High Dimensional Data Analysis : 9783639074215 : 10 Aug 2008 : 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