Matrix interpretation of multiple orthogonality

Multiple Representations for Orthogonality

Nonnegative Matrix Factorization with Orthogonality Constraints

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is to decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropria...

Multiple Orthogonality and Applications in Numerical Integration

In this paper a brief survey of multiple orthogonal polynomials defined using orthogonality conditions spread out over r different measures are given. We consider multiple orthogonal polynomials on the real line, as well as on the unit semicircle in the complex plane. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recur...

Improved Matrix Interpretation

We present a new technique to prove termination of Term Rewriting Systems, with full automation. A crucial task in this context is to find suitable well-founded orderings. A popular approach consists in interpreting terms into a domain equipped with an adequate well-founded ordering. In addition to the usual interpretations: natural numbers or polynomials over integer/rational numbers, the rece...

Projective Nonnegative Matrix Factorization: Sparseness, Orthogonality, and Clustering

Abstract In image compression and feature extraction, linear expansions are standardly used. It was pointed out by Lee and Seung that the positivity or non-negativity of a linear expansion is a very powerful constraint, that seems to lead to sparse representations for the images. Their technique, called Non-negative Matrix Factorization (NMF), was shown to be useful in approximating high dimens...