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Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods…
The multivariate tool of Principal Component Analysis (PCA) is applied to 23 fields in the FCRAO CO Survey of the Outer Galaxy. PCA enables the identification of line profile differences which are assumed to be generated from fluctuations…
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…
Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can…
Geometric phase analysis (GPA) is a widely used technique for extracting displacement and strain fields from scanning probe images. Here, we demonstrate that GPA should be implemented with caution when several fundamental lattices…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…
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…
After a short introduction to the generalized uncertainty principle (GUP), we review some of the physical predictions of the GUP, and we focus in particular on the bounds that present experimental tests can put on the value of the…
We implement and investigate a method for measuring departures from scale-invariance, both scale-dependent as well as scale-free, in the primordial power spectrum of density perturbations using cosmic microwave background (CMB) C_l data and…
We study generic tests of strong-field General Relativity using gravitational waves emitted during the inspiral of compact binaries. Previous studies have considered simple extensions to the standard post-Newtonian waveforms that differ by…
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components…
General Relativity (GR) describes gravitation well at the energy scales which we have so far been able to achieve or detect. However, we do not know whether GR is behind the physics governing stronger gravitational field regimes, such as…
Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution…
The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…
The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to the PCMW…
Principal component analysis (PCA) is a powerful method that can identify patterns in large, complex data sets by constructing low-dimensional order parameters from higher-dimensional feature vectors. There are increasing efforts to use…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…
By reaching through shrouding blastwaves, efficiently discovering off-axis events, and probing the central engine at work, gravitational wave (GW) observations will soon revolutionize the study of gamma-ray bursts. Already, analyses of GW…
The increasing sensitivity of current and upcoming gravitational-wave (GW) detectors poses stringent requirements on the accuracy of the GW models used for data analysis. If these requirements are not met, systematic errors could dominate…