English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

Banerjee, A., Dhillon, I., Ghosh, J., & Sra, S. (2005). Clustering on the Unit Hypersphere using von Mises-Fisher Distributions. The Journal of Machine Learning Research, 6, 1345-1382.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D419-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0004-D783-5
Genre: Journal Article

Files

show Files

Locators

show

Creators

show
hide
 Creators:
Banerjee, A, Author
Dhillon , I, Author
Ghosh, J, Author
Sra, S1, Author              
Affiliations:
1External Organizations, ou_persistent22              

Content

show
hide
Free keywords: -
 Abstract: Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a generative mixture-model approach to clustering directional data based on the von Mises-Fisher (vMF) distribution, which arises naturally for data distributed on the unit hypersphere. In particular, we derive and analyze two variants of the Expectation Maximization (EM) framework for estimating the mean and concentration parameters of this mixture. Numerical estimation of the concentration parameters is non-trivial in high dimensions since it involves functional inversion of ratios of Bessel functions. We also formulate two clustering algorithms corresponding to the variants of EM that we derive. Our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community, and obtains the spherical kmeans algorithm (kmeans with cosine similarity) as a special case of both variants. Empirical results on clustering of high-dimensional text and gene-expression data based on a mixture of vMF distributions show that the ability to estimate the concentration parameter for each vMF component, which is not present in existing approaches, yields superior results, especially for difficult clustering tasks in high-dimensional spaces.

Details

show
hide
Language(s):
 Dates: 2005-09
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 5126
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: The Journal of Machine Learning Research
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Cambridge, MA : MIT Press
Pages: - Volume / Issue: 6 Sequence Number: - Start / End Page: 1345 - 1382 Identifier: ISSN: 1532-4435
CoNE: https://pure.mpg.de/cone/journals/resource/111002212682020_1