Question

I’m looking for java code (or a library) that calculates the earth mover’s distance (EMD) between two histograms. This could be directly or indirectly (e.g. using the Hungarian algorithm). I found several implementations of this in c/c++ (e.g. “Fast and Robust Earth Mover’s Distances”, but I’m wondering if there is a Java version readily available.

I will be using the EMD calculation to evaluate the approach given by this paper in the context of a science project I’m working on.

Update

Using a variety of resources I estimate that the code below should do the trick. determineMinCostAssignment is the calculation of the optimal assignment as determined by the Hungarian algorithm. For this I will be using the code from http://konstantinosnedas.com/dev/soft/munkres.htm
My main concern is the calculated flow: I am not sure if this is correct. Is there someone who can verify that this is correct or not?

    /**
 * Determines the Earth Mover's Distance between two histogram assuming an equal distance between two buckets of a histogram. The distance between
 * two buckets is equal to the differences in the indexes of the buckets.
 * 
 * @param threshold
 *          The maximum distance to use between two buckets.
 */
public static double determineEarthMoversDistance(double[] histogram1, double[] histogram2, int threshold) {
    if (histogram1.length != histogram2.length)
        throw new InvalidParameterException("Each histogram must have the same number of elements");

    double[][] groundDistances = new double[histogram1.length][histogram2.length];
    for (int i = 0; i < histogram1.length; ++i) {
        for (int j = 0; j < histogram2.length; ++j) {
            int abs_diff = Math.abs(i - j);
            groundDistances[i][j] = Math.min(abs_diff, threshold);
        }
    }

    int[][] assignment = determineMinCostAssignment(groundDistances);
    double costSum = 0, flowSum = 0;
    for (int i = 0; i < assignment.length; i++) {
        double cost = groundDistances[assignment[i][0]][assignment[i][1]];
        double flow = histogram2[assignment[i][1]];
        costSum += cost * flow;
        flowSum += flow;
    }
    return costSum / flowSum;
}

Answer 1

Here’s a pure Java port of the FastEMD algorithm, that I just released:
https://github.com/telmomenezes/JFastEMD