Related papers: On multivariable matrix spectral factorization met…
Using spectral factorization techniques, a method is given by which rational matrix solutions to the Leech equation with rational matrix data can be computed explicitly. This method is based on an approach by J.A. Ball and T.T. Trent, and…
A new algebraic multilevel algorithm for computing the second eigenvector of a column-stochastic matrix is presented. The method is based on a deflation approach in a multilevel aggregation framework. In particular a square and stretch…
Probabilistic programming provides the means to represent and reason about complex probabilistic models using programming language constructs. Even simple probabilistic programs can produce models with infinitely many variables. Factored…
Matrix functions with potential applications have a major role in science and engineering. One of the fundamental matrix functions, which is particularly important due to its connections with certain matrix differential equations and other…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
In this paper the Levy-Leblond procedure for linearizing the Schr\"odinger equation to obtain the Pauli equation for one particle is generalized to obtain an $N$-particle equation with spin. This is achieved by using the more universal…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to…
We develop a fourth order simulation algorithm for solving the stochastic Langevin equation. The method consists of identifying solvable operators in the Fokker-Planck equation, factorizing the evolution operator for small time steps to…
Perhaps it is not completely superfluous to remind that Clauser-Horne factorability, introduced in [1], is only necessary when \lambda, the hidden variable (HV), is sufficiently deterministic: for {M_i} a set of possible measurements…
A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…
Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis. Many applications require a least-squares (LS) Khatri-Rao factorization. In broadband sensor array problems, polynomial…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
The Matrix Factorization models, sometimes called the latent factor models, are a family of methods in the recommender system research area to (1) generate the latent factors for the users and the items and (2) predict users' ratings on…
This work developed novel complex matrix factorization methods for face recognition; the methods were complex matrix factorization (CMF), sparse complex matrix factorization (SpaCMF), and graph complex matrix factorization (GraCMF). After…
Nowadays, nonnegative matrix factorization (NMF) based methods have been widely applied to blind spectral unmixing. Introducing proper regularizers to NMF is crucial for mathematically constraining the solutions and physically exploiting…
This work extends the factorization method to the inverse scattering problem of reconstructing the shape and location of an absorbing penetrable scatterer embedded in a thin infinite elastic (Kirchhoff--Love) plate. With the assumption that…