Smith, Elin Rose, authorPeterson, Christopher Scott, 1963-, advisorBates, Daniel J. (Daniel James), 1979-, committee memberKirby, Michael, 1961-, committee memberMcConnell, Ross M., committee member2007-01-032007-01-032010http://hdl.handle.net/10217/44768We apply and develop pattern analysis techniques in the setting of data sets that are invariant under a group action. We apply Principal Component Analysis to data sets of images of a rotating object in Chapter 5 as a means of obtaining visual and low-dimensional representations of data. In Chapter 6, we propose an algorithm for finding distributions of points in a base space that are (locally) optimal in the sense that subspaces in the associated data bundle are distributed with locally maximal distance between neighbors. In Chapter 7, we define a distortion function that measures the quality of an approximation of a vector bundle by a set of points. We then use this function to compare the behavior of four standard distance metrics and one non-metric. Finally, in Chapter 8, we develop an algorithm to find the approximate intersection of two data sets.born digitaldoctoral dissertationsengCopyright 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.principal component analysispattern analysisminimal energy configurationimage analysisgroup actionsdata bundleGeometric group theoryGeometric analysisInvariant measuresCluster analysisPattern perceptionText