Related papers: SVD-based unfolding: implementation and experience
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
We introduce the Singular Value Representation (SVR), a new method to represent the internal state of neural networks using SVD factorization of the weights. This construction yields a new weighted graph connecting what we call spectral…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
High-energy physics experiments rely heavily on precise measurements of energy and momentum, yet face significant challenges due to detector limitations, calibration errors, and the intrinsic nature of particle interactions. Traditional…
Monocular depth estimation is a critical task for autonomous driving and many other computer vision applications. While significant progress has been made in this field, the effects of viewpoint shifts on depth estimation models remain…
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…
A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful tool that is the workhorse of many methods both in…
We provide a methodology for estimating the losses due to shade in power generation data sets produced by real-world photovoltaic (PV) systems. We focus this work on estimating shade loss from data that are unlabeled, i.e. power…
The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread…
Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…
We address the reduction to compact band forms, via unitary similarity transformations, for the solution of symmetric eigenvalue problems and the computation of the singular value decomposition (SVD). Concretely, in the first case we…
Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…
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…
The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…
In this work we present a novel methodology that combines Higher Order Singular Value Decomposition (HOSVD) with Deep Learning (DL) techniques for super-resolution in computational fluid dynamics (CFD) and sparse experimental datasets. This…
This work introduces Structured 3D-SVD as a practical framework for the reconstruction, compression, and analysis of biological volumetric data. Inspired by the logic of matrix singular value decomposition (SVD), the proposed approach…
This paper presents a new method for reconstructing regions of interest (ROI) from a limited number of computed tomography (CT) measurements. Classical model-based iterative reconstruction methods lead to images with predictable features.…
We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients…
SVD (singular value decomposition) is one of the basic tools of machine learning, allowing to optimize basis for a given matrix. However, sometimes we have a set of matrices $\{A_k\}_k$ instead, and would like to optimize a single common…