netflix - Mathematical Formulation Given a matrix M(very...

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The Netflix Problem The Netflix dataset contains more than 100 million date stamped movie ratings performed by anonymous Netflix customers between Dec 31, 1999 and Dec 31, 2005 [4]. This dataset gives ratings about m = 480,189 users and n = 17,770 movies (aka, items). The goal is to make predictions of movie preferences
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1 2 17000 3 4 4 5 5 1 2 3 5 5 Movies (17,000) Users ½ million This is an n x m matrix M Entries are: 0 – no information 1-5 - rating
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The Netflix Problem - The contest was designed in a training-test set format. - A Hold-out set of about 4.2 million ratings was created consisting of the last nine movies rated by each user Mathematical Formulation Given a matrix M (very sparse) Find a matrix N (full) such that M ( i , j ) = N ( i , j ) ( i , j ) R
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Formulation -Ill posed problem - We must stipulate that matrix N is “intelligent”
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Unformatted text preview: Mathematical Formulation Given a matrix M (very sparse) Find a matrix N (full) such that M ( i , j ) = N ( i , j ) ( i , j ) ∈ R Recall that the row rank of a matrix is the number of linearly independent rows The Matrix Completion Problem -3 rows are linearly dependent if one is a linear combination of the other two min rank ( N ) subject to M ( i , j ) = N ( i , j ) ( i , j ) ∈ R N ( i , j ) ≥ Recommendation Systems There are many other such recommendation systems proposed by Amazon, Barnes and Noble, Google, Apple to name just a few. In each instance, we have a partial list about a user's preferences for a few rated items, and would like to predict his/her preferences for all items from this and other information gleaned from many other users....
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This note was uploaded on 01/15/2012 for the course ECON 101 taught by Professor N/a during the Fall '11 term at Middlesex CC.

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netflix - Mathematical Formulation Given a matrix M(very...

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