Metric-Preserving Reduction of Earth Mover’s Distance and its Application to Non-negative Matrix Factorization

Abstract

We prove that the earth mover’s distance problem reduces to a problem withhalf the number of constraints regardless of the ground distance, and propose a furtherreduced formulation when the ground distance comes from a graph with a homogeneousneighborhood structure. We also propose to apply our formulation to the non-negativematrix factorization