Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Féjer-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. F...

We present a dedicated algorithm for the nonnegative factorization of a correlation matrix from an application in financial engineering. We look for a low-rank approximation. The origin of the problem is discussed in some detail. Next to the description of the algorithm, we prove, by means of a counter example, that an exact nonnegative decomposition of a general positive semidefinite matrix is...

An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...

Recently Dritschel proves that any positive multivariate Laurent polynomial can be factorized into a sum of square magnitudes of polynomials. We first give another proof of the Dritschel theorem. Our proof is based on the univariate matrix Féjer-Riesz theorem. Then we discuss a computational method to find approximates of polynomial matrix factorization. Some numerical examples will be shown. F...

The main aim of this paper is to study quaternion matrix factorization for low-rank completion and its applications in color image processing. For the real-world images, we proposed a novel model called (LRQC), which adds total variation Tikhonov regularization factor matrices preserve spatial/temporal smoothness. Moreover, proximal alternating minimization (PAM) algorithm was tackle correspond...

Abstract Non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to mining machine learning community, due its advantages such as simple form, good interpretability less storage space. In this paper, we give detailed survey on existing NMF methods, including comprehensive analysis of their design principles, characteristics d...

A novel fixed point algorithm for positive tensor factorization (PTF) is introduced. The update rules efficiently minimize the reconstruction error of a positive tensor over positive factors. Tensors of arbitrary order can be factorized, which extends earlier results in the literature. Experiments show that the factors of PTF are easier to interpret than those produced by methods based on the s...