Chapter 9: Principal Component Analysis
A. M. Mathai, Serge B. Provost, H. J. Haubold
Abstract
Abstract The requisite theory for the study of Principal Component Analysis has already been introduced in Chap. 1 , namely, the problem of optimizing a real quadratic form that is subject to a constraint. We formulate the problem with respect to a practical situation consisting of selecting the most ``relevant'' variables in a study. Principal component analysis is actually a dimension reduction technique that projects the data onto a set of orthogonal axes. Sample principal components are defined and certain associated distributional aspects are discussed.
Topics & Concepts
Principal component analysisConstraint (computer-aided design)Dimension (graph theory)Principal (computer security)Set (abstract data type)Dimensionality reductionMathematicsComputer scienceMathematical optimizationArtificial intelligenceStatisticsCombinatoricsGeometryOperating systemProgramming languageRandom Matrices and ApplicationsBayesian Methods and Mixture ModelsAdvanced Combinatorial Mathematics