Recommender Systems Content and Collaborative Filtering

CS246: Mining Massive Datasets
Jure Leskovec, StanfordUniversity
http://cs246.stanford.edu
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High dim.
data
Locality
sensitive
hashing
Clustering
Dimension-
ality
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
Recommen-
der systems
Association
Rules
Duplicate
document
detection
1/25/22 Jure Leskovec, Stanford CS246:MiningMassive Datasets 2

 Customer X
▪ Buys Metallica CD
▪ Buys Megadeth CD
 Customer Y
▪ Clicks on Metallica album
▪ Recommender system
suggests Megadeth from
data collected about
customerX

Items
Retrieval Recommendations
Products, web sites,
blogs, news items, …
1/25/22 4
Jure Leskovec, Stanford CS246:MiningMassive Datasets
Examples:

 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
▪ Association rules: How Into Thin Air made Touching
the Void a bestseller:
http://www.wired.com/wired/archive/12.10/tail.html

Source: Chris Anderson (2004)
1/25/22 6

 Non-personalized recommendations:
▪ Editorial and hand curated
▪ List of favorites
▪ List of “essential” items
▪ Simple aggregates
▪ Top 10, Most Popular, Recent Uploads
 Personalized recommendations:
▪ Tailored to individual users
▪ Examples: Amazon, Netflix, Youtube,…
1/25/22 7
Today’s class

 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., 1-5 stars, real number in [0,1]
1/25/22 8

0.4
1
0.2
0.3
0.5
0.2
1
Avatar LOTR Matrix Pirates
Alice
Bob
Carol
David
1/25/22 9

 (1) Gathering “known” ratings for matrix
▪ How to collect the data in the utility matrix
 (2) Extrapolatingunknown 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
1/25/22 10

 Explicit
▪ Ask people to rate items
▪ Doesn’t work well in practice – people
don’t like being bothered
▪ Crowdsourcing: Pay people to label items
 Implicit
▪ Learn ratings from user actions
▪ E.g., purchase implies high rating
▪ What about low ratings?
1/25/22 11

 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 filtering
▪ 3) Latent factor based
1/25/22 12
Today!

Recommender Systems Content and Collaborative Filtering

 Main idea:
▪ Items have profiles:
▪ Video -> [genre, director, actors, plot, release year]
▪ News -> [set of keywords]
▪ 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

likes
Item profiles
Red
Circles
Triangles
User profile
match
recommend
build
1/25/22 15

 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
1/25/22 16

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
1/25/22 17
Note: we normalize TF
to discount for “longer”
documents

 User profile possibilities:
▪ Weighted average of rated item profiles
▪ Variation: weight by difference from average
rating for item
 Prediction heuristic: Cosine similarity of user
and item profiles
▪ Given user profile x and item profile i, estimate
𝑢 𝒙, 𝒊 = cos 𝒙, 𝒊 =
𝒙·𝒊
𝒙 ⋅ 𝒊
 How do you quickly find items closest to 𝒙?
▪ Job for LSH!

 +: No need for data on other users
▪ No item cold-start problem, no sparsity problem
 +: 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

 –: Finding the appropriate features is hard
▪ E.g., images, movies, music
 –: Recommendationsfor 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

Harnessing quality judgments of other users

 Does not build item profile or user profile
 In place of item-profile (user-profile) we use
its row (column) in the utility matrix.
 Comes in two flavors:
▪ User-user collaborative filtering
▪ Item-Item 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
1/25/22 23
x
N

 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) =
𝑟𝑥⋅𝑟𝑦
||𝑟𝑥||⋅||𝑟𝑦||
▪ Problem: Treats some missing ratings as “negative”
 Pearson correlation coefficient
▪ Sxy = items rated by both users x and y
rx = [1, _, _, 1, 3]
ry = [1, _, 2, 2, _]
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}
rx, ry … avg.
rating of x, y
𝒔𝒊𝒎 𝒙, 𝒚 =
σ𝒔∈𝑺𝒙𝒚
𝒓𝒙𝒔 − 𝒓𝒙 𝒓𝒚𝒔 − 𝒓𝒚
σ𝒔∈𝑺𝒙𝒚
𝒓𝒙𝒔 − 𝒓𝒙
𝟐 σ𝒔∈𝑺𝒙𝒚
𝒓𝒚𝒔 − 𝒓𝒚
𝟐

 Intuitively we want: sim(A, B) > sim(A, C)
 Jaccard similarity: 1/5 < 2/4
 Cosine similarity: 0.380 > 0.322
▪ Considers missing ratings as “negative”
▪ Solution: subtract the (row) mean
sim A,B vs. A,C:
0.092 > -0.559
Notice cosine sim. is
correlation when
data is centered at 0
𝒔𝒊𝒎(𝒙, 𝒚) =
σ𝒊 𝒓𝒙𝒊 ⋅ 𝒓𝒚𝒊
σ𝒊 𝒓𝒙𝒊
𝟐
⋅ σ𝒊 𝒓𝒚𝒊
𝟐
Cosine sim:

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 i of user x:
▪ 𝑟𝑥𝑖 =
1
𝑘
σ𝑦∈𝑁 𝑟𝑦𝑖
▪ Or even better: 𝑟𝑥𝑖 =
σ𝑦∈𝑁 𝑠𝑥𝑦⋅𝑟𝑦𝑖
σ𝑦∈𝑁 𝑠𝑥𝑦
 Many other tricks possible…
1/25/22 26
Shorthand:
𝒔𝒙𝒚 = 𝒔𝒊𝒎 𝒙, 𝒚

 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

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ij
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s
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s
r sij… similarity of items i and j
rxj…rating of user x on item j
N(i;x)… set of items which were rated by x
and similar to i

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users
movies
- unknown rating - rating between 1 to 5
1/25/22 28

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- estimate rating of movie 1 by user 5
1/25/22 29
movies

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users
Neighbor selection:
Identify movies similar to
movie 1, rated by user 5
1/25/22 30
movies
1.00
-0.18
0.41
-0.10
-0.31
0.59
Here we use Pearson correlation as similarity:
1) Subtract mean rating mi from each movie i
m1 = (1+3+5+5+4)/5 = 3.6
row 1: [-2.6, 0, -0.6, 0, 0, 1.4, 0, 0, 1.4, 0, 0.4, 0]
2) Compute dot products between rows
s1,m

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users
Compute similarity weights:
s1,3=0.41, s1,6=0.59
1/25/22 31
movies
1.00
-0.18
0.41
-0.10
-0.31
0.59
s1,m

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users
Predict by taking weighted average:
r1.5 = (0.41*2 + 0.59*3) / (0.41+0.59) = 2.6
1/25/22 32
movies
𝒓𝒊𝒙 =
σ𝒋∈𝑵(𝒊;𝒙) 𝒔𝒊𝒋 ⋅ 𝒓𝒋𝒙
σ𝒔𝒊𝒋

 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

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Before:
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𝒃𝒙𝒊 = 𝝁 + 𝒃𝒙 + 𝒃𝒊

0.4
1
8
.
0
1
0.9
0.3
0.5
0.8
1
Avatar LOTR Matrix Pirates
Alice
Bob
Carol
David
1/25/22 34
 In practice, it has been observed that item-item
often works better than user-user
 Why? Items are “simpler”, users have multiple
tastes

 + 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

 Implement two or more different
recommenders and combine predictions
▪ Perhaps using a linear model
 Add content-based methods to
collaborative filtering
▪ Item profiles for new item problem
▪ Demographics to deal with new user problem
1/25/22 36

- Evaluation
- Error metrics
- Complexity / Speed

1 3 4
3 5 5
4 5 5
3
3
2 2 2
5
2 1 1
3 3
1
movies
users

1 3 4
3 5 5
4 5 5
3
3
2 ? ?
?
2 1 ?
3 ?
1
Test Data Set
users
movies

 Compare predictions with known ratings
▪ Root-mean-square error (RMSE)
▪
1
𝑁
σ𝑥𝑖 𝑟𝑥𝑖 − 𝑟𝑥𝑖
∗ 2
where 𝒓𝒙𝒊 is predicted, 𝒓𝒙𝒊
∗
is the true rating of x on i
▪ N is the number of points we are making comparisons on
▪ Precision at top 10:
▪ % of relevant items in top 10
 Another approach: 0/1 model
▪ Coverage:
▪ Number of items/users for which the system can make predictions
▪ Precision:
▪ Accuracy of predictions
▪ Receiver operating characteristic (ROC)
▪ Tradeoff curve between false positives and false negatives

 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
1/25/22 41

 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
1/25/22 42

 Leverage all the 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
http://anand.typepad.com/datawocky/2008/03/more-data-usual.html

 Training data
▪ 100 million ratings, 480,000 users, 17,770 movies
▪ 6 years of data: 2000-2005
 Test data
▪ Last few ratings of each user (2.8 million)
▪ Evaluation criterion: root mean squared error
(RMSE)
▪ Netflix Cinematch RMSE: 0.9514
 Competition
▪ 2,700+ teams
▪ $1 million prize for 10% improvement on Cinematch

 Next topic: Recommendations via
Latent Factor models
Overview of Coffee Varieties
FR
TE
S6
S5
L5
S3
S2
S1
R8
R6
R5
R4
R3
R2
L4
C7
S7
F9 F8 F6
F5
F4
F3 F2F1
F0
I2
C6
I1
C4
C3
C2
C1
B2
B1
S4
Complexity of Flavor
Exoticness
/
Price
Flavored
Exotic
Popular Roasts
and Blends
a1
The bubbles above represent products sized by sales volume.
Products close to each other are recommended to each other.

Geared
towards
females
Geared
towards
males
serious
escapist
The Princess
Diaries
The Lion
King
Braveheart
Independence
Day
Amadeus
The Color
Purple
Ocean’s 11
Sense and
Sensibility
Gus
Dave
[BellkorTeam]
1/25/22 47
Lethal
Weapon
Dumb and
Dumber

Koren, Bell, Volinksy, IEEE Computer, 2009
1/25/22 48

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