Related papers: Nonlinear Peculiar-Velocity Analysis and PCA

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be…

We present updated observational constraints on the spatially flat $\phi$CDM model, where dark energy is described by a minimally coupled scalar field $\phi$ with an inverse power-law potential $V=V_0 \phi^{-\alpha}$. Using Planck 2018 CMB…

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…

In this paper, we combine the latest observational data, including the WMAP five-year data (WMAP5), BOOMERanG, CBI, VSA, ACBAR, as well as the Baryon Acoustic Oscillations (BAO) and Type Ia Supernoave (SN) "Union" compilation (307 sample)…

Autoencoders (AE) provide a useful method for nonlinear dimensionality reduction but are ill-suited for low data regimes. Conversely, Principal Component Analysis (PCA) is data-efficient but is limited to linear dimensionality reduction,…

We use an ensemble of N-body simulations of the currently favoured (concordance) cosmological model to measure the amount of information contained in the non-linear matter power spectrum about the amplitude of the initial power spectrum.…

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…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

We present a likelihood analysis of the parameter space of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the input scalar masses m_0 and fermion masses m_{1/2} are each assumed to be universal. We…

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Line intensity mapping (LIM) is emerging as a powerful technique to map the cosmic large-scale structure and to probe cosmology over a wide range of redshifts and spatial scales. We perform Fisher forecasts to determine the optimal design…

In contrast to our understanding of density field tracers, the modelling of direct statistics pertaining to the cosmic velocity field remains open to significant opportunities for improvement. The lack of accurate modelling for the…

The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

Dark energy can be investigated in two complementary ways, by considering either general parameterizations or physically well-defined models. Following the second route, we explore the constraints on quintessence models where the…

Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…

Principal component analysis (PCA) is one of the most popular dimension reduction methods. The usual PCA is known to be sensitive to the presence of outliers, and thus many robust PCA methods have been developed. Among them, the Tyler's…