Computer Science Department
School of Computer Science, Carnegie Mellon University


Computing the Volume Element of a
Family of Metrics on the Multinomial Simplex

Guy Lebanon

May 2003

Keywords: Riemannian geometry, information geometry, metric learning, text classification

We compute the differential volume element and the total volume of a family of metrics on the multinomial simplex. The metric family is composed of pull-back of the Fisher information metric through a continuous group of transformations. This note complements the paper by Lebanon that describes a metric learning framework and applies the results below to text classification.

10 pages

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