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Multilevel spectral clustering : graph partitions and image segmentation

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dc.contributor.advisor Gilbert Strang. en_US Kong, Tian Fook en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US 2009-04-29T17:19:04Z 2009-04-29T17:19:04Z 2008 en_US 2008 en_US
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. en_US
dc.description Includes bibliographical references (p. 145-146). en_US
dc.description.abstract While the spectral graph partitioning method gives high quality segmentation, segmenting large graphs by the spectral method is computationally expensive. Numerous multilevel graph partitioning algorithms are proposed to reduce the segmentation time for the spectral partition of large graphs. However, the greedy local refinement used in these multilevel schemes has the tendency of trapping the partition in poor local minima. In this thesis, I develop a multilevel graph partitioning algorithm that incorporates the inverse powering method with greedy local refinement. The combination of the inverse powering method with greedy local refinement ensures that the partition quality of the multilevel method is as good as, if not better than, segmenting the large graph by the spectral method. In addition, I present a scheme to construct the adjacency matrix, W and degree matrix, D for the coarse graphs. The proposed multilevel graph partitioning algorithm is able to bisect a graph (k = 2) with significantly shorter time than segmenting the original graph without the multilevel implementation, and at the same time achieving the same normalized cut (Ncut) value. The starting eigenvector, obtained by solving a generalized eigenvalue problem on the coarsest graph, is close to the Fiedler vector of the original graph. Hence, the inverse iteration needs only a few iterations to converge the starting vector. In the k-way multilevel graph partition, the larger the graph, the greater the reduction in the time needed for segmenting the graph. For the multilevel image segmentation, the multilevel scheme is able to give better segmentation than segmenting the original image. The multilevel scheme has higher success of preserving the salient part of an object. en_US
dc.description.abstract (cont.) In this work, I also show that the Ncut value is not the ultimate yardstick for the segmentation quality of an image. Finding a partition that has lower Ncut value does not necessary means better segmentation quality. Segmenting large images by the multilevel method offers both speed and quality. en_US
dc.description.statementofresponsibility by Tian Fook Kong. en_US
dc.format.extent 146 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title Multilevel spectral clustering : graph partitions and image segmentation en_US
dc.type Thesis en_US S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 310969204 en_US

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