In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvec...

Motivated by (and using tools from) communication complexity, we investigate the relationship between the following two ranks of a 0-1 matrix: its nonnegative rank and its binary rank (the log of the latter being the unambiguous nondeterministic communication complexity). We prove that for partial 0-1 matrices, there can be an exponential separation. For total 0-1 matrices, we show that if the ...

In this paper a necessary and sufficient condition is established for the existence of the reflexive re-nonnegative definite solution to the quaternion matrix equation AXA∗ = B, where ∗ stands for conjugate transpose. The expression of such solution to the matrix equation is also given. Furthermore, a necessary and sufficient condition is derived for the existence of the general re-nonnegative ...

In this paper a necessary and sufficient condition is established for the existence of the reflexive re-nonnegative definite solution to the quaternion matrix equation AXA∗ = B, where ∗ stands for conjugate transpose. The expression of such solution to the matrix equation is also given. Furthermore, a necessary and sufficient condition is derived for the existence of the general re-nonnegative ...

In this paper, we study the problem of nonnegative graph embedding, originally investigated in [14] for reaping the benefits from both nonnegative data factorization and the specific purpose characterized by the intrinsic and penalty graphs [13]. Our contributions are two-fold. On the one hand, we present a multiplicative iterative procedure for nonnegative graph embedding, which significantly ...

In this article, we integrate the spatial-spectral information of hyperspectral image (HSI) samples into nonnegative matrix factorization (NMF) for affinity learning to address issue HSI clustering. This technique consists three main components: 1) oversegmentation computing spectral-spatial matrix; 2) NMF with guidance obtained and 3) density-based spectral clustering on final matrix. First, i...

Is it possible to perform numerical linear algebra with structured matrices to high relative accuracy at a reasonable cost? In our talk we answer this question affirmatively for a class of structured matrices whose applications range from approximation theory to combinatorics to multivariate statistical analysis [1, 2, 4]—the Totally Nonnegative (TN) matrices, i.e. matrices all of whose minors ...

Nonnegative Matrix Factorization (NMF) has gathered a lot of attention in the last decade and has been successfully applied in numerous applications. It consists in the factorization of a nonnegative matrix by the product of two low-rank nonnegative matrices: M ≈ VW . In this paper, we attempt to solve NMF problems in a recursive way. In order to do that, we introduce a new variant called Nonne...

We present a nonnegative rank factorization of a nonnegative matrix A for the case in which one or both of A(1)A and AA(1) are nonnegative. This gives, in particular, a known result for characterizing nonnegative matrices when A†A or AA† is nonnegative. We applied this characterization to the derivation of known results based on the characterization of nonnegative monotone matrices. A matrix A ...