Recommender Systems

Based Rajaraman and Ullman: Mining Massive Data Sets &

Francesco Ricci et al. Recommender Systems Handbook.

Recommender System

All of th

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User Generat

ed Content (UGC)!

Recommender System

Central Theme :o Predict ratings for unrated itemso Recommend top-k items

RS – Major Approaches

• Basic question: Given (highly incomplete/sparse), given predict

1 3 5

1 4 4

4 2 3

3 5 4

4 4 3

RS – Approaches

• Content-based: how similar is to items has rated/liked in the past?– Use metadata for measuring similarity. + works even when no ratings available on affected items. - Requires metadata!

• Collaborative Filtering: Identify items (users) with their rating vector; no need for metadata; but cold-start is a problem.

RS – Approaches • CF can be memory-based (as sketched on p5): item ’s

“characteristics captured by the ratings it has received (rating vector).

• Or it can be model-based: model user/item’s behavior via latent factors (to be learned from data). – Dimensionality reduction – Original ratings matrix is usually (very) low rank. Matrix completion:

• using Singular value decomposition (SVD). • Using matrix factorization (MF) [and variants].

• MovieLens – example of RS using CF.

Collaborative Filtering

Key concepts/questions

• How is user f/b expressed: ratings or implicit? • How to measure similarity? • How many nearest neighbors to pick (if

memory- or neighborhood-based). • How to predict unknown ratings? • Distinguished (also called active) user and

(target) item.

A Naïve Algorithm (memory-based)

• Find top- most similar neighbors to distinguished user (using chosen similarity or proximity measure).

• item rated by sufficiently many of these, compute by aggregating by chosen neighbors above.

• Sort items with predicted ratings and recommend top- items to

An Example 4 5 1 5 5 4 2 4 5 3 3

• Jaccard(A,B) = 1/5 <2/4 = Jaccard(A,C)! • – OK, but ignores internal “rating scales” easy/hard

graders. • See the Rajaraman et al. book for “rounded” Jaccard/Cosine. • A more principled approach: subtract from each rating the

corresponding user’s mean rating, then apply Jaccard/cosine.

An Example

2/3 5/3 -7/3 1/3 1/3 -2/3

-5/3 1/3 4/3 0 0

• See what just happened to the ratings! • Behavior and items more well-separated. • Cosine can now be + or -: check (A,B) and

(A,C).

Prediction using Memory/Neighborhood-based approaches

• A popular approach – using Pearson correlation coefficient.

• where• i.e., cosine of the “vectors of deviations from

the mean”. • – normalization factor = • See the RecSys handbook and [Adomavicius

and Tuzhilin TKDE 2005 for alternatives.

User-User vs Item-Item.

• User-User CF: what we just discussed! • Item-Item – dual in principle: find items most

similar to distinguished item ; for every user who did not rate the distinguished item but rated sufficiently many from the similarity group, compute

• In practice, item-item has been found to be better than user-user.

Simpler Alternatives for Rating Estimation • Simple average of ratings by most similar neighbors. • Weighted average. • User’s mean plus offset corresponding to weighted

average of offsets by most similar neighbors (Pearson!).

• Or you can see the popular vote by most similar neighbors: e.g., has 5 most similar neighbors who have rated . – rated 1; rated 3; rated 4; rated 5. – Simple majority: – Suppose 1.0. Then ie-breaking arbitrary.

Item-based CF • Dual to user-based CF, in principle. • “People who bought also bought ”. • Natural connection to association rules (each user = a

transaction). • Predict unknown rating of user on item as the aggregate of

ratings by on items similar to • E.g., using mean-centering and Pearson correlation for

item-item similarity,

where mean rating of by various users and similarity b/w and and – the usual normalization factor.

Item-based CF Computation Illustrated • Similarities: computing sim. b/w all pairs of items is prohibitive! • But do we need to? • How efficiently can we compute the sim. of all pairs of items for which

the sim. Is positive?

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Item-based CF – Recommendation Generation

X

X

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𝑢 X X X X X similar items?similar items?

How efficiently can we generate recommendations for a given user?

Some empirical facts re. user-based vs. item-based CF

• User profiles are typically thinner than item profiles; depends on application domain. – Certainly holds for movies (Netflix).

• as users provide more ratings, user-user sim. can chage more dyamically than item-item sim.

• Can we precompute item-item sim. and speed up prediction computation?

• What about refreshing sim. against updates? Can we do it incrementally? How often should we do this?

• Why not do this for user-user?

User & Item-based CF are both personalized

• Non-personalized would estimate an unknown rating as a global average.

• Every user gets the same recommendation list, modulo items s/he may have already rated.

• Personalized clearly leads to better predictions.