相关论文: Multi-parameter Tests of General Relativity Using …

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…

In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

In this paper, we study the problem of computing a Principal Component Analysis of data affected by Poisson noise. We assume samples are drawn from independent Poisson distributions. We want to estimate principle components of a fixed…

It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…

Screening mechanisms are essential components in many modified gravity theories, which satisfy local tests of General Relativity (GR) and address cosmic acceleration on cosmological scales. The strong gravitational lensing of gravitational…

Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this essay…

Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis~(PPGA) has been proposed to generalize conventional principal component analysis…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

PURPOSE: Multi-exponential relaxometry is a powerful tool for characterizing tissue, but generally requires high image signal-to-noise ratio (SNR). This work evaluates the use of principal-component-analysis (PCA) denoising to mitigate…

Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model…

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

Gravitational waves (GWs) provide a new tool to probe the nature of dark energy (DE) and the fundamental properties of gravity. We review the different ways in which GWs can be used to test gravity and models for late-time cosmic…

We present a study of spectrum estimation of relic gravitational waves (RGWs) as a Gaussian stochastic background from output signals of future space-borne interferometers, like LISA and ASTROD. As the target of detection, the analytical…

The upcoming Laser Interferometer Space Antenna (LISA), set for launch in the mid-2030s, will enhance our capability to probe the universe through gravitational waves (GWs) emitted from binary black holes (BBHs) across a broad range of…

The upcoming direct detection of gravitational waves will open a window to probing the strong-field regime of general relativity (GR). As a consequence, waveforms that include the presence of deviations from GR have been developed (e.g. in…

Independent component analysis (ICA) is a method to extract a set of time-series data using ``statistical independency" of each component. We applied ICA to extract gravitational wave (GW) signals directly from the detector data. Our idea…

There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…

Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…

This letter is a generalization of previous results on gravitational waves (GWs) from f(R) theories of gravity. In some previous papers, particular f(R) theories have been linearized for the first time in the literature. Now, the process is…