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Issue No. 11 - November (2009 vol. 31)
ISSN: 0162-8828
pp: 2093-2098
Alfred O. Hero III , University of Michigan, Ann Arbor
Raviv Raich , Oregon State University, Corvallis
William G. Finn , University of Michigan, Ann Arbor
Kevin M. Carter , Information Systems Technology Group, Lexington
ABSTRACT
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward euclidean representation exists. In this paper, we propose using the properties of information geometry and statistical manifolds in order to define similarities between data sets using the Fisher information distance. We will show that this metric can be approximated using entirely nonparametric methods, as the parameterization and geometry of the manifold is generally unknown. Furthermore, by using multidimensional scaling methods, we are able to reconstruct the statistical manifold in a low-dimensional euclidean space; enabling effective learning on the data. As a whole, we refer to our framework as Fisher Information Nonparametric Embedding (FINE) and illustrate its uses on practical problems, including a biomedical application and document classification.
INDEX TERMS
Information geometry, statistical manifold, dimensionality reduction, multidimensional scaling.
CITATION
Alfred O. Hero III, Raviv Raich, William G. Finn, Kevin M. Carter, "FINE: Fisher Information Nonparametric Embedding", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 31, no. , pp. 2093-2098, November 2009, doi:10.1109/TPAMI.2009.67
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