Skip to main content
Duke University Libraries
DukeSpace Scholarship by Duke Authors
  • Login
  • Ask
  • Menu
  • Login
  • Ask a Librarian
  • Search & Find
  • Using the Library
  • Research Support
  • Course Support
  • Libraries
  • About
View Item 
  •   DukeSpace
  • Theses and Dissertations
  • Duke Dissertations
  • View Item
  •   DukeSpace
  • Theses and Dissertations
  • Duke Dissertations
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Modes of Gaussian Mixtures and an Inequality for the Distance Between Curves in Space

Thumbnail
View / Download
3.6 Mb
Date
2012
Author
Fasy, Brittany Terese
Advisor
Edelsbrunner, Herbert
Repository Usage Stats
326
views
398
downloads
Abstract

This dissertation studiess high dimensional problems from a low dimensional perspective. First, we explore rectifiable curves in high-dimensional space by using the Fréchet distance between and total curvatures of the two curves to bound the difference of their lengths. We create this bound by mapping the curves into R^2 while preserving the length between the curves and increasing neither

the total curvature of the curves nor the Fr\'echet distance between them. The bound is independent of the dimension of the ambient Euclidean space, it improves upon a bound by Cohen-Steiner and Edelsbrunner for dimensions greater than three and it generalizes

a result by F\'ary and Chakerian.

In the second half of the dissertation, we analyze Gaussian mixtures. In particular, we consider the sum of n Gaussians, where each Gaussian is centered at the vertex of a regular n-simplex. Fixing the width of the Guassians and varying the diameter of the simplex from zero to infinity by increasing a parameter that we call the scale factor, we find the window of scale factors for which the Gaussian mixture has more modes, or local maxima, than components of the mixture.

We see that the extra mode created is subtle, but can be higher than the modes closer to the vertices of the simplex. In addition, we prove that all critical points are located on a set of one-dimensional lines (axes) connecting barycenters of complementary faces of

the simplex.

Type
Dissertation
Department
Computer Science
Subject
Computer science
Permalink
https://hdl.handle.net/10161/5793
Citation
Fasy, Brittany Terese (2012). Modes of Gaussian Mixtures and an Inequality for the Distance Between Curves in Space. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/5793.
Collections
  • Duke Dissertations
More Info
Show full item record
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.

Rights for Collection: Duke Dissertations


Works are deposited here by their authors, and represent their research and opinions, not that of Duke University. Some materials and descriptions may include offensive content. More info

Make Your Work Available Here

How to Deposit

Browse

All of DukeSpaceCommunities & CollectionsAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit DateThis CollectionAuthorsTitlesTypesBy Issue DateDepartmentsAffiliations of Duke Author(s)SubjectsBy Submit Date

My Account

LoginRegister

Statistics

View Usage Statistics
Duke University Libraries

Contact Us

411 Chapel Drive
Durham, NC 27708
(919) 660-5870
Perkins Library Service Desk

Digital Repositories at Duke

  • Report a problem with the repositories
  • About digital repositories at Duke
  • Accessibility Policy
  • Deaccession and DMCA Takedown Policy

TwitterFacebookYouTubeFlickrInstagramBlogs

Sign Up for Our Newsletter
  • Re-use & Attribution / Privacy
  • Harmful Language Statement
  • Support the Libraries
Duke University