Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n× d matrix W and a nonnegative d ×m matrix H . A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...

Due to high noise, low contrast, and other imaging artifacts, region boundaries in ultrasound images often do not conform to the assumptions of many image processing algorithms. Specifically, the beliefs that region boundaries have a high gradient magnitude or a high intensity can break down in this context. In this paper, we present an alternative way of detecting likely boundary points in ult...

In this work we show the de ciencies of the graph model for decomposing sparse matrices for parallel matrix vector multiplica tion Then we propose two hypergraph models which avoid all de cien cies of the graph model The proposed models reduce the decomposition problem to the well known hypergraph partitioning problem widely en countered in circuit partitioning in VLSI We have implemented fast ...

We are focused on numerical methods for decomposing a multivariate polynomial as a sum of univariate polynomials in linear forms. The main tool is the recent result on correspondence between the Waring rank of a homogeneous polynomial and the rank of a partially known quasi-Hankel matrix constructed from the coefficients of the polynomial. Based on this correspondence, we show that the original...

We describe an algorithm for decomposing a fundamental matrix computed from point correspondences over two images into the focal lengths of the two images and the camera motion parameters in a closed-form expression. Our algorithm is based on the decomposability condition of the essential matrix expressed in terms of its scalar invariants. We give a complete analysis for degenerate camera con g...

Linear methods yield data points xn = r1φn,1 +r ∗ 2φn,2 + . . .+ rMφn,M = R φn, which are d-dimensional linear combinations of the original D-dimensional data points φn. . Principal Component Analysis (PCA, Jolliffe (2002)): Preserves the global covariance structure by decomposition of the covariance matrix Σφ,φ = RS R. . Metric Multidimensional Scaling (MDS, Cox & Cox (1994)): Preserves inner ...

Carbon nanotube (CNT) is considered as a new generation of material possessing superior mechanical, thermal and electrical properties. The applications of CNT, especially in composite materials, i.e. carbon nanotube reinforced polymer have received great attention and interest in recent years. To characterize the influence of CNT on the stress intensity factor of nanocomposites, three fracture ...

Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information inc...

e nergy consumption has increased significantly in iran during the recent decades. in this study, an inter-industrial model has been improved to investigate the sources of the changes in the energy consumption of the country. the input-output tables of iran for the years 1988 and 2001 have been employed as the database of the model. the innovation of this research allows the researchers to stud...

We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron P(A, 1 ̄ ) = {x ∈ R | Ax ≥ 1 ̄ , x ≥ 0 ̄ }, when A is a totally unimodular matrix. Our algorithm is based on decomposing the hypergraph transversal problem for unimodular hypergraphs using Seymour’s decomposition of totally unimodular matrices, and may be of independent interest.