Pasik-Duncan, BozennaOderio, Nicholas2018-10-222018-10-222017-13-312017http://dissertations.umi.com/ku:15662https://hdl.handle.net/1808/26902This paper presents and explains several methods of dimensionality reduction of data sets, beginning with the well known PCA and moving onto techniques that deal with data on a nonlinear manifold. Methods for handling data whose underlying structure is a nonlinear manifold are separated by whether or not sparse matrices are involved in the computation. Additionally, the methods discussed are demonstrated and compared by running them on data sets whose underlying structure is known. Results from same methods with different values for input parameters are also examined. Finally, some results on a small set of Persyst EEG data collected as a part of the Epilepsy Bioinformatics Study for Antiepileptogenic Therapy from the Laboratory of Neuro Imaging at USC Stevens Institute of Neuroimaging and Informatics in the Keck School of Medicine of USC is analyzed using some of these methods.46 pagesenCopyright held by the author.Applied mathematicsMathematicsapplicationDimensionality reductionprincipal component analysisThesishttps://orcid.org/0000-0002-3949-2511openAccess