Eigenvalues and Eigenvectors in Data Dimension Reduction for Regression
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A 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.