Results 1 
1 of
1
Sketching EarthMover Distance on Graph Metrics ⋆
"... Abstract. We develop linear sketches for estimating the EarthMover distance between two point sets, i.e., the cost of the minimum weight matching between the points according to some metric. While Euclidean distance and Edit distance are natural measures for vectors and strings respectively, Earth ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We develop linear sketches for estimating the EarthMover distance between two point sets, i.e., the cost of the minimum weight matching between the points according to some metric. While Euclidean distance and Edit distance are natural measures for vectors and strings respectively, EarthMover distance is a wellstudied measure that is natural in the context of visual or metric data. Our work considers the case where the points are located at the nodes of an implicit graph and define the distance between two points as the length of the shortest path between these points. We first improve and simplify an existing result by Brody et al. [4] for the case where the graph is a cycle. We then generalize our results to arbitrary graph metrics. Our approach is to recast the problem of estimating EarthMover distance in terms of an ℓ1 regression problem. The resulting linear sketches also yield spaceefficient data stream algorithms in the usual way. 1