Consider the matrix equation AXA∗ + BY B∗ = C. A matrix pair (X0, Y0) is called a Hermitian nonnegative-definite solution to the matrix equation if X0 and Y0 are Hermitian nonnegative-definite and satisfy AX0A∗ + BY0B∗ = C. We give necessary and sufficient conditions for the existence of a Hermitian nonnegative-definite solution to the matrix equation, and further derive a representation of the...

Matrix factorization techniques have been frequently applied in information processing tasks. Among them, Non-negative Matrix Factorization (NMF) have received considerable attentions due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in human brain. On the other hand, from geometric perspective the data is usually sampl...

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far...

Abstract In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups p -adic general linear groups indexed by nonnegative integers and established the theory local newforms for irreducible generic representations. this paper, we extend their results to all To do this, define new certain tuples integers. For proof, introduce Rankin–Selberg integrals Speh

We define the commuting algebra determinant of a finite group action on a finite set, a notion dual to the group determinant of Dedekind. We show that the following combinatorial example is a commuting algebra determinant. Let Bq(n) denote the set of all subspaces of an n-dimensional vector space over Fq. The type of an ordered pair (U, V ) of subspaces, where U, V ∈ Bq(n), is the ordered tripl...

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...

We show a simple method for constructing larger dimension nonnegative matrices with somewhat arbitrary entries which can be irreducible or reducible but preserving the spectral radius via row sum expansions. This yields sufficient criteria two square of to have same radius, way compare radii matrices, and derive new upper lower bounds on give standard as special case.

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint for NMF, sparsity has been modeled making use of the L1 regularizer. Nonetheless, recent stud...

Real data are usually complex and contain various components. For example, face images have expressions and genders. Each component mainly reflects one aspect of data and provides information others do not have. Therefore, exploring the semantic information of multiple components as well as the diversity among them is of great benefit to understand data comprehensively and in-depth. However, th...