Related papers: Nonlinear PCA for Spatio-Temporal Analysis of Eart…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a…
Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…
Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…
Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…
Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A prime example of such a dataset is a collection of cell cycle…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed…
We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is…
Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not…
(Abridged) Environmental differences in the stellar populations of early-type galaxies are explored using principal component analysis (PCA), focusing on differences between elliptical galaxies in Hickson Compact Groups (HCGs) and in the…
We introduce a method for decomposition of trend, cycle and seasonal components in spatio-temporal models and apply it to investigate the existence of climate changes in temperature and rainfall series. The method incorporates critical…
Regional Climate Models (RCM) describe the meso scale global atmospheric and oceanic dynamics and serve as dynamical downscaling models. In other words, RCMs use atmospheric and oceanic climate output from General Circulation Models (GCM)…
Cryo-electron microscopy nowadays often requires the analysis of hundreds of thousands of 2D images as large as a few hundred pixels in each direction. Here we introduce an algorithm that efficiently and accurately performs principal…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…
Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…