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Modeling data using directional distributions: Part II

2007

Technical Report

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High-dimensional data is central to most data mining applications, and only recently has it been modeled via directional distributions. In [Banerjee et al., 2003] the authors introduced the use of the von Mises-Fisher (vMF) distribution for modeling high-dimensional directional data, particularly for text and gene expression analysis. The vMF distribution is one of the simplest directional distributions. TheWatson, Bingham, and Fisher-Bingham distributions provide distri- butions with an increasing number of parameters and thereby commensurately increased modeling power. This report provides a followup study to the initial development in [Banerjee et al., 2003] by presenting Expectation Maximization (EM) procedures for estimating parameters of a mixture of Watson (moW) distributions. The numerical challenges associated with parameter estimation for both of these distributions are significantly more difficult than for the vMF distribution. We develop new numerical approximations for estimating the parameters permitting us to model real- life data more accurately. Our experimental results establish that for certain data sets improved modeling power translates into better results.

Author(s): Sra, S. and Jain, P. and Dhillon, I.
Number (issue): TR-07-05
Year: 2007
Month: February
Day: 0

Department(s): Empirical Inference
Bibtex Type: Technical Report (techreport)

Institution: University of Texas, Austin, TX, USA

Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF

BibTex

@techreport{5506,
  title = {Modeling data using directional distributions: Part II},
  author = {Sra, S. and Jain, P. and Dhillon, I.},
  number = {TR-07-05},
  organization = {Max-Planck-Gesellschaft},
  institution = {University of Texas, Austin, TX, USA},
  school = {Biologische Kybernetik},
  month = feb,
  year = {2007},
  month_numeric = {2}
}