Related papers: A Semi-blind PCA-based Foreground Subtraction Meth…
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…
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…
Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…
The high dynamic range between contaminating foreground emission and the fluctuating 21cm brightness temperature field is one of the most problematic characteristics of 21cm intensity mapping data. While these components would ordinarily…
A basic algorithmic task in automated video surveillance is to separate background and foreground objects. Camera tampering, noisy videos, low frame rate, etc., pose difficulties in solving the problem. A general approach that classifies…
Singular-Value Decomposition (SVD) is a ubiquitous data analysis method in engineering, science, and statistics. Singular-value estimation, in particular, is of critical importance in an array of engineering applications, such as channel…
We make use of a large set of fast simulations of an intensity mapping experiment with characteristics similar to those expected of the Square Kilometre Array (SKA) in order to study the viability and limits of blind foreground subtraction…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
The redshifted 21~cm signal from neutral hydrogen (HI) is potentially a very powerful probe for cosmology, but a difficulty in its observation is that it is much weaker than foreground radiation from the Milky Way as well as extragalactic…
21cm intensity mapping experiments aim to observe the diffuse neutral hydrogen (HI) distribution on large scales which traces the Cosmic structure. The Square Kilometre Array (SKA) will have the capacity to measure the 21cm signal over a…
This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data. We describe SVD methods for visualization of gene expression data, representation of the data using a…
The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…
The 21-cm intensity mapping (IM) of neutral hydrogen (HI) is a promising tool to probe the large-scale structures. Sky maps of 21-cm intensities can be highly contaminated by different foregrounds, such as Galactic synchrotron radiation,…
An important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors…
We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…
In a sky-averaged 21-cm signal experiment, the uncertainty on the extracted signal depends mainly on the covariance between the foreground and 21-cm signal models. In this paper, we construct these models using the modes of variation…
21cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a…
Vision Transformers (ViT) have been established as large-scale foundation models. However, because self-attention operates globally, they lack an explicit mechanism to distinguish foreground from background. As a result, ViT may learn…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the…