Distance between Histograms with Shuffled Cost Matrix

Authors:
Sung-Hyuk Cha
Affiliations:
Department of Computer Science, Pace University, Pleasantville NY 10570
Venue:
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2008

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Abstract

Comparing two distributions is of fundamental importance to statistics and pattern recognition. The earth mover's distance (EMD ) has been considered an excellent distance measure between two distributions. It is defined to minimize the cost using a given cost matrix and formulated as the transportation problem which is a hard optimization problem. There are three special type cost matrices where efficient algorithms are known: nominal, ordinal, and modulo. Here the problem of identifying whether a given cost matrix has the shuffled ordinal property is considered and if so, the linear time complexity algorithm can be applied to compute the EMD efficiently.