Training Stage
Given the matrix of observations R of size m x n, where n is the number of users and m is the number of items, the problem is to find the matrix X of size m x f and the matrix Y of size f x n, where f is the number of factors that minimize the following cost function:
where
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c ui measures the confidence in observing p ui
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α is the rate of confidence
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r ui is the element of the matrix R
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λ is the parameter of the regularization
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denote the number of ratings of user
u and item
i respectively
Prediction Stage
Prediction of RatingsGiven user factors X, item factors Y, and the matrix D that describes for which pairs of factors X and Y the rating should be computed, the system calculates the matrix of recommended ratings Res:
