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These notes are not intended to substitute for a course in linear algebra on reduction of endomorphisms nor an exhaustive presentation of the Dunford's decomposition. We will limit ourselves to the case where the base is R or C, and the…

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we…

Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…

The principal component analysis approach is employed to extract the principal components contained in nuclear mass models for the first time. The effects coming from different nuclear mass models are reintegrated and reorganized in the…

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning,…

In this paper, we show how to carry out a relatively more realistic and complete reconstruction of supernova neutrino spectra in the future large liquid-scintillator detectors, by implementing the method of singular value decomposition with…

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

We present an algorithm to compute the primary decomposition of a submodule $\mathcal{N}$ of the free module $\Z[x_1, \ldots, x_n]^m$. For this purpose we use algorithms for primary decomposition of ideals in the polynomial ring over the…

The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…

The direct detection and characterization of exoplanets will be a major scientific driver over the next decade, involving the development of very large telescopes and requires high-contrast imaging close to the optical axis. Some complex…

We present a principal component analysis method which tracks and compensates for short-timescale variability in pulsar profiles, with a goal of improving pulsar timing precision. We couple this with a fast likelihood technique for…

We present a fingerprint-like method to analyze material defects after energetic particle irradiation by computing a rotation invariant descriptor vector for each atom of a given sample. For ordered solids this new method is easy to use,…

This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…

Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…

In this paper, we propose an interpretable feature selection method based on principal component analysis (PCA) and principal component regression (PCR), which can extract important features for underwater source localization by only…

Searching for departures from general relativity (GR) in more than one post-Newtonian (PN) phasing coefficients, called a \emph{multi-parameter test}, is known to be ineffective given the sensitivity of the present generation of…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…