Collaborative Filtering in Recommender Systems: A Deep Dive, Study notes of Computer Science

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CS 5350

Collaborative Filtering

Hal Daumé III

School of Computing

University of Utah

[email protected]

CS 5350

What do these have in common?

CS 5350

NetFlix Challenge

Beat the current NetFlix system by 10%

Reward: $1m

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Recommendations via Regression

1 5 3 4 2 1

2 2 2 5 1 1

5 5 1 2 4 2

2 3 2 1 3 1

5 4 3 3 3 1

2 1 5 2 2 5

3 3 3 4 1 1

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An Initial Attempt

ActionAction

Comedy

Drama

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An Initial Attempt

ActionAction

Comedy

Drama

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Initial Predictions

ActionAction

Comedy

Drama

U

n,k

V

k,d

Score  n , d =

k

U

n , k

V

k , d

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What's Wrong?

What are the right “genres”

How many “genres”

Generalization to Digg/Amazon/Match.com

How to find “ U ” values

Labor-intensive creation of “V” values

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A More Generic Approach

N

D

N

K

K

D

Score = U * V

Score

n , d

k

U

n , k

V

k , d

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Instantiated for NetFlix

N

D

=

N

K

K

D

Score = U * V

---

Users

Movies Genres

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Instantiated for Digg

N

D

=

N

K

K

D

Score = U * V

---

Users

Stories Topics

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Instantiated for Match.com

N

D

=

N

K

K

D

Score = U * V

---

Men

Women Qualities

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The Linear Algebra Approach

Suppose X were completely known

Task: Find U,V such that X=U*V and U,V

have rank K

N

D

N

K

K

D

X = U * V

Essentially a

“singular value

decomposition”

problem

CS 5350

The Linear Algebra Approach

Suppose X is not completely known

Task: Find U,V such that the observed

X=U*V and U,V have rank K

Difficult optimization problem: iterate

between finding U and V

N

D

N

K

K

D

X = U * V