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dc.contributor.authorAliyari Ghassabeh, Youness
dc.contributor.otherQueen's University (Kingston, Ont.). Theses (Queen's University (Kingston, Ont.))en
dc.date2013-09-30 18:01:12.959en
dc.date.accessioned2013-10-01T22:56:21Z
dc.date.available2013-10-01T22:56:21Z
dc.date.issued2013-10-01
dc.identifier.urihttp://hdl.handle.net/1974/8365
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-30 18:01:12.959en
dc.description.abstractMean shift (MS) and subspace constrained mean shift (SCMS) algorithms are non-parametric, iterative methods to find a representation of a high dimensional data set on a principal curve or surface embedded in a high dimensional space. The representation of high dimensional data on a principal curve or surface, the class of mean shift type algorithms and their properties, and applications of these algorithms are the main focus of this dissertation. Although MS and SCMS algorithms have been used in many applications, a rigorous study of their convergence is still missing. This dissertation aims to fill some of the gaps between theory and practice by investigating some convergence properties of these algorithms. In particular, we propose a sufficient condition for a kernel density estimate with a Gaussian kernel to have isolated stationary points to guarantee the convergence of the MS algorithm. We also show that the SCMS algorithm inherits some of the important convergence properties of the MS algorithm. In particular, the monotonicity and convergence of the density estimate values along the sequence of output values of the algorithm are shown. We also show that the distance between consecutive points of the output sequence converges to zero, as does the projection of the gradient vector onto the subspace spanned by the D-d eigenvectors corresponding to the D-d largest eigenvalues of the local inverse covariance matrix. Furthermore, three new variations of the SCMS algorithm are proposed and the running times and performance of the resulting algorithms are compared with original SCMS algorithm. We also propose an adaptive version of the SCMS algorithm to consider the effect of new incoming samples without running the algorithm on the whole data set. As well, we develop some new potential applications of the MS and SCMS algorithm. These applications involve finding straight lines in digital images; pre-processing data before applying locally linear embedding (LLE) and ISOMAP for dimensionality reduction; noisy source vector quantization where the clean data need to be estimated before the quanization step; improving the performance of kernel regression in certain situations; and skeletonization of digitally stored handwritten characters.en_US
dc.languageenen
dc.language.isoenen_US
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectSubspace constrained mean shift algorithmen_US
dc.subjectNoisy source vector quantizationen_US
dc.subjectDimensionality reductionen_US
dc.subjectPrincipal curveen_US
dc.subjectUnsupervised learningen_US
dc.subjectConvergenceen_US
dc.subjectPrincipal surfaceen_US
dc.subjectMean shift algorithmen_US
dc.titleOn the Convergence and Applications of Mean Shift Type Algorithmsen_US
dc.typethesisen_US
dc.description.degreePh.Den
dc.contributor.supervisorLinder, Tamásen
dc.contributor.supervisorTakahara, Glenen
dc.contributor.departmentMathematics and Statisticsen


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