On-line recommender system
First Claim
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1. A computer implemented method for recommending items to consumers in a recommender system, comprising the steps of:
- receiving a stream of rating on items from consumers via a network;
updating sequentially, by a computer, a singular value decomposition of a preference matrix using the stream of ratings, in which each rating is processed one at a time and independent of any other ratings, while receiving the ratings, and wherein the updating is a sequential rank-1 update of the singular value decomposition to produce a thin SVD, and wherein the preference matrix is X, and wherein the singular value decomposition factors the preference matrix X into two orthogonal matrices U and V, and a diagonal matrix S≐
diag(s), such that USVT=X, and UTXV=S, where T represents the SVD transform, the elements of s are singular values and columns of U and V are left and right singular vectors, respectively, and further comprising;
arranging non-negative elements on the diagonal of S in descending order, and a first non-zero element in each column of U is positive so that the thin SVD is unique; and
discarding all but a predetermined number of the r largest singular values and the corresponding singular vectors so that a product of the resulting thinned matrices, U′
S′
V′
≈
X, is a best rank-r approximation of X in a least-squares sense, and a matrix U′
TX=S′
V′
T;
predicting recommendations of particular items for a particular consumer based on the updated singular value decomposition while receiving the ratings and updating the singular value decomposition; and
displaying the recommendations for the particular consumer on a graphical consumer interface via the network.
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Abstract
A method and system recommends items such as products and services to consumers. Rating on items are received from consumers as a sequential stream of data. A thin singular value decomposition is updated, one rating at the time, while receiving the ratings. A prediction of a recommendations of particular items for a particular consumer is based on the updated singular value decomposition while receiving the ratings and updating the singular value decomposition. The ratings are discarded after the updating so that a size, structure, and content of an underlying preference matrix is unknown.
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Citations
16 Claims
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1. A computer implemented method for recommending items to consumers in a recommender system, comprising the steps of:
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receiving a stream of rating on items from consumers via a network; updating sequentially, by a computer, a singular value decomposition of a preference matrix using the stream of ratings, in which each rating is processed one at a time and independent of any other ratings, while receiving the ratings, and wherein the updating is a sequential rank-1 update of the singular value decomposition to produce a thin SVD, and wherein the preference matrix is X, and wherein the singular value decomposition factors the preference matrix X into two orthogonal matrices U and V, and a diagonal matrix S≐
diag(s), such that USVT=X, and UTXV=S, where T represents the SVD transform, the elements of s are singular values and columns of U and V are left and right singular vectors, respectively, and further comprising;arranging non-negative elements on the diagonal of S in descending order, and a first non-zero element in each column of U is positive so that the thin SVD is unique; and discarding all but a predetermined number of the r largest singular values and the corresponding singular vectors so that a product of the resulting thinned matrices, U′
S′
V′
≈
X, is a best rank-r approximation of X in a least-squares sense, and a matrix U′
TX=S′
V′
T;predicting recommendations of particular items for a particular consumer based on the updated singular value decomposition while receiving the ratings and updating the singular value decomposition; and displaying the recommendations for the particular consumer on a graphical consumer interface via the network. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
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Specification