Multiresolution Analysis on the Symmetric Group
Abstract
There is no generally accepted way to define wavelets on permutations. We address this issue by introducing the notion of coset based multiresolution analysis (CMRA) on the symmetric group; find the corresponding wavelet functions; and describe a fast wavelet transform of O(n^p) complexity with small p for sparse signals (in contrast to the O(n^q n!) complexity typical of FFTs). We discuss potential applications in ranking, sparse approximation, and multi-object tracking.
Cite
Text
Kondor and Dempsey. "Multiresolution Analysis on the Symmetric Group." Neural Information Processing Systems, 2012.Markdown
[Kondor and Dempsey. "Multiresolution Analysis on the Symmetric Group." Neural Information Processing Systems, 2012.](https://mlanthology.org/neurips/2012/kondor2012neurips-multiresolution/)BibTeX
@inproceedings{kondor2012neurips-multiresolution,
title = {{Multiresolution Analysis on the Symmetric Group}},
author = {Kondor, Risi and Dempsey, Walter},
booktitle = {Neural Information Processing Systems},
year = {2012},
pages = {1637-1645},
url = {https://mlanthology.org/neurips/2012/kondor2012neurips-multiresolution/}
}