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Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used "preprocessing" step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and…

Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…

We seek to remove foreground contaminants from 21cm intensity mapping observations. We demonstrate that a deep convolutional neural network (CNN) with a UNet architecture and three-dimensional convolutions, trained on simulated…

Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…

In the age of information explosion, image classification is the key technology of dealing with and organizing a large number of image data. Currently, the classical image classification algorithms are mostly based on RGB images or…

We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting…

This paper explores signal and image analysis by using the Singular Value Decomposition (SVD) and its extension, the Generalized Singular Value Decomposition (GSVD). A key strength of SVD lies in its ability to separate information into…

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first…

Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the…

The VVC codec is applied to the task of multispectral image (MSI) compression using adaptive and scalable coding structures. In a 'plain' VVC approach, concepts from picture-to-picture temporal prediction are employed for decorrelation…

We study Principal Component Analysis (PCA) in a setting where a part of the corrupting noise is data-dependent and, as a result, the noise and the true data are correlated. Under a bounded-ness assumption on the true data and the noise,…

A sample-relaxed two-dimensional color principal component analysis (SR-2DCPCA) approach is presented for face recognition and image reconstruction based on quaternion models. A relaxation vector is automatically generated according to the…

We compared the regular Singular Value Decomposition (SVD), truncated SVD, Krylov method and Randomized PCA, in terms of time and space complexity. It is well-known that Krylov method and Randomized PCA only performs well when k << n, i.e.…

In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…

Patch-based low-rank minimization for image processing attracts much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle…

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event…

Robust tensor principal component analysis (RTPCA) aims to separate the low-rank and sparse components from multi-dimensional data, making it an essential technique in the signal processing and computer vision fields. Recently emerging…