Baraniuk, Richard G.2013-03-082013-03-082012Dyer, Eva L.. "Endogenous Sparse Recovery." (2012) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/70235">https://hdl.handle.net/1911/70235</a>.https://hdl.handle.net/1911/70235Sparsity has proven to be an essential ingredient in the development of efficient solutions to a number of problems in signal processing and machine learning. In all of these settings, sparse recovery methods are employed to recover signals that admit sparse representations in a pre-specified basis. Recently, sparse recovery methods have been employed in an entirely new way; instead of finding a sparse representation of a signal in a fixed basis, a sparse representation is formed "from within" the data. In this thesis, we study the utility of this endogenous sparse recovery procedure for learning unions of subspaces from collections of high-dimensional data. We provide new insights into the behavior of endogenous sparse recovery, develop sufficient conditions that describe when greedy methods will reveal local estimates of the subspaces in the ensemble, and introduce new methods to learn unions of overlapping subspaces from local subspace estimates.82 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Applied sciencesApplied mathematicsElectrical engineeringThesisDyerETHESIS E.E. 2012 DYER