Efficient Clustering Earth Mover’s Distance

Abstract

The two-class clustering problem is formulated as an integer convex optimisation problem which determines the maximum of the Earth Movers Distance (EMD) between two classes, constructing a bipartite graph with minimum flow and maximum inter-class EMD between two sets. Subsequently including the nearest neighbours of the start point in feature space and calculating the EMD for this labellings quickly converges to a robust optimum. A histogram of grey values with the number of bins b as the only parameter is used as feature, which makes run time complexity independent of the number of pixels. After convergence in $\mathcal{O}(b)$ steps, spatial correlations can be taken into account by total variational smoothing. Testing the algorithm on real world images from commonly used databases reveals that it is competitive to state-of-the-art methods, while it deterministically yields hard assignments without requiring any a priori knowledge of the input data or similarity matrices to be calculated.