Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.
 

Spectral curvature clustering for hybrid linear modeling.

Loading...
Thumbnail Image

Persistent link to this item

Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

Spectral curvature clustering for hybrid linear modeling.

Published Date

2009-07

Publisher

Type

Thesis or Dissertation

Abstract

The problem of Hybrid Linear Modeling (HLM) is to model and segment data using a mixture of affine subspaces. Many algorithms have been proposed to solve this problem, however, probabilistic analysis of their performance is missing. In this thesis we develop the Spectral Curvature Clustering (SCC) algorithm as a combination of Govindu's multi-way spectral clustering framework (CVPR 2005) and Ng et al.'s spectral clustering algorithm (NIPS 2001) while introducing a new affinity measure. Our analysis shows that if the given data is sampled from a mixture of distributions concentrated around affine subspaces, then with high sampling probability the SCC algorithm segments well the different underlying clusters. The goodness of clustering depends on the within-cluster errors, the between-clusters interaction, and a tuning parameter applied by SCC. Supported by the theory, we then present several novel techniques for improving the performance of the algorithm. Specifically, we suggest an iterative sampling procedure to improve the existing uniform sampling strategy, an automatic scheme of inferring the tuning parameter from data, a precise initialization procedure for K-means, as well as a simple strategy for isolating outliers. The resulting algorithm requires only linear storage and takes linear running time in the size of the data. We compare it with other state-of-the-art methods on a few artificial instances of affine subspaces. Application of the algorithm to several real-world problems is also discussed.

Description

University of Minnesota Ph.D. dissertation. July 2009 Major: Mathematics. Advisor: Gilad Lerman. 1 computer file (PDF); ix, 91 pages, appendices A. Ill. (some col.)

Related to

Replaces

License

Collections

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Other identifiers

Suggested citation

Chen, Guangliang. (2009). Spectral curvature clustering for hybrid linear modeling.. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/53398.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.