Related papers: Principal Component Analysis of Spectral Line Data…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but (sometimes) poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on…
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over…
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…
Emission in spectral lines can provide unique information on interstellar turbulence. Doppler shifts due to supersonic motions contain information on turbulent velocity field which is otherwise difficult to measure. However, the problem of…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…
Observations of molecular lines are a key tool to determine the main physical properties of prestellar cores. However, not all the information is retained in the observational process or easily interpretable, especially when a larger number…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…
We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of…