Search · four archives
Search · four archives
13 papers · ranked by Valyu relevance
Nicolò Colombo, Nikos Vlassis
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…
Marco Congedo, Bijan Afsari, Alexandre Barachant, Maher Moakher + 1 more
'Jesus Malo'] We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest…
Anatoly Khina, Idan Livni, Ayal Hitron, Uri Erez
—The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equippe d with an arbitrary number of antennas. A closed-loop scenari o is assumed, for which a practical capacity-approaching scheme is developed. By…
Haoze He, Daniel Kressner, Bor Plestenjak
It is well known that a family of ${n}\times{n}$ commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to…
Mario Thüne
In graph theory a partition of the vertex set of a graph is called equitable if for all pairs of cells all vertices in one cell have an equal number of neighbours in the other cell. Considering the implications for the adjacency matrix one may generalize that concept as a block partition of a complex square matrix s.t.…
Maximilian Ramgraber, Daniel Sharp, Mathieu Le Provost, Youssef Marzouk
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box models, however, these representations are rarely known. We discuss how to…
Abd‐Krim Seghouane, Yousef Saad
Given a set of p symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these p matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural…
Cristian Rusu, Lorenzo Rosasco
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider extended orthogonal Givens or scaling and shear transformations). The number of…
Manuel Schürch, Dario Azzimonti, Alessio Benavoli, Marco Zaffalon
Gaussian processes (GPs) are an important tool in machine learning and statistics. However, off-the-shelf GP inference procedures are limited to datasets with several thousand data points because of their cubic computational complexity. For this reason, many sparse GPs techniques have been developed over the past…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Junhua Wang, Zhitao Huang, Yiyu Zhou
We present a DOA estimation algorithm, called Joint-Sparse DOA to address the problem of Direction-of-Arrival (DOA) estimation using sensor arrays. Firstly, DOA estimation is cast as the joint-sparse recovery problem. Then, norm is approximated by an arctan function to represent joint sparsity and DOA estimation can be…
Zachary Smith, Pratyush Tiwary
Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain…
Takuya Okuyama, André Röhm, Takatomo Mihana, Makoto Naruse + 1 more
Matrix multiplication is important in various information-processing applications, including the computation of eigenvalues and eigenvectors, and in combinatorial optimization algorithms. Therefore, reducing the computation time of matrix products is essential to speed up scientific and practical calculations. Several…