Stochastic Sampling of the Hyperspherical von Mises-Fisher Distribution Without Rejection Methods
Abstract:
We propose a novel sampling algorithm for the
von Mises–Fisher distribution on the unit hypersphere. Unlike
previous works, we show a solution for an arbitrary number of
dimensions without requiring rejection sampling. As a result, the
proposed algorithm has a deterministic runtime. The key idea
consists in applying the inversion method to a one-dimensional
subproblem and analytically calculating the integral occurring in
the distribution function. The proposed method is most efficient
for odd numbers of dimensions. We compare the algorithm to a
state-of-the-art rejection sampling method in simulations.
von Mises–Fisher distribution on the unit hypersphere. Unlike
previous works, we show a solution for an arbitrary number of
dimensions without requiring rejection sampling. As a result, the
proposed algorithm has a deterministic runtime. The key idea
consists in applying the inversion method to a one-dimensional
subproblem and analytically calculating the integral occurring in
the distribution function. The proposed method is most efficient
for odd numbers of dimensions. We compare the algorithm to a
state-of-the-art rejection sampling method in simulations.
| Zugehörige Institution(en) am KIT | Deutsch-Französisches Institut für Umweltforschung - Teilinstitut Karlsruhe (DFIU - Teilinstitut Karlsruhe) Institut für Anthropomatik und Robotik (IAR) |
| Publikationstyp | Proceedingsbeitrag |
| Jahr | 2015 |
| Sprache | Englisch |
| Identifikator | ISBN: 978-1-4673-7175-9 KITopen ID: 1000051079 |
| Erschienen in | Proceedings of the 10th IEEE ISIF Workshop on Sensor Data Fusion: Trends, Solutions, Applications (SDF 2015), 06 - 08 October 2015, Bonn, Germany |
| Verlag | IEEE, Piscataway (NJ) |