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Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Galactic core-collapse supernovae are among the possible sources of gravitational waves. We investigate the ability of gravitational-wave observatories to extract the properties of the collapsing progenitor from the gravitational waves…

We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of $^{48}$Ca, $^{76}$Ge, and $^{82}$Se. We…

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…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current…

We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a…

Very high dynamical range coronagraphs targeting direct exo-planet detection (10^9 - 10^10 contrast) at small angular separation (few lambda/D units) usually require an input wavefront quality on the order of ten thousandths of wavelength…

Principal Component Analysis (PCA)-based techniques can separate data into different uncorrelated components and facilitate the statistical analysis as a pre-processing step. Independent Component Analysis (ICA) can separate statistically…

The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…

We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…

We present an implementation of a blind source separation algorithm to remove foregrounds off millimeter surveys made by single-channel instruments. In order to make possible such a decomposition over single-wavelength data: we generate…

We show that if we have an orthogonal base ($u_1,\ldots,u_p$) in a $p$-dimensional vector space, and select $p+1$ vectors $v_1,\ldots, v_p$ and $w$ such that the vectors traverse the origin, then the probability of $w$ being to closer to…

Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…

Environmental health researchers often aim to identify sources/behaviors that give rise to potentially harmful exposures. We adapted principal component pursuit (PCP)-a robust technique for dimensionality reduction in computer vision and…

The different orthogonal relationships that exists in the Lowdin orthogonalizations is presented. Other orthogonalization techniques such as polar decomposition (PD), principal component analysis (PCA) and reduced singular value…

In this letter, a methodology is proposed to improve the scattering powers obtained from model-based decomposition using Polarimetric Synthetic Aperture Radar (PolSAR) data. The novelty of this approach lies in utilizing the intrinsic…

The leading difficulty in achieving the contrast necessary to directly image exoplanets and associated structures (eg. protoplanetary disks) at wavelengths ranging from the visible to the infrared are quasi-static speckles, and they are…

Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant…

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…