An Assessment of Alternative Strategies for Constructing EMD-Based Kernel Functions for Use in an SVM for Image Classification

Because of their sound theoretical underpinnings, support vector machines (SVMs) have very impressive performance in classification. However, the use of SVMs is constrained by the fact that the affinity measure that is used to build the classifier must produce a kernel matrix that is positive semi-definite (PSD). This is normally not a problem, however many very effective affinity measures are known that will not produce a PSD kernel matrix. One such measure is the Earth-Mover's distance (EMD) for quantifying the difference between images. In this paper we consider three methods for producing a PSD kernel from the EMD and compare SVM-based classifiers that use these measures against a nearest neighbour classifier built directly on the EMD. We find that two of these kernelised EMD measures are effective and the resulting SVMs are better than the nearest neighbour alternatives.