matrix factorization

Recommendation systems techniques based on generative models and matrix factorization: a survey

Collaborative filtering (CF) is a technique that can filter out items that a user might like based on the behaviors and preferences of similar users.  It is a key en-abler technique for an effective recommendation system (RS).  Model-based recommendation systems, a subset of CF, use data, typically ratings, to construct models for providing personalized suggestions to users.  Our objective in this work is to provide a comprehensive overview of various techniques employed in Model-based RS, focusing on their theoretical foundations and practical applications.  We explore

Triangular form of Laurent polynomial matrices and their factorization

The issue of the semiscalar equivalence of Laurent polynomial matrices is investigated and the triangular form of such matrices and their finite sets is established with respect to this equivalence.  The theorem on regularization of a Laurent polynomial matrix is proved.  This theorem is used in the problem of factorization of such matrices.  The factorization criterion of a Laurent polynomial matrix with a regular multiplier with a predetermined Smith normal form is obtained.