Related papers: Being PC: Principal Components and Dark Energy
We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing ADI and LOCI for increasing the contrast achievable next to a bright star. The stellar PSF is…
Some issues of the cosmological constant or dark energy are briefly reviewed. There are an increasing number of observations that constrain the equation of state of dark energy more stringently and favor the time-independent cosmological…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
We propose a simple dark energy model with the following properties: the model predicts a late-time dark radiation component that is not ruled out by current observational data, but which produces a distinctive time-dependent equation of…
Equation of state parameter plays a significant role for guessing the real nature of dark energy. In the present paper polytropic equation of state $p=\omega\rho^n$ is chosen for some of the kinematical $\Lambda$-models viz., $\Lambda \sim…
The coincidence problems and other dynamical features of dark energy are studied in cosmological models with variable cosmological parameters and in models with the composite dark energy. It is found that many of the problems usually…
When CMB data are used to derive cosmological parameters, their very choice does matter: some parameter values can be biased if the parameter space does not cover the "true" model. This is a problem, because of the difficulty to parametrize…
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…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state $p_{x}=w_{x}(a(z)) \rho_{x}$ in which the coefficient $w_{x}$ is parameterized by the scale factor $a$ or redshift $z$. We…
We consider the 2-Wasserstein space of probability measures supported on the unit-circle, and propose a framework for Principal Component Analysis (PCA) for data living in such a space. We build on a detailed investigation of the optimal…
Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…
Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…
In an introductory manner, the nature of dark energy is addressed, how it is observed and what further tests are needed to reconstruct its properties. Several theoretical approaches to dark energy will be discussed. Finally, the dark…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
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 demonstrate the use of a variant of Principal Component Analysis (PCA) for discrimination problems in astronomy. This variant of PCA is shown to provide the best linear discrimination between data classes. As a test case, we present the…
Ferroic domain walls are currently investigated by several state-of-the art techniques in order to get a better understanding of their distinct, functional properties. Here, Principal Component Analysis (PCA) of Raman maps is used to study…
We develop a theoretical method of constructing the quintessence potential directly from the effective equation of state function $w(z)$, which describes the properties of the dark energy. We apply our method to four parametrizations of…
We apply Principal Component Analysis (PCA) to ~100,000 stellar spectra obtained by the Sloan Digital Sky Survey (SDSS). In order to avoid strong non-linear variation of spectra with effective temperature, the sample is binned into 0.02 mag…