An Optimal Transport Perspective on Gamma Gaussian Inverse-Wishart Mixture Reduction

Date

2022-01-01

Author

D'Ortenzio, Alessandro
Manes, Costanzo
Orguner, Umut

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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Recent advances in the Optimal Transport theory allow to rewrite several known problems in a neat way, while providing a more general perspective. When dealing with mixture densities, or in general with intensities, such a framework naturally induces composite dissimilarities, together with corresponding Greedy Reduction and Refinement algorithms. In applications like target tracking in clutter, it is common to deal with the Mixture Reduction problem, since the optimal Bayesian recursion leads to a combinatorial explosion of hypotheses for the posterior distribution. Moreover, in the extended target case, more complex distributions are being considered to describe the features of an object, for instance the Gamma Gaussian inverse-Wishart density, which makes the reduction problem intrinsically more difficult. For the reasons above, having theoretically sound reduction algorithms results to be important for many practical problems. In this work, we will provide an optimal transport perspective to the Gamma Gaussian inverse-Wishart mixture reduction problem, together with algorithms which are suitable for real-time applications.

Subject Keywords

Optimal transport, Gamma distribution, Gaussian distribution, inverse-Wishart distribution, Mixture reduction

URI

https://hdl.handle.net/11511/99983

DOI

https://doi.org/10.23919/fusion49751.2022.9841295

Conference Name

25th International Conference of Information Fusion (FUSION)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

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Citation Formats

A. D’Ortenzio, C. Manes, and U. Orguner, “An Optimal Transport Perspective on Gamma Gaussian Inverse-Wishart Mixture Reduction,” presented at the 25th International Conference of Information Fusion (FUSION), Linköping, İsveç, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99983.