Principal component analysis: Difference between revisions
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The Principle Components (PCs) of a data set are the set of [[orthogonal]] components ascertained by the [[eigenanalysis]] of the data sets [[covariance matrix]]. The most important components are found along the dimensions with the largest covariance values and they reveal the uncorrelated structure of the data set. The data set or signal can be processed independently along each of these dimensions. The goal of PCA, therefore, is to decompose a data set (such as a image from a satellite) into an orthogonal set of Principle Components so that it may be represented accurately without the need to store the entire signal. | The Principle Components (PCs) of a data set are the set of [[orthogonal]] components ascertained by the [[eigenanalysis]] of the data sets [[covariance matrix]]. The most important components are found along the dimensions with the largest covariance values and they reveal the uncorrelated structure of the data set. The data set or signal can be processed independently along each of these dimensions. The goal of PCA, therefore, is to decompose a data set (such as a image from a satellite) into an orthogonal set of Principle Components so that it may be represented accurately without the need to store the entire signal. | ||
[[Category:Signal Processing]] | |||
Revision as of 20:02, 2 August 2010
Principle Components Analysis (PCA) is a popular data analysis method with applications in data compression, signal and noise separation, model order reduction, pattern recognition and feature extraction. In some contexts, PCA is also known as Karhunen-Loeve Transform or the Hotelling Transform.
The Principle Components (PCs) of a data set are the set of orthogonal components ascertained by the eigenanalysis of the data sets covariance matrix. The most important components are found along the dimensions with the largest covariance values and they reveal the uncorrelated structure of the data set. The data set or signal can be processed independently along each of these dimensions. The goal of PCA, therefore, is to decompose a data set (such as a image from a satellite) into an orthogonal set of Principle Components so that it may be represented accurately without the need to store the entire signal.