相关论文: Nonlinear Peculiar-Velocity Analysis and PCA
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
The Correlated Component Analysis (CCA) allows us to estimate how the different diffuse emissions mix in CMB experiments, exploiting also complementary information from other surveys. It is especially useful to deal with possible additional…
We compare the accuracy of published formulae that transform the linear perturbation theory power spectrum into the nonlinear regime against the results of an ensemble of large N-body simulations. We find that the modified transformation…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
The velocity divergence power spectrum is a key ingredient in modelling redshift space distortion effects on quasi-linear and nonlinear scales. We present an improved model for the z=0 velocity divergence auto and cross power spectrum which…
Nonlinear component analysis such as kernel Principle Component Analysis (KPCA) and kernel Canonical Correlation Analysis (KCCA) are widely used in machine learning, statistics and data analysis, but they can not scale up to big datasets.…
PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…
Context. The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the…
We employ Bayesian Model Averaging (BMA) as a powerful statistical framework to address key cosmological questions about the universe's fundamental properties. We explore extensions beyond the standard $\Lambda$CDM model, considering a…
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…
It has been argued recently that the galaxy peculiar velocity field provides evidence of excessive power on scales of $50\hmpc$, which seems to be inconsistent with the standard $\Lambda$CDM cosmological model. We discuss several…
Continuum fitting is an important aspect of Lyman-alpha forest science, since errors in the estimated optical depths scale with the fractional continuum error. However, traditional methods of estimating continua in noisy and…
The precision of Cosmic Microwave Background (CMB) experiments, specifically its lensing reconstruction, has reached the limit where non-linear corrections cannot be ignored. Neglecting these corrections results in biased constraints on…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
The Cosmological Principle states that the universe is statistically isotropic and homogeneous on large length scales, typically $\gtrsim 70$Mpc. A detection of significant deviation would help us falsify the simplest models of inflation.…
Accurate modeling of power flow behavior is essential for a wide range of power system applications, yet the nonlinear and nonconvex structure of the underlying equations often limits their direct use in large-scale optimization problems.…
We present a method for suppressing contributions from higher-order terms in perturbation theory, greatly increasing the amount of information which may be extracted from the matter power spectrum. In an evolved cosmological density field…
Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…
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…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…