Hyperspherical Dirac Mixture Reapproximation
@article{Li2021HypersphericalDM, title={Hyperspherical Dirac Mixture Reapproximation}, author={Kailai Li and Florian Pfaff and Uwe D. Hanebeck}, journal={ArXiv}, year={2021}, volume={abs/2110.10411} }
We propose a novel scheme for efficient Dirac mixture modeling of distributions on unit hyperspheres. A so-called hyperspherical localized cumulative distribution (HLCD) is introduced as a local and smooth characterization of the underlying continuous density in hyperspherical domains. Based on HLCD, a manifold-adapted modification of the Cramér–von Mises distance (HCvMD) is established to measure the statistical divergence between two Dirac mixtures of arbitrary dimensions. Given a (source…
3 Citations
Dirac Mixture Reduction Using Wasserstein Distances on Projected Cumulative Distributions
- Computer Science2022 25th International Conference on Information Fusion (FUSION)
- 2022
The Wasserstein distance is established as a suitable measure to compare two Dirac mixtures and an iterative algorithm is proposed to minimize the sliced Wasserstone distance between the given distribution and approximation.
Circular Discrete Reapproximation
- Computer Science2022 25th International Conference on Information Fusion (FUSION)
- 2022
The circular Cramer-von Mises distance (CCvMD) is proposed to measure the statistical divergence between two circular discrete models based on a smooth characterization of the localized cumulative distribution.
Deterministic Sampling on the Circle Using Projected Cumulative Distributions
- Mathematics2022 25th International Conference on Information Fusion (FUSION)
- 2022
This work compares cumulatives of probability densities in the Radon space and proposes a method for deterministic sampling of arbitrary continuous angular density functions that can draw arbitrary numbers of deterministic samples and therefore improve the quality of state estimation.
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