Work

On the Definiteness of Earth Mover’s Distance and Its Relation to Set Intersection

Year: 2017

Type: article

Abstract: Positive definite (PD) kernels are an important tool in machine learning that enable efficient solutions to otherwise difficult or intractable problems by implicitly linearizing the problem geometry. In this paper, we develop a set-theoretic interpretation of the earth mover's distance (EMD) and propose earth mover's intersection (EMI), a PD analog to EMD for sets of different sizes. We provide conditions under which EMD or certain approximations to EMD are negative definite. We also present a PD-preserving transformation that can be applied to any kernel and can also be used to derive PD EMD-based kernels and show that the Jaccard index is simply the result of this transformation. Finally, we evaluate kernels based on EMI and the proposed transformation versus EMD in various computer vision tasks and show that EMD is generally inferior even with indefinite kernel techniques.

Source: IEEE Transactions on Cybernetics

DOI: 10.1109/tcyb.2017.2761798

Authors: Andrew Gardner, Christian A. Duncan, Jinko Kanno, Rastko R. Selmic

Institutions: Louisiana Tech University, Quinnipiac University, Concordia University

Language: English

Topic: Image Retrieval and Classification Techniques

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Aeronautics and Space Administration, Louisiana Space Consortium

Awards: G2486562457, LOUISIANA, THROUGH ITS COLLEGES AND UNIVERSITIES, SHOULD PLAY A SIGNIFICANT ROLE IN OUR NATION S AEROSPACE FUTURE. THIS IS OUR VISION. AS NASA IS AN