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High Dimensional Data Analysis
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A data mining and feature extraction techniquecalled Signal Fraction Analysis (SFA) is introduced.The method is applicable to high dimensional data.The row-energy and column-energy optimizationproblems for signal-to-signal ratios areinvestigated.A generalized singular value problem is presented.This setting is distinguished from the SingularValue Decomposition (SVD).Two new generalized SVD type problems for computingsubspace representations is introduced. A connectionbetween SFA and Canonical Correlation Analysis ismaintained. We implement and investigate a nonlinearextension to SFA based on a kernel method, i.e.,Kernel SFA.We include a detailed derivation of the methodologyusing kernel principal component analysis as aprototype. These methods are compared using toyexamples and the benefits of KSFA are illustrated.The book studies the applications of the proposedtechniques in the brain EEG data analysis and beam-forming in wireless communication systems.
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