Title:
Statistical Modeling of High-Dimensional Nonlinear Systems: A Projection Pursuit Solution

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dc.contributor.advisor Sadegh, Nader
dc.contributor.author Swinson, Michael D. en_US
dc.contributor.committeeMember Liang, Steven
dc.contributor.committeeMember Shapiro, Alexander
dc.contributor.committeeMember Ume, Charles
dc.contributor.committeeMember Vidakovic, Brani
dc.contributor.department Mechanical Engineering en_US
dc.date.accessioned 2006-01-18T22:23:04Z
dc.date.available 2006-01-18T22:23:04Z
dc.date.issued 2005-11-28 en_US
dc.description.abstract Despite recent advances in statistics, artificial neural network theory, and machine learning, nonlinear function estimation in high-dimensional space remains a nontrivial problem. As the response surface becomes more complicated and the dimensions of the input data increase, the dreaded "curse of dimensionality" takes hold, rendering the best of function approximation methods ineffective. This thesis takes a novel approach to solving the high-dimensional function estimation problem. In this work, we propose and develop two distinct parametric projection pursuit learning networks with wide-ranging applicability. Included in this work is a discussion of the choice of basis functions used as well as a description of the optimization schemes utilized to find the parameters that enable each network to best approximate a response surface. The essence of these new modeling methodologies is to approximate functions via the superposition of a series of piecewise one-dimensional models that are fit to specific directions, called projection directions. The key to the effectiveness of each model lies in its ability to find efficient projections for reducing the dimensionality of the input space to best fit an underlying response surface. Moreover, each method is capable of effectively selecting appropriate projections from the input data in the presence of relatively high levels of noise. This is accomplished by rigorously examining the theoretical conditions for approximating each solution space and taking full advantage of the principles of optimization to construct a pair of algorithms, each capable of effectively modeling high-dimensional nonlinear response surfaces to a higher degree of accuracy than previously possible. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 2922469 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/7554
dc.language.iso en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Prediction en_US
dc.subject Statistical modeling
dc.subject Function approximation
dc.subject High-dimensional modeling
dc.subject Regression
dc.subject Modeling
dc.subject PPLM
dc.subject PPLN
dc.subject Projection pursuit
dc.subject Data mining
dc.subject.lcsh Nonlinear systems Statistical methods en_US
dc.subject.lcsh Approximation theory en_US
dc.subject.lcsh Mathematical optimization en_US
dc.title Statistical Modeling of High-Dimensional Nonlinear Systems: A Projection Pursuit Solution en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Sadegh, Nader
local.contributor.corporatename George W. Woodruff School of Mechanical Engineering
local.contributor.corporatename College of Engineering
relation.isAdvisorOfPublication 43b818a8-518a-4721-bffc-becb11ba04e0
relation.isOrgUnitOfPublication c01ff908-c25f-439b-bf10-a074ed886bb7
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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