KMean 聚类

1 解决什么问题

假设二维坐标轴上有一些点，现在让你把这些点分个类。于是对我们来说，这个分类似乎就是把距离相近的点画到一类中去。

1. 假设要划分N类，坐标点M个
2. 从M个坐标点随机选取N个点，作为每个分类的中心点，这N个点的列表记录为centerPointList
3. 遍历M个坐标点中的每个点
   • 计算当前点和N个中心点的距离，dis1、dis2 ... disN
   • 从dis1、dis2 ... disN找到最小的距离的下标。下标记录为cluster，那么这个cluster就是这次遍历时候当前点归属的分类。
4. 步骤3结束后，每个点都会归属到某个分类。计算每个分类中点集合的均值，把这个均值作为新的中心点，替换掉centerPointList。
5. 重复3、4直到重复次数大于约定次数，或者中心点变化较小。此时就可以知道每个点归属的分类。

2 java实现计算二维点的聚类案例

package com.forezp.kmean;

import com.google.common.collect.Lists;
import com.google.common.collect.Maps;

import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.Random;

/**
 * @author yuegang
 */
public class KMeanCluster {
    /**
     * 表示二维空间中的点
     */
    public static class Point {
        Integer x = 0;
        Integer y = 0;

        public Point() {
        }

        public Point(Integer x, Integer y) {
            this.x = x;
            this.y = y;
        }

        public void incX(Integer x) {
            this.x += x;
        }

        public void incY(int y) {
            this.y += y;
        }

        public Integer getX() {
            return x;
        }

        public void setX(Integer x) {
            this.x = x;
        }

        public Integer getY() {
            return y;
        }

        public void setY(Integer y) {
            this.y = y;
        }

        @Override
        public String toString() {
            return "(" + x + ", " + y + ")";
        }
    }

    /**
     * 表示二维空间中的点
     * 下标是点的顺序
     */
    private final List<Point> pointIndexDataMap;

    private final List<List<Point>> centerPointList = Lists.newArrayList(); // 记录每一个分类的中心点

    private final List<Integer> pointClusterMap = Lists.newArrayList(); // 点所属的分类

    private int index = 0; // 计算次数
    private int clusterCount = 0; // 分类个数

    public KMeanCluster(List<Point> pointIndexDataMap, int clusterCount) {
        this.pointIndexDataMap = pointIndexDataMap;
        this.clusterCount = clusterCount;
        index = 0;
        initCenterPoint();
        initCluster(pointIndexDataMap);
    }

    private void initCluster(List<Point> pointIndexDataMap) {
        // 初始化每个点的分类，设置一个没有意义的值
        for (int j = 0; j < pointIndexDataMap.size(); ++j) {
            pointClusterMap.add(-1);
        }
    }

    private void initCenterPoint() {
        List<Point> objects = Lists.newArrayListWithExpectedSize(clusterCount);
        List<Integer> yList = Lists.newArrayListWithExpectedSize(clusterCount);
        Random random = new Random();

        for (int i = 0; i < clusterCount; ++i) { // 注意这个不能相同
            int i1 = random.nextInt(pointIndexDataMap.size());
            while (yList.contains(i1)) {
                i1 = random.nextInt(pointIndexDataMap.size());
            }
            yList.add(i1);
        }

        for (int i = 0; i < clusterCount; ++i) {
            objects.add(pointIndexDataMap.get(yList.get(i)));
        }
        centerPointList.add(objects);
    }

    public void calc() {
        List<Point> pointIndices = centerPointList.get(index);

        for (int i = 0; i < pointIndexDataMap.size(); ++i) {
            Point point = pointIndexDataMap.get(i);
            // 计算该点和那个簇最近，把把归属到这个簇中。

            int cluster = 0;
            double min = Double.MAX_VALUE;

            for (int inc = 0; inc < pointIndices.size(); ++inc) {
                Point point1 = pointIndices.get(inc);
                Integer x = point.getX();
                Integer y = point.getY();
                Integer x1 = point1.getX();
                Integer y1 = point1.getY();

                int i1 = x - x1;
                int i2 = y - y1;
                int total = i1 * i1 + i2 * i2;
                double sqrt = Math.sqrt(total);
                if (sqrt < min) {
                    min = sqrt;
                    cluster = inc;
                }
            }
            pointClusterMap.set(i, cluster);
        }
        // 计算每个族的中心点；
        int size = centerPointList.get(0).size();
        Map<Integer, Point> map = Maps.newTreeMap();
        Map<Integer, Integer> cluterCount = Maps.newHashMapWithExpectedSize(size);
        for (int i = 0; i < pointClusterMap.size(); ++i) {
            int cluster = pointClusterMap.get(i);

            Point point = map.computeIfAbsent(cluster, sss -> new Point());
            cluterCount.put(cluster, cluterCount.getOrDefault(cluster, 0) + 1);

            Point point1 = pointIndexDataMap.get(i);
            point.incX(point1.getX());
            point.incY(point1.getY());
        }

        for (Map.Entry<Integer, Point> integerPointEntry : map.entrySet()) {
            Integer key = integerPointEntry.getKey();
            Point point = integerPointEntry.getValue();
            Integer integer = cluterCount.get(key);

            point.setX(point.getX() / integer);
            point.setY(point.getY() / integer);
        }

        ++index;
        Map<Integer, List<Point>> curClassfiyMap = Maps.newTreeMap();
        for (int i = 0; i < pointClusterMap.size(); ++i) {
            Point point = pointIndexDataMap.get(i);
            Integer classfly = pointClusterMap.get(i);
            List<Point> points = curClassfiyMap.computeIfAbsent(classfly, k -> Lists.newArrayList());
            points.add(point);
        }
        List<Point> curCenterPointList = new ArrayList<>(map.values());
        centerPointList.add(curCenterPointList);
        show(curClassfiyMap, curCenterPointList);
    }

    private void show(Map<Integer, List<Point>> curClassfiyMap, List<Point> curCenterPointList) {
        System.out.println("计算次数：" + index);
        System.out.println("当前分类：" + curClassfiyMap);
        System.out.println("当前中心点：" + curCenterPointList);

    }


    public static void main(String[] args) {
        Point point = new Point(100, 100);
        Point point1 = new Point(1, 1);
        Point point2 = new Point(110, 120);
        Point point3 = new Point(10, 20);
        Point point4 = new Point(130, 160);

        List<Point> pointIndexDataMap = Lists.newArrayList(point, point1, point2, point3, point4);
        KMeanCluster oneCalc = new KMeanCluster(pointIndexDataMap, 2);

        for (int i = 0; i < 2; ++i) {
            oneCalc.calc();
        }
    }
}

输出

计算次数：1
当前分类：{0=[(110, 120), (130, 160)], 1=[(100, 100), (1, 1), (10, 20)]}
当前中心点：[(120, 140), (37, 40)]
计算次数：2
当前分类：{0=[(100, 100), (110, 120), (130, 160)], 1=[(1, 1), (10, 20)]}
当前中心点：[(113, 126), (5, 10)]