The Earth Mover's distance is the Mallows distance: some insights from statistics

@inproceedings{citeulike:1850072, abstract = {The Earth Mover's distanc1e was first introduced as a purely empirical ways to measure texture and color similarities. We show that it has a rigorous probabilistic interpretation and is conceptually equivalent to the Mallows distance on probability distributions. The two distances are exactly the same when applied to probability distributions, but behave differently when applied to unnormalized distributions with different masses, called signatures. We discuss the advantages and disadvantages of both distances, and statistical issues involved in computing them from data. We also report some texture classification results for the Mallows distance applied to texture features and compare several ways of estimating feature distributions. In addition, we list some known probabilistic properties of this distance}, author = {Levina, E. and Bickel, P.}, booktitle = {Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on}, citeulike-article-id = {1850072}, journal = {Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on}, pages = {251--256 vol.2}, posted-at = {2007-11-01 08:50:38}, priority = {2}, title = {The Earth Mover's distance is the Mallows distance: some insights from statistics}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=937632}, volume = {2}, year = {2001} }

TY - CONF ID - citeulike:1850072 L3 - citeulike-article-id:1850072 N2 - The Earth Mover's distanc1e was first introduced as a purely empirical ways to measure texture and color similarities. We show that it has a rigorous probabilistic interpretation and is conceptually equivalent to the Mallows distance on probability distributions. The two distances are exactly the same when applied to probability distributions, but behave differently when applied to unnormalized distributions with different masses, called signatures. We discuss the advantages and disadvantages of both distances, and statistical issues involved in computing them from data. We also report some texture classification results for the Mallows distance applied to texture features and compare several ways of estimating feature distributions. In addition, we list some known probabilistic properties of this distance JF - Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on EP - 256 vol.2 TI - The Earth Mover's distance is the Mallows distance: some insights from statistics VL - 2 T2 - Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on SP - 251 AU - Levina, E AU - Bickel, P PY - 2001/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=937632 ER -