相关论文: PCA Tomography: how to extract information from da…

A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…

To mitigate the severe information loss arising from widely adopted linear scale cuts in constraints on modified gravity parameterisations with Weak Lensing (WL) and Large-Scale Structure (LSS) data, we introduce a novel alternative method…

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…

Principal Component Analysis (PCA) and other multi-variate models are often used in the analysis of "omics" data. These models contain much information which is currently neither easily accessible nor interpretable. Here we present an…

The output of spectral clustering is a collection of eigenvalues and eigenvectors that encode important connectivity information about a graph or a manifold. This connectivity information is often not cleanly represented in the eigenvectors…

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…

Project 1640 is a high contrast near-infrared instrument probing the vicinities of nearby stars through the unique combination of an integral field spectrograph with a Lyot coronagraph and a high-order adaptive optics system. The…

The idea of representation has been used in various fields of study from data analysis to political science. In this paper, we define representativeness and describe a method to isolate data points that can represent the entire data set.…

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…

We present the first tests of a new method, the Correlated Component Analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave…

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…

This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…

Principal Component Analysis (PCA) is being extensively used in Astronomy but not yet exhaustively exploited for variability search. The aim of this work is to investigate the effectiveness of using the PCA as a method to search for…

We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which…

Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…

Data processing constitutes a critical component of high-contrast exoplanet imaging. Its role is almost as important as the choice of a coronagraph or a wavefront control system, and it is intertwined with the chosen observing strategy.…

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…