Earth mover distance over high-dimensional spaces

The Earth Mover Distance (EMD) between two equalsize sets of points in Rd is defined to be the minimum cost of a bipartite matching between the two pointsets. It is a natural metric for comparing sets of features, and as such, it has received significant interest in computer vision. Motivated by recent developments in that area, we address computational problems involving EMD over high-dimensional pointsets. A natural approach is to embed the EMD metric into 1, and use the algorithms designed for the latter space. However, Khot and Naor [KN06] show that any embedding of EMD over the d-dimensional Hamming cube into 1 must incur a distortion (d), thus practically losing all distance information. We circumvent this roadblock by focusing on sets with cardinalities upperbounded by a parameter s, and achieve a distortion of only O(log s

• Type: Conference
• Year: 2008
• Where: SODA
• Authors: Alexandr Andoni, Piotr Indyk, Robert Krauthgamer
• Keywords: Algorithms, Earth Mover Distance, Lower Bound, Problems Involving Emd, SODA 2008