1. CS728 The Collaboration Graph
Lecture 10

2. Review and Plan Today’s Plan Web Graph Ranking measure algorithms
PageRank
HITS
Personalization
Via teleporting bias in PageRank
How about In HITS?
Today’s Plan
Collaboration Graph
Using explicit and implicit connectivity links
Voting Algorithm, Correlation factors
Applications
Recommendation Systems (RS)
Collaborative Filtering (CF)

3. Collaborative Framework
Given a set of users and items
Items could be documents, products, other users …
Goal: Recommend items to a user based on
Past behavior of this and other users
Who has viewed/bought/liked what?
Additional information on users and items
Both users and items can have known attributes [age, genre, price, …]
Our Framework: generate links based on past behavior and attributes

4. Example-behavior Users Docs viewed ? U1 viewed d1, d2, d3.
U2 views d1, d2.
Recommend d3 to U2 ?

5. Linking Users
Link U2 to U1 as someone of interest (to talk to, to recommend)? U1 d1 d2 U2 d3

6. NNN-Naïve Nearest Neighborsd1 U d2
U viewed d1, d2, d5.
Look at who else viewed similar sets of docs V d5 W
Compute set distance between pairs
Recommend to U the doc(s) most “popular” among nearest users.

7. Typical Collaboration Issues
Large item space
Usually with item attributes
Large user base
Usually with user attributes (age, gender, city, …)
Some evidence of customer preferences
Explicit ratings (powerful, but harder to elicit)
Observations of user activity (purchases, page views, s, what was printed, …)
Typically extremely sparse, even when user has an opinion

8. The Collaboration Graph
Users
Items
Links derived from similar attributes, explicit and implicit connections
User-User
Links
Item-Item Links
Links derived from similar attributes, similar content, explicit cross references, implicit correlations
You have users, items, and then links between those items.
Ex: item links: two movies in the same genre or with the same director.
Ex: user links: two users have the same demographics (age, gender, etc)
Goal: Predict user i’s utility for item k
Observed preferences
(Ratings, purchases, page views, laundry lists, play lists)

9. Link types bias outcomes
Explicit attributes-based
Male, 18-35: Recommend The Matrix
Item content similarity-based
You liked The Matrix: recommend The Matrix Reloaded
Collaborative Filtering
Use implicit similarity links
People with interests like yours also liked the adventure-comedy Pirates

10. Matrix view of Collaboration Graph
Docs
A =
Users
Aij = 1 if user i viewed doc j,
= 0 otherwise.
AAt : Entries give # of docs commonly viewed by pairs of users.

11. Voting Algorithm
Row i of AAt : Vector whose jth entry is the # of docs viewed by both i and j.
Call this row ri’ e.g., (0, 7, 1, 13, 0, 2, ….)
Measures the similarity of user i with all other users.
Question: what values are on the diagonal?

12. How does this differ from
Voting Algorithm
Compute the utility of each doc
ri ° A is a vector whose kth entry gives a weighted vote count to doc k
emphasizes users who have high weights in ri .
Recommend doc(s) with highest vote counts. ri A
How does this differ from
the NNN algorithm?

13. Voting Algorithm - implementation issues
Wouldn’t implement using matrix operations
use weight-propagation on compressed adjacency lists
Need to log and maintain “user views doc” relationship.
typically, log into database
update vote-propagating structures periodically.
For efficiency, discard all but the heaviest weights in each ri
only in fast structures, not in back-end database.
Exercise:
Write
pseudo
code

14. Link Analysis Revisited
There are many connections between collaboration graph analysis and web link analysis:
The voting algorithm may be viewed as one iteration of the Hubs/Authorities algorithm

15. User Links via Correlation
Correlations measure similarity between vectors
E.g., dot-product, cosine measure, Pearson measure
Each user i rates some docs (products, … )
say a real-valued rating vik for doc k
in practice, one of several ratings on a form
Thus we have a ratings vector vi for each user
(with lots of zeros)
Compute a correlation coefficient between every pair of users i,j
normalized dot product of their ratings vectors
(symmetric, scalar) measure of how much user pair i,j agrees: corrij

16. Application: Predict user i’s utility for doc k
Sum (over users j such that vjk is non-zero)
corrij vjk
Output this as the predicted utility for user i on doc k.
So how does this differ
from the voting algorithm?

17. Math of Correlation
In statistics correlation, indicates the strength and direction of a linear relationship between two random variables. Refers to the departure of two variables from independence.
The best known example is the Pearson product-moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations.

18. Geometric Interpretation
Correlation can be viewed as the cosine of the angle between the two vectors
Caution: This method only works with centered data, i.e., data which have been shifted by the sample mean so as to have an average of zero. Some practitioners prefer an uncentered coefficient.
E.g., five countries are found to have gross national products of 1, 2, 3, 5, and 8 billion dollars and have 11%, 12%, 13%, 15%, and 18% poverty.
data: x = (1, 2, 3, 5, 8) and y = (0.11, 0.12, 0.13, 0.15, 0.18).
By the usual procedure for finding the angle between two vectors the uncentered correlation coefficient is:
Centering the data, that is shifting x by E(x) = 3.8 and y by E(y) = 0.138) yields
x = (-2.8, -1.8, -0.8, 1.2, 4.2) and
y = (-0.028, , , 0.012, 0.042)

19. Varieties of Meanings in Correlations
Implicit (user views doc) vs. Explicit (user assigns rating to doc)
Boolean vs. real-valued utility
In practice, must convert user ratings on a form (say on a scale of 1-5) to real-valued utilities
Can be fairly complicated mapping
E.g., Likeminds function (Greening white paper)
Requires understanding user’s interpretation of form

20. Sample Applications Ecommerce
Product recommendations – amazon, netflix
Corporate Intranets
Recommendation, finding domain experts, …
Digital Libraries
Finding pages/books people will like
Medical Applications
Matching patients to doctors, clinical trials, …
Customer Relationship Management
Matching customer problems to internal experts

21. Well-known recommender systems: Amazon and Netflix

22. Corporate intranets - document recommendation

23. Corporate intranets - “expert” finding

24. Rating interface

25. Resources GroupLens http://citeseer.nj.nec.com/resnick94grouplens.html
Has available data sets, including MovieLens
Greening, Dan R. Building Consumer Trust with Accurate Product Recommendations: A White Paper on LikeMinds WebSell 2.1
Shardanand/Maes
Sarwar et al.

26. Resources McLaughlin and Herlocker, SIGIR 2004
CoFE CoFE “Collaborative Filtering Engine”
Open source Java
Reference implementations of many popular CF algorithms