Multilevel spectral clustering : graph partitions and image segmentation

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Computation for Design and Optimization Program.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Kong, Tian Fook

Advisor dc:contributor.advisor

• Gilbert Strang.

• Computation for Design and Optimization Program.

Statement 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45275

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45275