Nonnegative Matrix Factorization (NMF) is an efficient technique to approximate a large matrix containing only nonnegative elements as a product of two nonnegative matrices of significantly smaller size. The guaranteed nonnegativity of the factors is a distinctive property that other widely used matrix factorization methods do not have. Matrices can also be seen as second-order tensors. For som...

This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and vanishing scalar curvature doesn’t imply flatness. We show that, in dimensions greater than 4, if a Ricci flow invariant condition is weaker than “Einstein w...

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive m...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

it is known that the directed cycle of order $n$ uniquely achieves the minimum spectral radius among all strongly connected digraphs of order $nge 3$. in this paper, among others, we determine the digraphs which achieve the second, the third and the fourth minimum spectral radii respectively among strongly connected digraphs of order $nge 4$.

Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n×n real eventually positive matrices; and WPFn, the set of matrices A ∈ R such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n× n real eventually nonnegative ...

Nonnegative matrix factorization NMF is a popular tool for analyzing the latent structure of nonnegative data. For a positive pairwise similarity matrix, symmetric NMF SNMF and weighted NMF WNMF can be used to cluster the data. However, both of them are not very efficient for the ill-structured pairwise similarity matrix. In this paper, a novel model, called relationship matrix nonnegative deco...

In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenv...

The Line Sum Scaling problem for a nonnegative matrix A is to find positive definite diagonal matrices Y , Z which result in prescribed row and column sums of the scaled matrix Y AZ. The Matrix Balancing problem for a nonnegative square matrix A is to find a positive definite diagonal matrix X such that the row sums in the scaled matrix XAX are equal to the corresponding column sums. We demonst...