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WIREs Computational Statistics, 2010
Principal Component Analysis (PCA, [24, 25]) is a technique which, quite literally, takes a di_erent viewpoint of multivariate data. In fact, PCA de_nes new variables, consisting of linear combinations of the original ones, in such a way that the _rst axis is in the direction containing most variation.
Aiyi Liu, Enrique F. Schisterman
+7 more sources
Principal Component Analysis (PCA, [24, 25]) is a technique which, quite literally, takes a di_erent viewpoint of multivariate data. In fact, PCA de_nes new variables, consisting of linear combinations of the original ones, in such a way that the _rst axis is in the direction containing most variation.
Aiyi Liu, Enrique F. Schisterman
+7 more sources
Applied Spectroscopy, 2021
Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal component analysis is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with ...
J. Beattie, Francis W. L. Esmonde-White
semanticscholar +1 more source
Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal component analysis is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with ...
J. Beattie, Francis W. L. Esmonde-White
semanticscholar +1 more source
A Review of Principal Component Analysis Algorithm for Dimensionality Reduction
, 2021Big databases are increasingly widespread and are therefore hard to understand, in exploratory biomedicine science, big data in health research is highly exciting because data-based analyses can travel quicker than hypothesis-based research.
Basna Mohammed Salih Hasan +1 more
semanticscholar +1 more source
Full regularization path for sparse principal component analysis
International Conference on Machine Learning, 2007Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a particular linear combination of the input variables while constraining the number of nonzero coefficients in this combination.
A. d'Aspremont +2 more
semanticscholar +1 more source
Principal component analysis in linear systems: Controllability, observability, and model reduction
, 1981Kalman's minimal realization theory involves geometric objects (controllable, unobservable subspaces) which are subject to structural instability. Specifically, arbitrarily small perturbations in a model may cause a change in the dimensions of the ...
B. Moore
semanticscholar +1 more source
Sparse Principal Component Analysis
, 2006Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However, PCA suffers from the fact that each principal component is a linear combination of all the original variables, thus it is often difficult to ...
H. Zou, T. Hastie, R. Tibshirani
semanticscholar +1 more source
2003
Chapter 9 presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix \({{\mathcal{X}}}\) will now be considered as observations from a p-variate random variable X. The
Léopold Simar, Wolfgang Karl Härdle
openaire +2 more sources
Chapter 9 presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix \({{\mathcal{X}}}\) will now be considered as observations from a p-variate random variable X. The
Léopold Simar, Wolfgang Karl Härdle
openaire +2 more sources
2012
Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data's variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data's variation are explored.
Stefanie Hartmann +3 more
openaire +2 more sources
Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data's variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data's variation are explored.
Stefanie Hartmann +3 more
openaire +2 more sources
Graph-Regularized Fast and Robust Principal Component Analysis for Hyperspectral Band Selection
IEEE Transactions on Geoscience and Remote Sensing, 2018A fast and robust principal component analysis on Laplacian graph (FRPCALG) method is proposed to select bands of hyperspectral imagery (HSI). The FRPCALG assumes that a clean band matrix lies in a unified manifold subspace with low-rank and clustering ...
Weiwei Sun, Q. Du
semanticscholar +1 more source