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Colorado State University

1. Stiverson, Shannon J. Adaptation of K-means-type algorithms to the Grassmann manifold, An.

Degree: MS(M.S.), Mathematics, 2019, Colorado State University

The Grassmann manifold provides a robust framework for analysis of high-dimensional data through the use of subspaces. Treating data as subspaces allows for separability between data classes that is not otherwise achieved in Euclidean space, particularly with the use of the smallest principal angle pseudometric. Clustering algorithms focus on identifying similarities within data and highlighting the underlying structure. To exploit the properties of the Grassmannian for unsupervised data analysis, two variations of the popular K-means algorithm are adapted to perform clustering directly on the manifold. We provide the theoretical foundations needed for computations on the Grassmann manifold and detailed derivations of the key equations. Both algorithms are then thoroughly tested on toy data and two benchmark data sets from machine learning: the MNIST handwritten digit database and the AVIRIS Indian Pines hyperspectral data. Performance of algorithms is tested on manifolds of varying dimension. Unsupervised classification results on the benchmark data are compared to those currently found in the literature. Advisors/Committee Members: Kirby, Michael (advisor), Adams, Henry (committee member), Ben-Hur, Asa (committee member).

Subjects/Keywords: Grassmannian; LBG; clustering; subspaces; K-means

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Stiverson, S. J. (2019). Adaptation of K-means-type algorithms to the Grassmann manifold, An. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/195396

Chicago Manual of Style (16th Edition):

Stiverson, Shannon J. “Adaptation of K-means-type algorithms to the Grassmann manifold, An.” 2019. Masters Thesis, Colorado State University. Accessed July 20, 2019. http://hdl.handle.net/10217/195396.

MLA Handbook (7th Edition):

Stiverson, Shannon J. “Adaptation of K-means-type algorithms to the Grassmann manifold, An.” 2019. Web. 20 Jul 2019.

Vancouver:

Stiverson SJ. Adaptation of K-means-type algorithms to the Grassmann manifold, An. [Internet] [Masters thesis]. Colorado State University; 2019. [cited 2019 Jul 20]. Available from: http://hdl.handle.net/10217/195396.

Council of Science Editors:

Stiverson SJ. Adaptation of K-means-type algorithms to the Grassmann manifold, An. [Masters Thesis]. Colorado State University; 2019. Available from: http://hdl.handle.net/10217/195396

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