- 1 -

Collaborative Filtering

Zeinab Noorian, PhD

- 2 -

AgendaCollaborative Filtering (CF)

– Pure CF approaches– User-based nearest-neighbor

The Pearson Correlation similarity measure– Memory-based and model-based approaches– Item-based nearest-neighbor

The cosine similarity measure– Data sparsity problems– Recent methods (Association Rule Mining, probabilistic

methods, Slope One, …)– The Google News personalization engine– Literature

- 3 -

Collaborative Filtering (CF)

The most prominent approach to generate recommendations– used by large, commercial e-commerce sites– various algorithms and variations exist– applicable in many domains (book, movies, DVDs, ..)

Approach– use the "wisdom of the crowd" to recommend items

Basic assumption and idea– Users give ratings to catalog items (implicitly or explicitly)– Customers who had similar tastes in the past, will have similar tastes in

the future

- 4 -

Pure CF Approaches

Input– Only a matrix of given user–item ratings

Output types– A (numerical) prediction indicating to what degree the current user

will like or dislike a certain item– A top-N list of recommended items

- 5 -

User-based nearest-neighbor collaborative filtering (1)

The basic technique– Given an "active user" (Alice) and an item not yet seen by Alice

find a set of users (peers/nearest neighbors) who liked the same items as Alice in the past and who have rated item

use, e.g. the average of their ratings to predict, if Alice will like item do this for all items Alice has not seen and recommend the best-rated

Basic assumption and idea– If users had similar tastes in the past they will have similar tastes in the future– User preferences remain stable and consistent over time

- 6 -

User-based nearest-neighbor collaborative filtering (2)

Example– A database of ratings of the current user, Alice, and some other users is given:

– The task of the Recommender system is to determine whether Alice will like or dislike Item5, which Alice has not yet rated or seen

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 3

User2 4 3 4 3 5

User3 3 3 1 5 4

User4 1 5 5 2 1

- 7 -

User-based nearest-neighbor collaborative filtering (3)

Some first questions– How do we measure similarity between other users and Alice?– How many neighbors should we consider?– How do we generate a prediction from the neighbors' ratings?

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 3

User2 4 3 4 3 5

User3 3 3 1 5 4

User4 1 5 5 2 1

- 8 -

Measuring user similarity (1)

A popular similarity measure in user-based CF: Pearson’s correlation coefficient.

o a, b : users

o P={p1,…,pm}: sets of products/items

o ra,p : the rating of user a for product p

o ŕa : the average rating of user a

Pearson Correlation takes a value between [-1, +1].

- 9 -

Measuring user similarity (2)

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 3

User2 4 3 4 3 5

User3 3 3 1 5 4

User4 1 5 5 2 1

sim = 0,85

sim = 0,70

sim = 0,00

sim = -0,79

If (r’Alice = r’a = 4 ) and (r’user1 = r’b = 2.4 ) the similarity of Alice with User1 is calculated as:

- 10 -

Pearson Correlation Highlights

Takes differences in rating behavior into account

Item1 Item2 Item3 Item4

0

1

2

3

4

5

6 Alice

User1

User4

Ratings

- 11 -

A common prediction function:

Calculate, whether the neighbors' ratings for the unseen item are higher or lower than their average

Combine the rating differences – use the similarity metric as a weight

Add/subtract the neighbors' bias from the active user's average and use this as a prediction

Making predictions

- 12 -

Improving the metrics / prediction function

Not all ratings of items should be equally ”important"– Agreement of two users on commonly liked items is not as

informative/valuable as the agreement of two users on the controversial items.

– Possible solution: Give more weight to items that have a higher variance in ratings

Value of number of co-rated items—the case where two users have only few co-rated items in common.– Use "significance weighting", by e.g., linearly reducing the similarity weight of

users when the number of co-rated items is low–(Herlook et. Al (1999)).

Case amplification– Intuition: Give more weight to "very similar" neighbors (amplifies their

similarity by the constant p =2.5, used in Breese et. Al, 1998), i.e., where the similarity value is close to 1.

Neighborhood selection– Use similarity threshold or fixed number of neighbors/ top-N neighbors.

- 13 -

Limitations of User-based Collaborative Filtering

In case of dealing with large rating database, the computational complexity will be high.

The rating matrix is typically very sparse such that users only rated a few subsets of available items.

How to deal with new users WITHOUT any previous ratings OR how to deal with new items with NO ratings have not been addressed in User-based CF.

- 14 -

Memory-based and model-based approaches

User-based CF is said to be "memory-based"– the rating matrix is kept in memory is directly used to find neighbors / make

predictions– does not scale for most real-world scenarios– large e-commerce sites have tens of millions of customers and millions of

items

Model-based approaches– based on an offline pre-processing or "model-learning" phase– at run-time, only the learned model is used to make predictions– models are updated / re-trained periodically– large variety of techniques used – model-building and updating can be computationally expensive– item-based CF is an example for model-based approaches

- 15 -

Item-based collaborative filtering

Basic idea: – Use the similarity between items (and not users) to make predictions

Example: – Look for items that are similar to Item5– Take Alice's ratings for these items to predict the rating for Item5

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 3

User2 4 3 4 3 5

User3 3 3 1 5 4

User4 1 5 5 2 1

- 16 -

The cosine similarity measure (1)

Items ratings are represented as a u-dimensional vectors over user space

Similarity is calculated based on the angle between two vectors

– a,b: the items’ rating vector– . Is a dot product of ratings vector.– |ā| is a Euclidian length of the vector, which is defined as the square root of

the dot product of the vector with itself. – Produce a value between [0,1].

Cosine similarity measure produces better results in item-to-item filtering

- 17 -

The cosine similarity measure (2) – Example 1

The cosine similarity of item5 and item1 is therefore calculated as:

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 3

User2 4 3 4 3 5

User3 3 3 1 5 4

User4 1 5 5 2 1

- 18 -

Cosine similarity measures—Example 2.

User 1 User2

Item1 2 5

Item2 4 5

Item 3 3 2

1.5 2 2.5 3 3.5 4 4.50

1

2

3

4

5

6Item 1

Item 2

Item 3

User 1

User

2

- 19 -

Adjusted cosine similarity (1)

First: We transform the original rating database and replace the original rating values with their deviation from the average ratings.

Second: we apply the original Cosine similarity measure to compute the similarity between items (i.e. item1 and item5).

- 20 -

Adjusted cosine similarity (2)– The formalization

– U : set of users who have rated both items a and b. – ŕu : the average rating of user u – ŕu,b : the average rating of user u for item b

- 21 -

Making predictions in item-based CF

A common prediction function:

– ratedItems(u): rated items similar to the target item p rated by user u.

Homework: Predict a rating of Alice for Item5 yourself!

- 22 -

Selecting Neighbors in Collaborative Filtering Algorithms

In theory, the more the better If you have a good similarity metric

In practice, noise from dissimilar neighbors decreases usefulness

Not all neighbors are taken into account for the prediction– Should filter out neighbors with low similarity/ low credibility– Should come up with adaptive credibility/similarity threshold

An analysis of the MovieLens dataset indicates that "in most real-world situations, a neighborhood of 20 to 50 neighbors seems reasonable" (Herlocker et al. 2002)

Fewer neighbors different opinions of newly-added neighbors considerably change the similarity degree, (low coverage).

Still remained as open problem!

- 23 -

Pre-processing for item-based filtering

Item-based filtering does scale better than User-based filtering!

Pre-processing approach by Amazon.com (in 2003)– Construct an item similarity matrix

Calculate all pair-wise item similarities offline– In the runtime, to make a prediction of Item p for user u, AMAZON

retrieve items similar to p, which have been rated by u. The number of items to be used at runtime is typically rather small,

because only items are taken into account which the active user has rated.

Pre-processing for user-based CF is also possible, however:– The number of overlapping ratings for two users are small.

Item similarities are more stable than user similarities.

User profiles/preferences change more frequently than item profiles/features

- 24 -

Pre-processing for item-based filtering

WRT memory requirements for item similarity matrix: – Item similarity matrix for N items can be up to N2 entries.

In real world, it is actually much smaller!– Techniques to reduce complexity

Consider items that have minimum number of co-ratings Memorize only a limited neighborhood for each item.

- 25 -

Question???

Think about a better approach to improve collaborative filtering!

How about changing the similarity measure in item-item CF?

But How we can do that??? Discuss it!

- 26 -

Data sparsity problems

Cold start problem– How to recommend new items? What to recommend to new users?

Straightforward approaches – Use another method (e.g., content-based, demographic or simply non-

personalized) in the initial phase– Ask/force users to rate a set of (controversial NOT popular) items– Default voting: assign default values to items that only one of the two users to

be compared has rated (Breese et al. 1998)

Alternatives– Use better algorithms (beyond nearest-neighbor approaches)– Example:

In nearest-neighbor approaches, the set of sufficiently similar neighbors might be too small to make good predictions

Assume "transitivity" of neighborhoods

- 27 -

Example algorithms for sparse datasets

Item1 Item2 Item3 Item4 Item5

Alice 5 3 4 4 ?

User1 3 1 2 3 ?

User2 4 3 4 3 5

User3 3 2 1 4 4

User4 1 5 5 2 1

sim = 0.85

Predict rating forUser1

Recursive Collaborative Filtering:– Assume that, Alice has a very close neighbor, User1, with similarity degree of 0.85

who however has not rated the target item, item5.– Idea

Use CF (recursively) to find a close neighbor for User1 (e.g. User3) who has rated a target item (i.e. item5), and predict the rating for User1.

Use the predicted rating to recommend item to Alice instead of personal rating from more distance neighbor.

sim = 0.9

- 28 -

Graph-based methods (1)

"Spreading activation" (Huang et al. 2004)– Exploit the supposed "transitivity" of customer tastes and thereby augment the matrix

with additional information– Assume that we are looking for a recommendation for User1– When using a standard CF approach, User2 will be considered a peer for User1 because

they both bought Item2 and Item4– Thus Item3 will be recommended to User1 because the nearest neighbor, User2, also

bought or liked it

- 29 -

Graph-based methods (2)

"Spreading activation" (Huang et al. 2004)– In a standard user-based or item-based CF approach, paths of length 3 will be

considered – that is, Item3 is relevant for User1 because there exists a three-step path (User1–Item2–User2–Item3) between them

– Because the number of such paths of length 3 is small in sparse rating databases, the idea is to also consider longer paths (indirect associations) to compute recommendations

– Using path length 5, for instance

- 30 -

Graph-based methods (3)

"Spreading activation" (Huang et al. 2004)– Idea: Recommend items with the longer path to fill the missing value.

Use paths of lengths > 3 to recommend items– Length 3: Recommend Item3 to User1 (Standard-CF method)– Length 5: Item1 also recommendable (Spreading Activation method)

- 31 -

More model-based approaches

Plethora of different recommendation techniques proposed in the last years, e.g.,– Association rule mining

compare: shopping basket analysis– Probabilistic models

clustering models, Bayesian networks,…– Matrix factorization techniques, statistics

singular value decomposition, principal component analysis– Various other machine learning approaches

- 32 -

Product Association Recommender

One interesting approach to recommend items is through product association recommender. – Observe which items are usually bought together, them recommend the item

to users, based on their shopping baskets– RS would not necessarily have information about products/users

Can work well for non-personalized recommender systems

Example: You are at a restaurant, order ice cream; you want a recommendation for a sauce:– Do you want to hear that Ketchup is the most popular sauce?– Or: do you want to hear which sauce is popular and associated with the ice

cream?

- 33 -

Product Association: People Who liked X also Liked Y

Commonly used for shopping behavior analysis– aims at detection of rules such as

"If a customer purchases baby food then he also buys diapers in 70% of the cases"

- 34 -

Association rule mining

Association rule mining algorithms– can detect rules of the form X → Y (e.g., baby food→ diapers) from a set of sales

transactions D = {t1, t2, … tn}– measure of quality: support, confidence

used e.g. as a threshold to cut off unimportant rules

Wont work well for one high favorable product popular and one less popular product! (Example?)– Works well for two less popular products.

- 35 -

Improve the product association algorithm...

Lets’ adjust by calculating whether buying X increase the chance of buying Y, than NOT buying X.

The formula focus on increase in Y associated with X.

Works well for different combinations of products:– Less popular with high popular (Vinegar and Banana)– Two less popular products (Vinegar and garlic)

- 36 -

Probabilistic methods

Basic idea (simplistic version for illustration):– given the user/item rating matrix– determine the probability that user Alice will like an item – base the recommendation on such these probabilities

Calculation of rating probabilities based on Bayes Theorem– How probable is rating value "1" for Item5 given Alice's previous ratings?– Corresponds to conditional probability P(Item5=1 | X), where

X = Alice's previous ratings = (Item1 =1, Item2=3, Item3= … )– Can be estimated based on Bayes' Theorem

– Assumption: Ratings are independent (?)

- 37 -

Calculation of probabilities in simplistic approach

Item1 Item2 Item3 Item4 Item5

Alice 1 3 3 2 ?

User1 2 4 2 2 4

User2 1 3 3 5 1

User3 4 5 2 3 3

User4 1 1 5 2 1

Xi = (Item1 =1, Item2=3, Item3= … )• P(X) = constant factor we omit it in

calculation• P(Y) i.e., (Y = item5)e.g. P(item5 =1) =2/4,

P(item5=2) =0, so forth; calculated from the rating matrix

• We only need to calculate the class conditional probability: P(Xi|Y)

- 38 -

Item1 Item5

Alice 2 ?

User1 1 2

Idea of Slope One predictors is simple and is based on a popularity differential between items for users

Example:

p(Alice, Item5) =

Basic scheme: Take the average of these differences of the co-ratings to make the prediction

In general: Find a function of the form f(x) = x + b– That is why the name is "Slope One"

Slope One predictors (Lemire and Maclachlan 2005)

-

2 + ( 2 - 1 ) = 3

- 39 -

Slope One Predictor (Example)

P(Alice, Item3)=?– Two co-ratings for Item1 and Item3: User1(Item1, item3), User2(item1, Item3)– One co-rating for Item2 and Item3 User1(Item2, Item3)– Take an average from the differences of either of these co-ratings – Prediction of item3’s rating for Alice based on item1: (2 + 0.5) = 2.5– Prediction of item3’s rating for Alice based on item2: (5+3 ) =8– Overall Prediction takes a number of co-ratings in to account to give more

weight to deviation that has more data.

- 40 -

Collaborative Filtering Issues

Pros: – well-understood, works well in some domains, no knowledge engineering required

Cons:– requires user community, sparsity problems, no integration of other knowledge sources,

no explanation of results

What is the best CF method?– In which situation and which domain? Inconsistent findings; always the same domains

and data sets; differences between methods are often very small (1/100)

How to evaluate the prediction quality?– MAE / RMSE: What does an MAE of 0.7 actually mean?– Serendipity (novelty and surprising effect of recommendations)

Not yet fully understood

What about multi-dimensional ratings?

- 41 -

The Google News personalization engine

- 42 -

Google News portal (1)

Aggregates news articles from several thousand sources

Displays them to signed-in users in a personalized way

Collaborative recommendation approach based on– the click history of the active user and– the history of the larger community

Main challenges– Vast number of articles and users– Generate recommendation list in real time (at most one second)– Constant stream of new items, other articles become out of date– Immediately react to user interaction

Significant efforts with respect to algorithms, engineering, and parallelization are required

- 43 -

Google News portal (2)

Pure memory-based approaches are not directly applicable and for model-based approaches, the problem of continuous model updates must be solved

A combination of model- and memory-based techniques is used

Model-based part: Two clustering techniques are used– Probabilistic Latent Semantic Indexing (PLSI) as proposed by (Hofmann 2004)– MinHash as a hashing method

Memory-based part: Analyze story co-visits for dealing with new users

The overall recommendation score for each item is computed as a linear combination of all the scores obtained by three methods – MinHash, PLSI and co-visits

Google's MapReduce technique is used for parallelization in order to make computation scalable

- 44 -

Assignment

Assignment 3 from the “Introduction to Recommendation Systems” course offered in Coursera. This website is available free!

Answer Part1 of the assignment3 https://www.coursera.org/learn/recommender-systems/supplement/pBm3G/assignment-3-instructions

Submit to <https://www.coursera.org/learn/recommender-systems/exam/cYxFI/assignment-3-user-user-collaborative-filtering-quiz>

Deadline Next Week (15.12.1393)

- 45 -

Literature (1)

[Adomavicius and Tuzhilin 2005] Toward the next generation of recommender systems: A survey of the state-of-the-art and possible extensions, IEEE Transactions on Knowledge and Data Engineering 17 (2005), no. 6, 734–749

[Breese et al. 1998] Empirical analysis of predictive algorithms for collaborative filtering, Proceedings of the 14th Conference on Uncertainty in Artificial Intelligence (Madison, WI) (Gregory F. Cooper and Seraf´in Moral, eds.), Morgan Kaufmann, 1998, pp. 43–52

[Gedikli et al. 2011] RF-Rec: Fast and accurate computation of recommendations based on rating frequencies, Proceedings of the 13th IEEE Conference on Commerce and Enterprise Computing - CEC 2011, Luxembourg, 2011, forthcoming

[Goldberg et al. 2001] Eigentaste: A constant time collaborative filtering algorithm, Information Retrieval 4 (2001), no. 2, 133–151

[Golub and Kahan 1965] Calculating the singular values and pseudo-inverse of a matrix, Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis 2 (1965), no. 2, 205–224

[Herlocker et al. 2002] An empirical analysis of design choices in neighborhood-based collaborative filtering algorithms, Information Retrieval 5 (2002), no. 4, 287–310

[Herlocker et al. 2004] Evaluating collaborative filtering recommender systems, ACM Transactions on Information Systems (TOIS) 22 (2004), no. 1, 5–53

- 46 -

Literature (2)

[Hofmann 2004] Latent semantic models for collaborative filtering, ACM Transactions on Information Systems 22 (2004), no. 1, 89–115

[Huang et al. 2004] Applying associative retrieval techniques to alleviate the sparsity problem in collaborative filtering, ACM Transactions on Information Systems 22 (2004), no. 1, 116–142

[Koren et al. 2009] Matrix factorization techniques for recommender systems, Computer 42 (2009), no. 8, 30–37

[Lemire and Maclachlan 2005] Slope one predictors for online rating-based collaborative filtering, Proceedings of the 5th SIAM International Conference on Data Mining (SDM ’05) (Newport Beach, CA), 2005, pp. 471–480

[Sarwar et al. 2000a] Application of dimensionality reduction in recommender systems – a case study, Proceedings of the ACM WebKDD Workshop (Boston), 2000

[Zhang and Pu 2007] A recursive prediction algorithm for collaborative filtering recommender systems, Proceedings of the 2007 ACM Conference on Recommender Systems (RecSys ’07) (Minneapolis, MN), ACM, 2007, pp. 57–64