Related papers: Being PC: Principal Components and Dark Energy
We propose a simple phenomenological parameterization of quintessence with a time-varying equation of state. In particular, it accounts for the possibility of early dark energy. The quintessence potential can be reconstructed in terms of…
This paper focuses on the utility of various data transformation techniques, which might be under the principal component analysis (PCA) category, on exoplanet research. The first section introduces the methodological background of PCA and…
Principal component analysis (PCA) is a powerful standard tool for reducing the dimensionality of data. Unfortunately, it is sensitive to outliers so that various robust PCA variants were proposed in the literature. This paper addresses the…
Recent data and new data analysis methods show that most probably the parameter $w$ in the equation of state of the dark energy is smaller than -1 at low redshifts. We briefly review some of the models with such a property and without…
The formalism in order to obtain the Dark Energy equation of state is extended to non-flat universes and we consider the inequalities that must be satisfied by Phantom Dark Energy in this case. We show that due to a non-vanishing spatial…
Power-law cosmology with scale factor as power of cosmic time, $a \propto t^{\a}$, is investigated. We review and discuss value of $\a$ obtained from various types of observation. Considering dark energy dominant era in late universe from…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…
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…
Observational constraints on time-varying dark energy ({\it e.g.}, quintessence) are commonly presented on a $w_0$-$w_a$ plot that assumes the equation of state of dark energy strictly satisfies $w(z)= w_0+ w_a z/(1+z)$ as a function of the…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies 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…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyze the measurement results statistically. Here we show that the…
Searching for departures from general relativity (GR) in more than one post-Newtonian (PN) phasing coefficients, called a \emph{multi-parameter test}, is known to be ineffective given the sensitivity of the present generation of…
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…
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.…
A generalized parameterization $w_\beta(z)$ for the dark energy equation of state (EoS) is proposed and some of its cosmological consequences are investigated. We show that in the limit of the characteristic dimensionless parameter $\beta…