In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...

It is today accepted that matrix factorization models allow a high quality of rating prediction in recommender systems. However, a major drawback of matrix factorization is its static nature that results in a progressive declining of the accuracy of the predictions after each factorization. This is due to the fact that the new obtained ratings are not taken into account until a new factorizatio...

It is today accepted that matrix factorization models allow a high quality of rating prediction in recommender systems. However, a major drawback of matrix factorization is its static nature that results in a progressive declining of the accuracy of the predictions after each factorization. This is due to the fact that the new obtained ratings are not taken into account until a new factorizatio...

Matrix factorization or factor analysis is an important task helpful in the analysis of high dimensional real world data. There are several well known methods and algorithms for factorization of real data but many application areas including information retrieval, pattern recognition and data mining require processing of binary rather than real data. Unfortunately, the methods used for real mat...

Factorsynth is a new software tool, developed in the Max environment, that implements sound processing based on matrix factorization techniques. In particular, Nonnegative Matrix Factorization is applied to the input sounds, which produces a set of temporal and spectral components that can be then freely manipulated and combined to produce new sounds. Based on a simple graphical interface that ...

It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without permutation) to allow an LU factorization wit...

— This work proposes a novel method of matrix factorization on the complex domain to obtain both intuitive features and high recognition results in a face recognition system. The real data matrix is transformed into a complex number based on the Euler representation of complex numbers. Base complex matrix factorization (CMF) is developed and two extensions including sparse complex matrix factor...

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We assume the prior of sparse matrix is Laplace distribution by taking matrix sparsity into consideration. Then we use several approximations for derivation of matri...

Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we introduce a new method for collaborative filtering based on Matrix Factorization ...