Nonnegative matrix factorization has been offered as a fast and effective method for analyzing nonnegative two-mode proximity data. The goal is to structurally represent a nonnegative proximity matrix as the product of two lower-dimensional nonnegative matrices. Goodness of fit is typically measured as the sum of the squared deviations between the observed matrix elements and the estimated elem...

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...

Let A k ; k 0, be a sequence of m m nonnegative matrices and let A(z) = P 1 k=0 A k z k be such that A(1) is an irreducible stochastic matrix. The unique power-bounded solution of the nonlinear matrix equation G = P 1 k=0 A k G k has been shown to play a key role in the analysis of Markov chains of M/G/1 type. Assuming that the matrix A(z) is rational, we show that the solution of this matrix e...