### Treating Cancer with infinite von Mises-Fisher Mixture Models

*Using an Infinite von Mises-Fisher Model to Cluster Treatment Beam Directions in External Radiation therapy* [pdf]

Mark Bangert, Philipp Hennig, and Uwe Oelfke

International Conference on Machine Learning and Applications (ICMLA),
2010, Washington D.C.

Finding optimal treatment plans in radiation therapy is a high-dimensional, nonconvex optimization problem. As is often the case in such problems, good heuristics can drastically reduce the complexity of such problems, albeit at the cost of some approximation error.

Here, we present such a heuristic. First, optimal beam directions are calculated independently for discretized regions of the treatment volume. In a second step, these beam directions are grouped into a smaller number of clusters, which provide a sufficiently simple basis for a numerical optimization scheme.

Since the treatment directions are points on a unit sphere, we require a nonparametric clustering method on this space. For this purpose, we construct a Dirichlet process mixture model of von Mises Fisher distributions, in which inference can be performed using Gibbs sampling. This is a reasonably straightforward extension of similar models using Gaussian distributions (see Rasmussen, NIPS 2000).