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Estimation of Sparse Matrix Rank in Recommender Systems

IP.com Disclosure Number: IPCOM000241756D
Publication Date: 2015-May-28
Document File: 4 page(s) / 107K

Publishing Venue

The IP.com Prior Art Database

Abstract

In this publication, a method is presented for estimating the parameters of a system, for which the relevant information is represented by a sparse vector or matrix. As an example of application, a system for collaborative filtering is considered, where users are asked to evaluate items, but they do not evaluate all of them. The problem is then to predict the missing evaluations from the sparse matrix of known evaluations. The estimation of a matrix and its rank is described as a solution for a recommender system.

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Estimation of Sparse Matrix Rank in Recommender Systems

    The task of recovering a sky image by determining the position and the intensity of sparse signal sources can be viewed as a special case of a more general problem of data mining, where the relevant information is represented by a sparse matrix, i.e., a matrix characterized by having a large number of zeros as elements. An example is given by collaborative filtering, where users are asked to evaluate items, but they do not evaluate all of them. The problem is then to predict the missing evaluations, or rankings, from the sparse matrix of known rankings. A well known application is a so-called recommender system, for example a recommender system for a server providing movies on demand with about a million clients and 25000 movies, with known ratings that are sparsely distributed. In this application, it is advantageous to reliably estimate the rank of the sparse matrix used by the recommender system in addition to the matrix itself, as this may provide useful information for optimization algorithms to refine the estimates of the unknown ratings. |

    In this publication, a method is presented for estimating the parameters of systems, for which the relevant information is represented by a sparse vector or matrix. For example, estimating a matrix and its rank as a solution for a recommender system adopted by a server providing movies on demand to clients from a set of movies, with known client ratings that are sparsely distributed.

    An example of the presented method is given by parameter estimation in collaborative filtering, where customers are asked to evaluate items, but they do not evaluate all of them. The problem is to predict the missing rankings from the sparse matrix of known rankings, as in the recommender system mentioned above. It turns out that the preferences of users are typically determined by a small number of factors, which lead to a low rank of the sparse matrix. The main goal of the disclosed method is to estimate the rank of the sparse matrix. In the proposed embodiment, joint estimates of the sparse matrix rank and of the missing elements of the matrix are provided. The estimates of the matrix rank and of the vector...