Eigenvalues and Eigenvectors in Data Dimension Reduction for Regression

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dc.contributor.advisorZhao, Qiang
dc.contributor.authorReiss, Randolf H.
dc.contributor.committeeMemberWhite, Alexander
dc.contributor.committeeMemberShen, Jian
dc.date.accessioned2013-08-28T20:27:59Z
dc.date.available2013-08-28T20:27:59Z
dc.date.issued2013-08
dc.description.abstractA basic theory of eigenvalues and eigenvectors as a means to reduce the dimension of data, is presented. Iterative methods for finding eigenvalues and eigenvectors are explored with proofs of the existence and uniqueness of solutions. Of particular focus is the Power Method as it is the basis of most eigenvector algorithms. Interpretations of the Power Method are presented in the context of linear algebra and data dimension reduction. It is shown that the algorithms for principal component analysis and partial least squares are extensions of the Power Method. The estimation of parameters for a computer-based pharmaceutical bioreactor simulator is presented as an application. Diagnostics methods of ordinary multiple least squares regression are applied to partial least squares, including detection of hidden extrapolation.
dc.description.departmentMathematics
dc.formatText
dc.format.extent107 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationReiss, R. H. (2013). <i>Eigenvalues and eigenvectors in data dimension reduction for regression</i> (Unpublished thesis). Texas State University-San Marcos, San Marcos, Texas.
dc.identifier.urihttps://hdl.handle.net/10877/4696
dc.language.isoen
dc.subjectEigenvector
dc.subjectEigenvalue
dc.subjectDimension reduction
dc.subjectPower method
dc.subjectPartial least squares
dc.subject.lcshEigenvaluesen_US
dc.subject.lcshEigenvectorsen_US
dc.subject.lcshData reductionen_US
dc.titleEigenvalues and Eigenvectors in Data Dimension Reduction for Regression
dc.typeThesis
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University-San Marcos
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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