Multi-object tracking with representations of the symmetric group

Risi Kondor, Andrew Howard, Tony Jebara
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:211-218, 2007.

Abstract

We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain “low frequency” Fourier components. The second is that Bayesian updates of these components can be efficiently realized by extensions of Clausen’s FFT for the symmetric group.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-kondor07a, title = {Multi-object tracking with representations of the symmetric group}, author = {Kondor, Risi and Howard, Andrew and Jebara, Tony}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {211--218}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/kondor07a/kondor07a.pdf}, url = {https://proceedings.mlr.press/v2/kondor07a.html}, abstract = {We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain “low frequency” Fourier components. The second is that Bayesian updates of these components can be efficiently realized by extensions of Clausen’s FFT for the symmetric group.} }
Endnote
%0 Conference Paper %T Multi-object tracking with representations of the symmetric group %A Risi Kondor %A Andrew Howard %A Tony Jebara %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-kondor07a %I PMLR %P 211--218 %U https://proceedings.mlr.press/v2/kondor07a.html %V 2 %X We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain “low frequency” Fourier components. The second is that Bayesian updates of these components can be efficiently realized by extensions of Clausen’s FFT for the symmetric group.
RIS
TY - CPAPER TI - Multi-object tracking with representations of the symmetric group AU - Risi Kondor AU - Andrew Howard AU - Tony Jebara BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-kondor07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 211 EP - 218 L1 - http://proceedings.mlr.press/v2/kondor07a/kondor07a.pdf UR - https://proceedings.mlr.press/v2/kondor07a.html AB - We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain “low frequency” Fourier components. The second is that Bayesian updates of these components can be efficiently realized by extensions of Clausen’s FFT for the symmetric group. ER -
APA
Kondor, R., Howard, A. & Jebara, T.. (2007). Multi-object tracking with representations of the symmetric group. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:211-218 Available from https://proceedings.mlr.press/v2/kondor07a.html.

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