Related papers: Quasar Main Sequence: a line or a plane?
We study 16,707 quasar spectra from the SDSS using the Karhunen-Lo\`eve (KL) transform (or Principal Component Analysis, PCA). The quasar eigenspectra of the full catalog reveal the following: 1st order - the mean spectrum; 2nd order - a…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
While the beta-VAE family is aiming to find disentangled representations and acquire human-interpretable generative factors, like what an ICA (from the linear domain) does, we propose Full Encoder, a novel unified autoencoder framework as a…
Principal Component Analysis (PCA) is a well-known technique used to decorrelate a set of vectors. It has been applied to explore the star formation history of galaxies or to determine distances of mass-lossing stars. Here we apply PCA to…
The Laser Interferometer Space Antenna (LISA) will provide us with a unique opportunity to observe the early inspiral phase of supermassive binary black holes (SMBBHs) in the mass range of $10^5-10^6\,M_{\odot}$, that lasts for several…
Quasars have long been known as intrinsically variable sources, but the physical mechanism underlying the temporal optical/UV variability is still not well understood. We propose a novel nonparametric method for modeling and forecasting the…
Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…
We present an X-ray and multiwavelength study of 33 weak emission-line quasars (WLQs) and 18 quasars that are analogs of the extreme WLQ, PHL 1811, at z ~ 0.5-2.9. New Chandra 1.5-9.5 ks exploratory observations were obtained for 32 objects…
Quasars accreting matter at very high rates (known as extreme Population A [xA] or super-Eddington accreting massive black holes) provide a new class of distance indicators covering cosmic epochs from the present-day Universe up to less…
Accretion processes in quasars and active galactic nuclei are still poorly understood, especially as far as the connection between observed spectral properties and physical parameters is concerned. Quasars show an additional degree of…
In this paper, we propose a cone projected power iteration algorithm to recover the first principal eigenvector from a noisy positive semidefinite matrix. When the true principal eigenvector is assumed to belong to a convex cone, the…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces…
We present a catalog of broad H$\beta$ variability properties for all spectra of quasars with $z<0.8$ and at least two observations included in the Sloan Digital Sky Survey (SDSS) Data Release 16 quasar catalog. For each spectrum, we…
A search for emission lines in foreground galaxies in quasar spectra (z(gal) < z(QSO)) of the Sloan Digital Sky Survey (SDSS) data release 5 (DR5) reveals 23 examples of quasars shining through low redshift, foreground galaxies at small…
Gravitational microlensing is a powerful tool allowing one to probe the structure of quasars on sub-parsec scale. We report recent results, focusing on the broad absorption and emission line regions. In particular microlensing reveals the…
We study the properties of the broad line region in blazars by comparing the virial estimate of black hole masses with that derived from the mass of the host galaxies. The former is sensitive to the width of broad lines, i.e., to the…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…