PowerPoint Presentation - Dimension reduction in large data sets

Finding PCs/EOFs

•The optimisation problem which defines PCs turns out, like many in multivariate analysis, to be an eigenvalue problem

•The variances of the PCs are eigenvalues of the covariance (or correlation) matrix of x, in descending order, and the vectors of coefficients ak are the corresponding eigenvectors

•This is the usual way of finding PCs, though other algorithms exist e.g using the singular value decomposition of the column-centred data matrix

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