Along with the growth of the Internet, automatic recommender systems have become popular. Due to being intuitive and useful, factorization based models, including the Nonnegative Matrix Factorization (NMF) model, are one of the most common approachs for building recommender systems. In this study, we focus on how a recommender system can be built for online services and how the parameters of an...

in this paper, we consider an arbitrary binary polynomial sequence {a_n} and then give a lower triangular matrix representation of this sequence. as main result, we obtain a factorization of the innite generalized pascal matrix in terms of this new matrix, using a riordan group approach. further some interesting results and applications are derived.

in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.

1 Structure Sheaves 7 1.1 C-Valued Sheaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 Factorization Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4 The Factorization System on StrG(X) . . . ....

The two-stage compensator designs of linear system are investigated in the framework of the factorization approach. First, we give “full feedback” two-stage compensator design. Based on this result, various types of the two-stage compensator designs with partial feedbacks are derived. Keywords—Linear System, Factorization Approach, Two-Stage Compensator Design, Parametrization of Stabilizing Co...

A simple definition of torsion theory is presented, as a factorization system with both classes satisfying the 3–for–2 property. Comparisons with the traditional notion are given, as well as connections with the notions of fibration and of weak factorization system, as used in abstract homotopy theory.

Traditionally, recommender systems have been approached as regression models aiming to predict the score that a user would give particular item. In this work, we propose system tackles problem classification task instead of regression. The new model, Dirichlet Matrix Factorization (DirMF), provides not only prediction but also its reliability, hence achieving better balance between quality and ...