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Recommender systems are commonly used to suggest content (movies, books, etc.) that is relevant to a given buyer. The most common approach is to predict the rating that a potential buyer might assign to an item and use the predicted ratings to recommend items. The problem thus reduces to completion of the rating matrix based on a sparse set of observations. This problem has been popularized by the Netflix Prize. A number of methods have been suggested to solve this problem. Recently, several authors have used the assumption of a low-rank rating matrix to propose provably good algorithms.
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