Calculating Geometric median of 2D points

问题

I am calculating Geometric median of some (x,y) points in java. To calculate Geometric median, first i am calculating centroid of all the points, then this centroid is used to calculate Geometric median. My code works fine, but sometimes it goes to an infinite loop (i think.). The problem is with my while condition. This while condition should be change according to input points, but i don't know how. Below I am putting the complete code.

import java.util.ArrayList;

public class GeometricMedian {

    private static ArrayList<Point> points = new ArrayList<Point>();

    private class Point {
        private double x;
        private double y;

        Point(double a, double b) {
            x = a;
            y = b;
        }
    }

    public static void main(String[] args) {
        GeometricMedian gm = new GeometricMedian();
        gm.addPoints();
        Point centroid = gm.getCentroid();
        Point geoMedian = gm.getGeoMedian(centroid);
        System.out.println("GeometricMedian= {" + (float) geoMedian.x + ", "
                + (float) geoMedian.y + "}");
    }

    public void addPoints() {
        points.add(new Point(0, 1));
        points.add(new Point(2, 5));
        points.add(new Point(3, 1));
        points.add(new Point(4, 0));
    }

    public Point getCentroid() {
        double cx = 0.0D;
        double cy = 0.0D;
        for (int i = 0; i < points.size(); i++) {
            Point pt = points.get(i);
            cx += pt.x;
            cy += pt.y;
        }
        return new Point(cx / points.size(), cy / points.size());
    }

    public Point getGeoMedian(Point start) {
        double cx = 0;
        double cy = 0;

        double centroidx = start.x;
        double centroidy = start.y;
        do {
            double totalWeight = 0;
            for (int i = 0; i < points.size(); i++) {
                Point pt = points.get(i);
                double weight = 1 / distance(pt.x, pt.y, centroidx, centroidy);
                cx += pt.x * weight;
                cy += pt.y * weight;
                totalWeight += weight;
            }
            cx /= totalWeight;
            cy /= totalWeight;
        } while (Math.abs(cx - centroidx) > 0.5
                || Math.abs(cy - centroidy) > 0.5);// Probably this condition
                                                    // needs to change

        return new Point(cx, cy);
    }

    private static double distance(double x1, double y1, double x2, double y2) {
        x1 -= x2;
        y1 -= y2;
        return Math.sqrt(x1 * x1 + y1 * y1);
    }
}

Please help me to fix the bug, also if there exitis any better way to calculate Geometric median of some 2D points, write here. Thank you.

回答1:

I don't see why you need two loops. You only need the loop over all the points. What is the reason for the other one, in your view?

回答2:

One way to solve this is to iterate certain number of times. This similar to K-Means method where it either converges to a specific threshold or stops after a predefined number of iterations.

来源：https://stackoverflow.com/questions/10162273/calculating-geometric-median-of-2d-points

标签

java

median