A data mining and feature extraction technique called Signal
Fraction Analysis (SFA) is introduced. The method is applicable to
high dimensional data. The row-energy and column-energy
optimization problems for signal-to-signal ratios are investigated.
A generalized singular value problem is presented. This setting is
distinguished from the Singular Value Decomposition (SVD). Two new
generalized SVD type problems for computing subspace
representations is introduced. A connection between SFA and
Canonical Correlation Analysis is maintained. We implement and
investigate a nonlinear extension to SFA based on a kernel method,
i.e., Kernel SFA. We include a detailed derivation of the
methodology using kernel principal component analysis as a
prototype. These methods are compared using toy examples and the
benefits of KSFA are illustrated. The book studies the applications
of the proposed techniques in the brain EEG data analysis and beam-
forming in wireless communication systems.
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