Geometric Data Analysis based on Optimal Mass Transportation

Simon Kai Hung Lam Deerfield Academy

S.-T. Yau High School Science Awarded Papers mathscidoc:1801.35016

Yau Science Award (Math), 2017.12
3D shape classification plays a fundamental role in geometric big data analysis. This work proposes a novel method for shape classification based on optimal mass transportation theory. The Riemann surfaces are mapped onto canonical domains conformally based on uniformization theorem. The conformal factor function is treated as probability distribution on the canonical domain. For each pair of probability distributions, the optimal mass transportation map is computed by solving Monge-AmperĀ“e equation. The transportation cost is theWasserstein distance between two distributions. By using this distance, geometric classification based on clustering can be performed. The method is applied to 3D human facial expression recognition, which demonstrates the efficiency and efficacy of the method.
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@inproceedings{simon2017geometric,
  title={Geometric Data Analysis based on Optimal Mass Transportation},
  author={Simon Kai Hung Lam},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113195659310123889},
  booktitle={Yau Science Award (Math)},
  year={2017},
}
Simon Kai Hung Lam. Geometric Data Analysis based on Optimal Mass Transportation. 2017. In Yau Science Award (Math). http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180113195659310123889.
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