Related papers: X-ray spectral variability of blazars using princi…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
Understanding the inverse equivalent width - luminosity relationship (Baldwin Effect), the topic of this meeting, requires extracting information on continuum and emission line parameters from samples of AGN. We wish to discover whether,…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
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…
Principal Component Analysis (PCA) is being extensively used in Astronomy but not yet exhaustively exploited for variability search. The aim of this work is to investigate the effectiveness of using the PCA as a method to search for…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
We present a study aimed at understanding the physical phenomena underlying the formation and evolution of galaxies following a data-driven analysis of spectroscopic data based on the variance in a carefully selected sample. We apply…
We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…
Principal Components Analysis (PCA) and Independent Component Analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It…
The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…
Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…
We discuss spectral principal component analysis (SPCA) and show examples of its application in analyzing AGN spectra in both small and large samples. It can be used to identify peculiar spectra and classify AGN spectra. Its application to…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…
We analyse 400 ks of XMM-Newton data on the active galactic nucleus NGC 1365 using principal component analysis (PCA) to identify model independent spectral components. We find two significant components and demonstrate that they are…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
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…
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…