv = 1 Iu · v=u Iu|Iv Iv · Iv The order of recommendations for the user u is the same than the ones got with sim(u, v) = Iu|Iv √ Iv . → In practice we can use sim(u, v) = Iu|Iv √ Iv .
- 36. The different approaches Model Based Memory Based Collaborative filtering using graph libraries Context A simple example Cosine similarity R code More formally Notations Similarity function Cosine similarity Conclusion
- 37. Conclusion Two different approaches : Model Based Memory Based → Choose the number of users in Atrain to fit your practical constraints, → The definition of similarity between users can be modified to consider users and context.
- 38. Conclusion However This algorithm is based on past behavior, so it never suggests new content. → It is necessary to often refresh the training set.
- 39. Thanks!