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Signal fraction analysis for subspace processing of high dimensional data

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dc.contributor.authorEmdad, Fatemeh, author
dc.contributor.authorKirby, Michael, advisor
dc.date.accessioned2024-03-13T19:26:14Z
dc.date.available2024-03-13T19:26:14Z
dc.date.issued2007
dc.description.abstractA general tool for computing subspaces that decomposes data into potentially useful features is proposed. The technique is called Signal Fraction Analysis (SFA). 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). Preprocessing mappings of the data is used in situations where domain specific knowledge is available as a guide. We suggest an optimization problem where these mapping functions may be adapted using a problem dependent objective function. These ideas are illustrated using Wavelet and Fourier filters applied to EEG data. A self-contained description of the motivating maximum noise fraction method is included and a procedure for estimating the covariance matrix of the noise is described. We extend SFA by introducing novel constraints and propose two new generalized SVD type problems for computing subspace representations. 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. Moreover, a second algorithm that uses noise adjustment in the data domain prior to kernelization is suggested. 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. This work establishes the potential of a SFA beamforming technique via its merger with a wide band MC-CDMA system. The details of non-overlapping window adaptive realization of SFA are introduced. We discuss the relationship between the SFA and DOA estimation via MUSIC. A novel structure for wide band MC-CDMA systems that utilizes the benefits of path diversity (inherent in direct sequence CDMA) and frequency diversity (inherent in MC-CDMA systems) is introduced. Simulations were performed to study the impact of noise perturbations on the performance of SFA. Simulations confirm that SFA enhances the performance and separability of interfering users. KSFA is applied to the classification of EEG data arising in the Brain Computer Interface Problem. We use Fourier and Wavelet filters to generate signal fractions as well as differencing methods.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Emdad_2007_3299779.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237709
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectclassification
dc.subjectcomponent analysis
dc.subjectkernel
dc.subjectnonlinear
dc.subjectsignal fraction analysis
dc.subjectsignal separation
dc.subjectsubspaces
dc.subjectmathematics
dc.titleSignal fraction analysis for subspace processing of high dimensional data
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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