Code repository for the study
"A solution for the mean parametrization of the von Mises-Fisher distribution"
This code repository contains an implementation of (gradient / Hessian of) the log-partition function and negative entropy function for the D-dimensional von Mises-Fisher distribution, alongside code for fitting mixtures of vMF distribution in both natural and mean parametrization, all in Python. Sparse matrix support allows fast execution in high-dimensional feature spaces when features are sparse, as is common in document embeddings such as TF-IDF.
We make use of the mean-parameterized form in Bregman clustering for document clustering in high-dimensional (>25k dim) text embedding spaces, for the classical document datasets '20-newsgroups' and 'classic3'.
The example notebook contains a small toy example of Bregman clustering that fits a mixture of von Mises-Fisher distribution in mean paramtrization to several hundred data points in
The von Mises-Fisher distribution vMF(
with base measure
As a natural exponential family with strictly convex log-partition function, the vMF family of distributions can equivalently be written as
with 'negative entropy' function
and mean parameter
We derived a second-order ODE on