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Low-rank matrix factorization with attributes

Author: Abernethy, Jacob ; Evgeniou, Theodoros ; Vert, Jean-PhilippeINSEAD Area: Decision Sciences ; Technology and Operations Management ; Technology and Operations Management Series: Working Paper ; 2006/68/TOM/DS Publisher: Fontainebleau : INSEAD, 2006.Language: EnglishDescription: 15 p.Type of document: INSEAD Working Paper Online Access: Click here Abstract: We develop a new collaborative filtering (CF) method that combines both previously known users'preferences, i.e., standard CF, as well as product/user attributes, i.e., classical function approximation, to predict a given user's interest in a particular product. Our method is a generalized low rank matrix completion problem, where we learn a function whose inputs are pairs of vectors - the standard low rank matrix completion problem being a special case wherethe inputs to the function are the row and column indices of the matrix. We solve this generalized matrix completion problem using tensor product kernels for which we also formally generalize standard kernel properties. Benchmark experiments on movie ratings show the advantages of our generalized matrix completion method over the standard matrix completion one with no information about movies or people, as well as over standard multi-task or single task learning methods.
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We develop a new collaborative filtering (CF) method that combines both previously known users'preferences, i.e., standard CF, as well as product/user attributes, i.e., classical function approximation, to predict a given user's interest in a particular product. Our method is a generalized low rank matrix completion problem, where we learn a function whose inputs are pairs of vectors - the standard low rank matrix completion problem being a special case wherethe inputs to the function are the row and column indices of the matrix. We solve this generalized matrix completion problem using tensor product kernels for which we also formally generalize standard kernel properties. Benchmark experiments on movie ratings show the advantages of our generalized matrix completion method over the standard matrix completion one with no information about movies or people, as well as over standard multi-task or single task learning methods.

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