Related papers: Principal Components for Model-Agnostic Modified G…
The next generation of weak lensing surveys will trace the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. Along with constraining the dynamics of dark energy, they will probe the…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general,…
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…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
We perform a principal component analysis to assess ability of future observations to measure departures from General Relativity in predictions of the Poisson and anisotropy equations on linear scales. In particular, we focus on how the…
Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
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…
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…
The idea that we live in a Universe undergoing a period of acceleration is a strongly held notion in cosmology. As this can, potentially, be explained with a modification to General Relativity we look at current cosmological data with the…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
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…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…
The aim of this paper is to constrain modified gravity with redshift space distortion observations and supernovae measurements. Compared with a standard LCDM analysis, we include three additional free parameters, namely the initial…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
In the near future, space-borne gravitational wave (GW) detector LISA can open the window of low-frequency band of GW and provide new tools to test gravity theories. In this work, we consider multi-parameter tests of GW generation and…
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…