Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Convergence of the k-means minimization problem using Γ-convergence

Tools
- Tools
+ Tools

Thorpe, Matthew, Theil, Florian, Johansen, Adam M. and Cade, Neil (2015) Convergence of the k-means minimization problem using Γ-convergence. SIAM Journal on Applied Mathematics, 75 (6). pp. 2444-2474. doi:10.1137/140974365

An open access version can be found in:
  • ArXiv
Official URL: http://dx.doi.org/10.1137/140974365

Request Changes to record.

Abstract

The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply the $k$-means method to infinite dimensional problems, for example, multiple target tracking and smoothing problems in the presence of unknown data association. Via a $\Gamma$-convergence argument, the associated optimization problem is shown to converge in the sense that both the $k$-means minimum and minimizers converge in the large data limit to quantities which depend upon the observed data only through its distribution. The theory is supplemented with two examples to demonstrate the range of problems now accessible by the $k$-means method. The first example combines a nonparametric smoothing problem with unknown data association. The second addresses tracking using sparse data from a network of passive sensors.

Item Type: Journal Article
Alternative Title:
Divisions: Faculty of Science > Statistics
Journal or Publication Title: SIAM Journal on Applied Mathematics
Publisher: Society for Industrial and Applied Mathematics
ISSN: 0036-1399
Official Date: 12 November 2015
Dates:
DateEvent
12 November 2015Available
31 August 2015Accepted
24 June 2014Submitted
Volume: 75
Number: 6
Page Range: pp. 2444-2474
DOI: 10.1137/140974365
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Open Access Version:
  • ArXiv

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us