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A common machine learning task is to discriminate between normal and anomalous data points. In practice, it is not always sufficient to reach high accuracy at this task, one also would like to understand why a given data point has been…

In this paper we propose an approach to approximate a truncated singular value decomposition of a large structured matrix. By first decomposing the matrix into a sum of Kronecker products, our approach can be used to approximate a large…

The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…

This paper presents the modal truncation and singular value decomposition (SVD) technique as two main algorithms for dynamic model reduction of the power system. The significance and accuracy of the proposed methods are investigated with…

In the field of model predictive control, Data-enabled Predictive Control (DeePC) offers direct predictive control, bypassing traditional modeling. However, challenges emerge with increased computational demand due to recursive data…

Low-rank approximation methods such as singular value decomposition (SVD) and its variants (e.g., Fisher-weighted SVD, Activation SVD) have recently emerged as effective tools for neural network compression. In this setting, decomposition…

We carry out the convergence analysis of the Scalar Auxiliary Variable (SAV) method applied to the nonlinear Schr\"odinger equation which preserves a modified Hamiltonian on the discrete level. We derive a weak and strong convergence…

Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…

The paper presents a new Kalman filter (KF) implementation useful in applications where the accuracy of numerical solution of the associated Riccati equation might be crucially reduced by influence of roundoff errors. Since the appearance…

With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value…

In this work we demonstrate that SVD-based model reduction techniques known for ordinary differential equations, such as the proper orthogonal decomposition, can be extended to stochastic differential equations in order to reduce the…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…

The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…

Timeseries classification as stochastic (noise-like) or non-stochastic (structured), helps understand the underlying dynamics, in several domains. Here we propose a two-legged matrix decomposition-based algorithm utilizing two complementary…

The ELM method has become widely used for classification and regressions problems as a result of its accuracy, simplicity and ease of use. The solution of the hidden layer weights by means of a matrix pseudoinverse operation is a…

The Nystr\"{o}m method is routinely used for out-of-sample extension of kernel matrices. We describe how this method can be applied to find the singular value decomposition (SVD) of general matrices and the eigenvalue decomposition (EVD) of…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

Rank minimization can be converted into tractable surrogate problems, such as Nuclear Norm Minimization (NNM) and Weighted NNM (WNNM). The problems related to NNM, or WNNM, can be solved iteratively by applying a closed-form proximal…