Related papers: The Multi-parameter Test of Gravitational Wave Dis…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Apart from omnidirectional, a solid elastic sphere is a natural multimode and multifrequency device for the detection of Gravitational Waves (GW). Motion sensing in a spherical GW detector thus requires a multiple set of transducers…

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…

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…

Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent…

In general relativity, there is no dispersion in gravitational waves, while some modified gravity theories predict dispersion phenomena in the propagation of gravitational waves. In this paper, we demonstrate that this dispersion will…

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

In a modified gravity theory, the propagation equation of gravitational waves will be presented in a non-standard way. Therefore this tenor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique…

Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity…

In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects,…

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

Gravitational wave observations have great potential to reveal new information about the fundamental nature of gravity, but extracting that information can be difficult. One popular technique is the parametrized inspiral test of general…

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…

This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best…

We analyze the propagation of gravitational waves in a medium containing bounded subsystems ("molecules"), able to induce significant Macroscopic Gravity effects. We establish a precise constitutive relation between the average quadrupole…

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…