1. Recommender Systems: Content-based Systems & Collaborative Filtering
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Recommender Systems: Content-based Systems & Collaborative Filtering

2. High Dimensional Data High dim. data Graph data Infinite data
Locality sensitive hashing
Clustering
Dimensionality reduction
Graph data
PageRank, SimRank
Community Detection
Spam Detection
Infinite data
Filtering data streams
Web advertising
Queries on streams
Machine learning
SVM
Decision Trees
Perceptron, kNN
Apps
Recommender systems
Association Rules
Duplicate document detection

3. Example: Recommender Systems
Customer X
Buys Metallica CD
Buys Megadeth CD
Customer Y
Does search on Metallica
Recommender system suggests Megadeth from data collected about customer X

4. Recommendations Examples: Search Recommendations Items
Products, web sites, blogs, news items, …

5. From Scarcity to Abundance
Shelf space is a scarce commodity for traditional retailers
Also: TV networks, movie theaters,…
Web enables near-zero-cost dissemination of information about products
From scarcity to abundance
More choice necessitates better filters
Recommendation engines
How Into Thin Air made Touching the Void a bestseller:
In 1988, a British mountain climber named Joe Simpson wrote a book called Touching the Void, a harrowing account of near death in the Peruvian Andes. It got good reviews but, only a modest success, it was soon forgotten. Then, a decade later, a strange thing happened. Jon Krakauer wroteInto Thin Air, another book about a mountain-climbing tragedy, which became a publishing sensation. SuddenlyTouching the Void started to sell again.
Random House rushed out a new edition to keep up with demand. Booksellers began to promote it next to their Into Thin Air displays, and sales rose further. A revised paperback edition, which came out in January, spent 14 weeks on theNew York Times bestseller list. That same month, IFC Films released a docudrama of the story to critical acclaim. NowTouching the Void outsells Into Thin Air more than two to one.
What happened? In short, Amazon.com recommendations. The online bookseller's software noted patterns in buying behavior and suggested that readers who liked Into Thin Airwould also like Touching the Void. People took the suggestion, agreed wholeheartedly, wrote rhapsodic reviews. More sales, more algorithm-fueled recommendations, and the positive feedback loop kicked in.

6. Sidenote: The Long Tail
Source: Chris Anderson (2004)

7. Read http://www.wired.com/wired/archive/12.10/tail.html to learn more!
Physical vs. Online
Read to learn more!

8. Types of Recommendations
Editorial and hand curated
List of favorites
Lists of “essential” items
Simple aggregates
Top 10, Most Popular, Recent Uploads
Tailored to individual users
Amazon, Netflix, …

9. Formal Model X = set of Customers S = set of Items
Utility function u: X × S  R
R = set of ratings
R is a totally ordered set
e.g., 0-5 stars, real number in [0,1]

10. Utility Matrix Avatar LOTR Matrix Pirates Alice Bob Carol David
Find out blank
David

11. Key Problems (1) Gathering “known” ratings for matrix
How to collect the data in the utility matrix
(2) Extrapolate unknown ratings from the known ones
Mainly interested in high unknown ratings
We are not interested in knowing what you don’t like but what you like
(3) Evaluating extrapolation methods
How to measure success/performance of recommendation methods

12. (1) Gathering Ratings Explicit Implicit Ask people to rate items
Doesn’t work well in practice – people can’t be bothered
Implicit
Learn ratings from user actions
E.g., purchase implies high rating
What about low ratings?

13. More on ratings – Explicit ratings
Probably the most precise ratings
Most commonly used (1 to 5, 1 to 7 Likert response scales)
Research topics
Optimal granularity of scale; indication that 10-point scale is better accepted in movie dom.
An even more fine-grained scale was chosen in the joke recommender discussed by Goldberg et al. (2001), where a continuous scale (from −10 to +10) and a graphical input bar were used
No precision loss from the discretization
User preferences can be captured at a finer granularity
Users actually "like" the graphical interaction method
Multidimensional ratings (multiple ratings per movie such as ratings for actors and sound)
Main problems
Users not always willing to rate many items
number of available ratings could be too small → sparse rating matrices → poor recommendation quality
How to stimulate users to rate more items?

14. More on ratings – Implicit ratings
Typically collected by the web shop or application in which the recommender system is embedded
When a customer buys an item, for instance, many recommender systems interpret this behavior as a positive rating
Clicks, page views, time spent on some page, demo downloads …
Implicit ratings can be collected constantly and do not require additional efforts from the side of the user
Main problem
One cannot be sure whether the user behavior is correctly interpreted
For example, a user might not like all the books he or she has bought; the user also might have bought a book for someone else
Implicit ratings can be used in addition to explicit ones; question of correctness of interpretation

15. (2) Extrapolating Utilities
Key problem: Utility matrix U is sparse
Most people have not rated most items
Cold start:
New items have no ratings
New users have no history
Three approaches to recommender systems:
1) Content-based
2) Collaborative
3) Latent factor based
Today!

16. Content-based Recommender Systems

17. Content-based Recommendations
Main idea: Recommend items to customer x similar to previous items rated highly by x
Example:
Movie recommendations
Recommend movies with same actor(s), director, genre, …
Websites, blogs, news
Recommend other sites with “similar” content

18. Plan of Action Item profiles User profile likes build recommend Red
Circles
Triangles
match
User profile

19. Item Profiles For each item, create an item profile
Profile is a set (vector) of features
Movies: author, title, actor, director,…
Text: Set of “important” words in document
How to pick important features?
Usual heuristic from text mining is TF-IDF (Term frequency * Inverse Doc Frequency)
Term … Feature
Document … Item

20. Sidenote: TF-IDF fij = frequency of term (feature) i in doc (item) j
ni = number of docs that mention term i
N = total number of docs
TF-IDF score: wij = TFij × IDFi
Doc profile = set of words with highest TF-IDF scores, together with their scores
Note: we normalize TF to discount for “longer” documents

21. User Profiles and Prediction
User profile possibilities:
Weighted average of rated item profiles
Variation: weight by difference from average rating for item …
Prediction heuristic:
Given user profile x and item profile i, estimate 𝑢(𝒙,𝒊) = cos⁡(𝒙,𝒊) = 𝒙·𝒊 | 𝒙 |⋅| 𝒊 |

22.  Item profile: vector with 0 or 1 for each Actor
 Items are movies, only feature is “Actor”
 Item profile: vector with 0 or 1 for each Actor
 Suppose user x has watched 5 movies
 2 movies featuring actor A
 3 movies featuring actor B
 User profile = mean of item profiles
 Feature A’s weight = 2/5 = 0.4
 Feature B’s weight = 3/5 = 0.6

23.  Actor A’s movies rated 3 and 5  Actor B’s movies rated 1, 2 and 4
 Same example, 1-­‐5 star ratings
 Actor A’s movies rated 3 and 5
 Actor B’s movies rated 1, 2 and 4
 Useful step: Normalize ratings by subtracting user’s mean rating (3)
 Actor A’s normalized ratings = 0, +2
 Profile weight = (0 + 2)/2 = 1
 Actor B’s normalized ratings = -­‐2, -­‐1, +1
 Profile weight = -­‐2/3

24. θ  User profile x, Item profile i
 Estimate U(x,i) = cos(θ) = (x . i)/(|x||i|) x i θ
Technically, the cosine distance is actually the angle θ
And the cosine similarity is the angle 180-θ
For convenience, we use cos(θ) as our similarity measure and call it the “cosine similarity” in this context. 10

25. Pros: Content-based Approach
+: No need for data on other users
No cold-start or sparsity problems
+: Able to recommend to users with unique tastes
+: Able to recommend new & unpopular items
No first-rater problem
+: Able to provide explanations
Can provide explanations of recommended items by listing content-features that caused an item to be recommended

26. Cons: Content-based Approach
–: Finding the appropriate features is hard
E.g., images, movies, music
–: Recommendations for new users
How to build a user profile?
–: Overspecialization
Never recommends items outside user’s content profile
People might have multiple interests
Unable to exploit quality judgments of other users

27. Collaborative Filtering
Harnessing quality judgments of other users

28. Collaborative Filtering
Consider user x
Find set N of other users whose ratings are “similar” to x’s ratings
Estimate x’s ratings based on ratings of users in N x N

29. Similarity Metric Consider user x and y with rating vector rx and ry
We need a similarity metric sim(x, y)
Intuitively we want: sim(A, B) > sim(A, C)

30. Finding “Similar” Users
rx = [*, _, _, *, ***]
ry = [*, _, **, **, _]
Let rx be the vector of user x’s ratings
Jaccard similarity measure
Problem: Ignores the value of the rating
Cosine similarity measure
sim(x, y) = cos(rx, ry) = 𝑟 𝑥 ⋅ 𝑟 𝑦 || 𝑟 𝑥 ||⋅ ||𝑟 𝑦 ||
Problem: Treats missing ratings as “negative”
Pearson correlation coefficient
Sxy = items rated by both users x and y
rx, ry as sets:
rx = {1, 4, 5}
ry = {1, 3, 4}
rx, ry as points:
rx = {1, 0, 0, 1, 3}
ry = {1, 0, 2, 2, 0}
-- Jaccard is not appropriate as we want to consider weights
0，-1，-1,0,2
0,-1，1,1，-1
𝒔𝒊𝒎 𝒙,𝒚 = 𝒔∈ 𝑺 𝒙𝒚 𝒓 𝒙𝒔 − 𝒓 𝒙 𝒓 𝒚𝒔 − 𝒓 𝒚 𝒔∈ 𝑺 𝒙𝒚 𝒓 𝒙𝒔 − 𝒓 𝒙 𝟐 𝒔∈ 𝑺 𝒙𝒚 𝒓 𝒚𝒔 − 𝒓 𝒚 𝟐
rx, ry … avg. rating of x, y

31. Similarity Metric Intuitively we want: sim(A, B) > sim(A, C)
Cosine sim:
Similarity Metric
𝒔𝒊𝒎(𝒙, 𝒚) = 𝒊 𝒓 𝒙𝒊 ⋅ 𝒓 𝒚𝒊 𝒊 𝒓 𝒙𝒊 𝟐 ⋅ 𝒊 𝒓 𝒚𝒊 𝟐
Intuitively we want: sim(A, B) > sim(A, C)
Jaccard similarity: 1/5 < 2/4
Cosine similarity: > 0.322
Considers missing ratings as “negative”
Solution: subtract the (row) mean
sim A,B vs. A,C:
0.092 >
Notice cosine sim. is correlation when data is centered at 0

32. Rating Predictions From similarity metric to recommendations:
Let rx be the vector of user x’s ratings
Let N be the set of k users most similar to x who have rated item i
Prediction for item s of user x:
𝑟 𝑥𝑖 = 1 𝑘 𝑦∈𝑁 𝑟 𝑦𝑖
𝑟 𝑥𝑖 = 𝑦∈𝑁 𝑠 𝑥𝑦 ⋅ 𝑟 𝑦𝑖 𝑦∈𝑁 𝑠 𝑥𝑦
Other options?
Many other tricks possible…
Shorthand: 𝒔 𝒙𝒚 =𝒔𝒊𝒎 𝒙,𝒚

33. Item-Item Collaborative Filtering
So far: User-user collaborative filtering
Another view: Item-item
For item i, find other similar items
Estimate rating for item i based on ratings for similar items
Can use same similarity metrics and prediction functions as in user-user model
sij… similarity of items i and j
rxj…rating of user u on item j
N(i;x)… set items rated by x similar to i

34. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 movies
- unknown rating
- rating between 1 to 5

35. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 ? movies
- estimate rating of movie 1 by user 5

36. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 ? sim(1,m) 1.00
-0.18
0.41
-0.10
-0.31
0.59
movies
Here we use Pearson correlation as similarity:
1) Subtract mean rating mi from each movie i m1 = ( )/5 = row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0]
2) Compute cosine similarities between rows
Neighbor selection: Identify movies similar to movie 1, rated by user 5

37. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 ? sim(1,m) 1.00
-0.18
0.41
-0.10
-0.31
0.59
movies
Compute similarity weights: s1,3=0.41, s1,6=0.59

38. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 movies
2.6
movies
Predict by taking weighted average:
r1.5 = (0.41* *3) / ( ) = 2.6
𝒓 𝒊𝒙 = 𝒋∈𝑵(𝒊;𝒙) 𝒔 𝒊𝒋 ⋅ 𝒓 𝒋𝒙 ∑ 𝒔 𝒊𝒋

39. Item-Item vs. User-User
Avatar
LOTR
Matrix
Pirates
Alice
Bob
Carol
David
There is a difference in the typical behavior of users and items, as it
pertains to similarity. Intuitively, items tend to be classifiable in simple
terms. For example, music tends to belong to a single genre. It is impossi-
ble, e.g., for a piece of music to be both 60’s rock and 1700’s baroque. On
the other hand, there are individuals who like both 60’s rock and 1700’s
baroque, and who buy examples of both types of music.
The consequence is that it is easier to discover items that are similar because they belong
to the same genre, than it is to detect that two users are similar because
they prefer one genre in common, while each also likes some genres that
the other doesn’t care for.
In practice, it has been observed that item-item often works better than user-user
Why? Items are simpler, users have multiple tastes

40. Pros/Cons of Collaborative Filtering
+ Works for any kind of item
No feature selection needed
- Cold Start:
Need enough users in the system to find a match
- Sparsity:
The user/ratings matrix is sparse
Hard to find users that have rated the same items
- First rater:
Cannot recommend an item that has not been previously rated
New items, Esoteric items
- Popularity bias:
Cannot recommend items to someone with unique taste
Tends to recommend popular items

41. Hybrid Methods
Implement two or more different recommenders and combine predictions
Perhaps using a linear model
Global baseline + collaborative filtering
Add content-based methods to collaborative filtering
Item profiles for new item problem
Demographics to deal with new user problem

42. Global baseline estimate
Estimate Joe’s rating for the movie The Sixth Sense
No feature selection needed
Problem: Joe has not rated any movie similar to The Sixth Sense
Global baseline estimate
Mean movie rating: 3.7 stars
The Six Sense is 0.5 stars above avg
Joe rates 0.2 stars below avg
Baseline estimate: – 0.2 = 4 stars

43. Combining Global Baseline with CF
Global baseline estimate
Joe with give The Six Sense is 4 stars
Local neighborhood (CF/NN)
Joe didn’t like movie Signs
Rate 1 star below his average rating
Final estimate
Joe will rate The Sixth Sense 3 stars

44. Global Baseline Estimate
Define similarity sij of items i and j
Select k nearest neighbors N(i; x)
Items most similar to i, that were rated by x
Estimate rating rxi as the weighted average:
baseline estimate for rxi
μ = overall mean movie rating
bx = rating deviation of user x
= (avg. rating of user x) – μ
bi = rating deviation of movie i
𝒃 𝒙𝒊 =𝝁+ 𝒃 𝒙 + 𝒃 𝒊

45. baseline estimate for rxi
Before:
CF: Common Practice
Define similarity sij of items i and j
Select k nearest neighbors N(i; x)
Items most similar to i, that were rated by x
Estimate rating rxi as the weighted average:
baseline estimate for rxi
μ = overall mean movie rating
bx = rating deviation of user x
= (avg. rating of user x) – μ
bi = rating deviation of movie i
𝒃 𝒙𝒊 =𝝁+ 𝒃 𝒙 + 𝒃 𝒊

46. Item-Item CF (|N|=2) users 12 11 10 9 8 7 6 5 4 3 2 1 movies
2.6
movies
Predict by taking weighted average:
r1.5 = (0.41* *3) / ( ) = 2.6
𝒓 𝒊𝒙 = 𝒋∈𝑵(𝒊;𝒙) 𝒔 𝒊𝒋 ⋅ 𝒓 𝒋𝒙 ∑ 𝒔 𝒊𝒋

47. Remarks & Practical Tips
- Evaluation
- Error metrics
- Complexity / Speed

48. Evaluation
movies 1 3 4 5 2
users

49. Evaluation
movies 1 3 4 5 2 ?
users
Test Data Set

50. Evaluating Predictions
Compare predictions with known ratings
Root-mean-square error (RMSE)
𝑥𝑖 𝑟 𝑥𝑖 − 𝑟 𝑥𝑖 ∗ where 𝒓𝒙𝒊 is predicted, 𝒓 𝒙𝒊 ∗ is the true rating of x on i
Precision at top 10:
% of those in top 10
Rank Correlation:
Spearman’s correlation between system’s and user’s complete rankings

51. Problems with Error Measures
Narrow focus on accuracy sometimes misses the point
Prediction Diversity
Prediction Context
Order of predictions
In practice, we care only to predict high ratings:
RMSE might penalize a method that does well for high ratings and badly for others

52. Collaborative Filtering: Complexity
Expensive step is finding k most similar customers: O(|X|)
Too expensive to do at runtime
Could pre-compute
Naïve pre-computation takes time O(k ·|X|)
X … set of customers
We already know how to do this!
Near-neighbor search in high dimensions (LSH)
Clustering
Dimensionality reduction

53. Pre-processing for item-based filtering
Item-based filtering does not solve the scalability problem itself
Pre-processing approach by Amazon.com (in 2003)
Calculate all pair-wise item similarities in advance
The neighborhood to be used at run-time is typically rather small, because only items are taken into account which the user has rated
Item similarities are supposed to be more stable than user similarities
Memory requirements
Up to N2 pair-wise similarities to be memorized (N = number of items) in theory
In practice, this is significantly lower (items with no co-ratings)
Further reductions possible
Minimum threshold for co-ratings
Limit the neighborhood size (might affect recommendation accuracy)

54. Tip: Add Data Leverage all the data Add more data
Don’t try to reduce data size in an effort to make fancy algorithms work
Simple methods on large data do best
Add more data
e.g., add IMDB data on genres
More data beats better algorithms

55. Homework
9.3.1
9.2.3