Principal component analysis
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Abstract
Abstract Principal component analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter‐correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the PCA model can be evaluated using cross‐validation techniques such as the bootstrap and the jackknife. PCA can be generalized as correspondence analysis (CA) in order to handle qualitative variables and as multiple factor analysis (MFA) in order to handle heterogeneous sets of variables. Mathematically, PCA depends upon the eigen‐decomposition of positive semi‐definite matrices and upon the singular value decomposition (SVD) of rectangular matrices. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction
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The record
- Venue
- Wiley Interdisciplinary Reviews Computational Statistics
- Topic
- Sensory Analysis and Statistical Methods
- Field
- Agricultural and Biological Sciences
- Canadian institutions
- The Scarborough HospitalUniversity of Toronto
- Funders
- —
- Keywords
- Principal component analysisSingular value decompositionCorrespondence analysisDimensionality reductionJackknife resamplingMultiple correspondence analysisMathematicsMultivariate statisticsDimension (graph theory)Sparse PCATable (database)Similarity (geometry)Data setComputer scienceStatisticsPattern recognition (psychology)Data miningArtificial intelligenceAlgorithmCombinatorics
- Has abstract in OpenAlex
- yes