相关论文: Nonlinear Peculiar-Velocity Analysis and PCA

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

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…

Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on…

Systematic uncertainties that have been subdominant in past large-scale structure (LSS) surveys are likely to exceed statistical uncertainties of current and future LSS data sets, potentially limiting the extraction of cosmological…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

We demonstrate the capability of Principal Component Analysis (PCA) as applied by Heyer & Schloerb (1997) to extract the statistics of turbulent interstellar velocity fields as measured by the energy spectrum, E(k)= k^-beta. Turbulent…

We report the results of an analysis of the redshift power spectrum $P^S(k,\mu)$ in three typical Cold Dark Matter (CDM) cosmological models, where $\mu$ is the cosine of the angle between the wave vector and the line-of-sight. Two distinct…

Reconstruction of the linear power spectrum from observational data provides a way to compare cosmological models to a large amount of data, as Peacock & Dodds (1994, 1996) have shown. By applying the appropriate corrections to the…

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…

We analyze the SDSS Ly-alpha forest P_F(k,z) measurement to determine the linear theory power spectrum. Our analysis is based on fully hydrodynamic simulations, extended using hydro-PM simulations. We account for the effect of absorbers…

We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…

We investigate methods to best estimate the normalisation of the mass density fluctuation power spectrum (sigma_8) using peculiar velocity data from a survey like the Six degree Field Galaxy Velocity Survey (6dFGSv). We focus on two…

The Eulerian cosmological fluid equations are used to study the nonlinear mode coupling of density fluctuations. We evaluate the second-order power spectrum including all four-point contributions. In the weakly nonlinear regime we find that…

Analyses of peculiar velocity surveys face several challenges, including low signal--to--noise in individual velocity measurements and the presence of small--scale, nonlinear flows. This is the second in a series of papers in which we…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

A variety of interstellar complex organic molecules (COMs) have been detected in various physical conditions. However, in the protostellar and protoplanetary environments, their complex kinematics make line profiles blend each other and the…

Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

We study the significance of non-Gaussianity in the likelihood of weak lensing shear two-point correlation functions, detecting significantly non-zero skewness and kurtosis in one-dimensional marginal distributions of shear two-point…

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…