A Data-Dependent Algorithm for Querying Earth Mover's Distance with Low Doubling Dimensions

In this paper, we consider the following query problem: given two weighted point sets A and B in the Euclidean space ℝd, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than a pre-specified threshold T≥ 0. The problem finds a number of important applications in the fields of machine learning and data mining. In particular, we assume that the dimensionality d is not fixed and the sizes |A| and |B| are large. Therefore, most of existing EMD algorithms are not quite efficient to solve this problem due to their high complexities. Here, we consider the problem under the assumption that A and B have low doubling dimensions, which is common for high-dimensional data in real world. Inspired by the geometric method em net tree, we propose a novel ``data-dependent'' algorithm to avoid directly computing the EMD between A and B, so as to solve this query problem more efficiently. We also study the performance of our method on synthetic and real datasets. The experimental results suggest that our method can save a large amount of running time comparing with existing EMD algorithms.