Related papers: Tighter bound of Sketched Generalized Matrix Appro…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
We consider the synthesis problem of Compressed Sensing - given s and an MXn matrix A, extract from it an mXn submatrix A', certified to be s-good, with m as small as possible. Starting from the verifiable sufficient conditions of…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gained popularity as an effective computational approximation…
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure. However, estimating the rank has been done largely in an…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…
Neural networks, a central tool in machine learning, have demonstrated remarkable, high fidelity performance on image recognition and classification tasks. These successes evince an ability to accurately represent high dimensional…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…
Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
CUR matrix decomposition is a randomized algorithm that can efficiently compute the low rank approximation for a given rectangle matrix. One limitation with the existing CUR algorithms is that they require an access to the full matrix A for…
We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
In all state-of-the-art sketching and coreset techniques for clustering, as well as in the best known fixed-parameter tractable approximation algorithms, randomness plays a key role. For the classic $k$-median and $k$-means problems, there…