Related papers: Efficient Thresholded Correlation using Truncated …
The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…
We investigate the solution of low-rank matrix approximation problems using the truncated SVD. For this purpose, we develop and optimize GPU implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work…
Trajectory data, including time series and longitudinal measurements, are increasingly common in health-related domains such as biomedical research and epidemiology. Real-world trajectory data frequently exhibit heterogeneity across…
Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power…
We examine holographic renormalization by the singular value decomposition (SVD) of matrix data generated by the Monte Carlo snapshot of the 2D classical Ising model at criticality. To take the continuous limit of the SVD enables us to find…
Motivated by the problem of identifying correlations between genes or features of two related biological systems, we propose a model of \emph{feature selection} in which only a subset of the predictors $X_t$ are dependent on the…
In this article we present some statistical applications of the functional singular value decomposition (FSVD). This tool allows us to decompose the sample mean of a bivariate stochastic process into components that are functions of…
We consider the problem of updating the SVD when augmenting a "tall thin" matrix, i.e., a rectangular matrix $A \in \RR^{m \times n}$ with $m \gg n$. Supposing that an SVD of $A$ is already known, and given a matrix $B \in \RR^{m \times…
We describe two algorithms for computing a sparse solution to a least-squares problem where the coefficient matrix can have arbitrary dimensions. We show that the solution vector obtained by our algorithms is close to the solution vector…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
Memory and network bandwidth are decisive bottlenecks when handling high-resolution multidimensional data sets in visualization applications, and they increasingly demand suitable data compression strategies. We introduce a novel lossy…
Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
Recent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe…
The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the authors is shown to compute the left singular vector possibly much less accurately than the right singular vector and may be numerically backward unstable when a…
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…
Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the $k$-core decomposition problem, the classic peeling algorithm…