K-Means聚类算法

目的：将数据分为K组

基本思路

1. 随机选取K个对象作为初始的聚类中心
2. 计算每个对象与各个聚类中心之间的距离，将每个对象分配给距离它最近的聚类中心
3. 将属于同一类的对象求均值，将这个均值作为该类的新的聚类中心
4. 重复2，3步，直到求出的聚类中心满足某个条件（收敛、没有对象被重新分配）

初始聚类中心的选择会对最终求出的分类结果有一定的影响，所以初始点的选取尽量离散，间隔大

K-Means算法对大数据挖掘有很高的效率，它的时间复杂度为O（NKT），其中N表示数据集中的对象个数，K表示聚类个数，T表示迭代次数

例题

​ 将以下数据分为三类 consumption.csv

Id,R,F,M
1,27,6,232.61
2,3,5,1507.11
3,4,16,817.62
4,3,11,232.81
5,14,7,1913.05
6,19,6,220.07
7,5,2,615.83
8,26,2,1059.66
9,21,9,304.82
10,2,21,1227.96
11,15,2,521.02
12,26,3,438.22
13,17,11,1744.55
14,30,16,1957.44
15,5,7,1713.79
16,4,21,1768.11
17,93,2,1016.34
18,16,3,950.36
19,4,1,754.93
20,27,1,294.23
21,5,1,195.3
22,17,3,1845.34
23,12,13,1434.29
24,21,3,275.85
25,18,5,449.76
26,30,21,1628.68
27,4,2,1795.41
28,7,12,1786.24
29,18,1,679.44
30,60,7,5318.81
31,4,22,873.68
32,16,1,654.69
33,3,2,230.37
34,14,11,1165.68
35,13,21,1276.31
36,10,16,334.21
37,5,5,759.19
38,1,1,1383.39
39,24,8,3280.77
40,19,4,154.65
41,9,1,501.38
42,1,24,1721.93
43,14,1,107.18
44,10,1,973.36
45,10,17,764.55
46,7,6,1251.4
47,23,11,923.28
48,15,1,1011.18
49,1,15,1847.61
50,3,21,1669.46
51,10,3,1758.05
52,30,8,1865.99
53,28,8,1791.44
54,4,15,874.6
55,24,5,557.17
56,16,2,1025.35
57,7,2,1261.47
58,66,4,2920.81
59,4,2,1266.02
60,21,11,626.37
61,6,4,1105.63
62,26,21,1465.58
63,8,21,630.74
64,26,2,1546.45
65,14,11,1577.91
66,17,6,170.16
67,20,5,1558.75
68,5,5,1272.06
69,26,3,111.02
70,15,7,1578.37
71,26,24,720.26
72,25,16,873.22
73,4,7,935.19
74,23,11,723.67
75,15,9,1833.01
76,6,3,681.26
77,78,11,1461.63
78,15,17,560.57
79,9,18,1761.19
80,8,7,1707.25
81,28,2,227.14
82,22,3,223.57
83,8,6,940.46
84,23,6,256.3
85,5,1,312.44
86,15,14,929.52
87,27,15,1296.66
88,22,11,591.62
89,2,2,755.72
90,18,17,1424.07
91,61,8,940.93
92,3,7,414.24
93,1,14,576.56
94,12,22,1037.14
95,26,5,1200.17
96,1,3,1727.36
97,13,16,503.71
98,19,7,703.36
99,12,17,1583.05
100,3,18,602.9
101,5,1,798.41
102,25,7,1202.09
103,85,4,1605.36
104,28,21,1222.34
105,25,19,593.17
106,8,6,94.75
107,14,1,89.7
108,21,15,1061.56
109,29,15,978.85
110,14,3,155.9
111,20,5,938.15
112,3,24,1477.97
113,10,6,1976.23
114,8,5,181.17
115,17,4,499.65
116,49,1,76.22
117,13,11,267.1
118,23,1,137.62
119,65,5,1383.47
120,20,22,1311.2
121,22,13,496.61
122,21,6,1921.8
123,14,11,304.1
124,26,1,468.09
125,27,9,432.67
126,30,1,368.35
127,11,4,759.69
128,26,3,1110.81
129,28,1,53
130,39,11,1314.21
131,11,6,1895.95
132,23,1,417.23
133,3,2,679.58
134,5,1,533.97
135,24,8,1134.64
136,25,6,825.39
137,10,6,165.39
138,29,9,1234.64
139,80,11,1829.32
140,23,1,89
141,4,2,1557.88
142,3,8,1328.01
143,15,7,304.65
144,17,23,1505.55
145,16,7,711.1
146,16,1,539.76
147,5,1,65.83
148,16,3,776.21
149,22,18,1820.61
150,19,4,1997
151,4,22,1846.69
152,23,7,1252.41
153,7,13,987.17
154,3,6,1130.03
155,18,1,148.32
156,28,1,135.57
157,6,2,1641.79
158,7,2,242.83
159,21,8,1803.02
160,12,12,1557.95
161,25,4,1494.81
162,26,13,1280.06
163,28,1,160
164,22,9,440.12
165,14,1,746.95
166,12,2,351.09
167,6,2,556.91
168,7,3,957.83
169,16,16,1212.37
170,11,2,946.65
171,16,13,1442.68
172,5,12,1612.7
173,0,21,1281.68
174,9,13,1928.8
175,24,7,335.35
176,3,8,1589.35
177,20,11,797.72
178,17,1,793.47
179,13,16,569.47
180,10,3,149.5
181,17,21,515.38
182,8,4,187.76
183,20,7,1441.83
184,27,1,121.61
185,25,11,934.58
186,16,15,591.06
187,15,4,951.31
188,12,11,914
189,3,22,1058
190,9,2,1111.51
191,17,9,458.52
192,27,18,927.59
193,73,1,1370.25
194,17,1,946.53
195,10,1,1474.41
196,16,3,1661.03
197,0,9,1465.18
198,17,3,1813.45
199,5,7,772.54
200,4,1,172.82
201,14,4,552.37
202,12,8,946.28
203,26,2,651.99
204,6,9,857.79
205,7,4,1016.55
206,5,6,1766.44
207,25,3,908.53
208,28,2,403.75
209,25,4,1270.75
210,13,3,1157.92
211,13,1,497.09
212,2,1,216.78
213,23,16,1454.58
214,2,17,1027.58
215,24,12,722.09
216,15,7,282.19
217,11,4,106.96
218,18,1,999.75
219,24,14,1139.33
220,24,5,836.72
221,3,2,1678.54
222,3,17,1337.34
223,1,4,1335.77
224,11,2,810.2
225,29,11,943.9
226,51,12,5135.77
227,6,9,984.12
228,6,5,1413.55
229,1,6,381.95
230,6,14,788.22
231,29,1,80.8
232,21,1,611.13
233,24,4,1766.35
234,0,2,1516.76
235,9,6,1925.2
236,17,1,344.23
237,49,1,204.1
238,5,2,1257.59
239,7,3,1095.09
240,2,1,123.76
241,3,2,696.82
242,26,2,1487.35
243,19,3,1278.43
244,28,14,627.97
245,12,1,95
246,14,4,1827.01
247,10,6,754.05
248,19,2,922.93
249,12,12,257.4
250,1,14,676.34
251,3,19,984.32
252,27,32,1914.06
253,13,4,1953.81
254,1,4,768.02
255,61,13,1379.86
256,42,1,1054.24
257,21,11,298.34
258,17,5,841.04
259,8,9,1757.87
260,22,11,1010.7

算法分析

​ 采用map存储数据，key存id，value使用List存储R、F、M，中心点可以使用三个List存储，最大迭代次数m由命令行输入

算法代码实现

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.util.*;

public class Test {
    static String filePath = System.getProperty("user.dir")+"\\src\\sources\\consumption.csv";
    static Map<Integer,List<Float>> map = new HashMap<>();//总数据
    static Map<Integer,List<Float>> map1 = new HashMap<>();//第一类数据
    static Map<Integer,List<Float>> map2 = new HashMap<>();//第二类数据
    static Map<Integer,List<Float>> map3 = new HashMap<>();//第三类数据
    static List<Float> list1 = new ArrayList();//第一个中心
    static List<Float> list2 = new ArrayList();//第二个中心
    static List<Float> list3 = new ArrayList();//第三个中心
    //判断是否是数字
    public static boolean isNumeric(String str){
        for (int i = str.length();--i>=0;){
            if (!Character.isDigit(str.charAt(i))){
                return false;
            }
        }
        return true;
    }
    //读取数据，存入map
    public static void  ReadFile(){
        BufferedReader br = null;
        String line = "";
        String csvSplitBy = ",";
        try {
            br = new BufferedReader(new FileReader(filePath));
            while ((line = br.readLine()) != null) {
                // 分割点为
                List<String> post = Arrays.asList(line.split(csvSplitBy));
                if (isNumeric(post.get(0))) {
                    int x = Integer.parseInt(post.get(0));
                    List<Float> list = new ArrayList<>();
                    list.add(Float.valueOf(post.get(1)));
                    list.add(Float.valueOf(post.get(2)));
                    list.add(Float.valueOf(post.get(3)));
                    map.put(x,list);
                }
            }

        } catch (FileNotFoundException e) {
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        } finally {
            if (br != null) {
                try {
                    br.close();
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
        }
    }
    //第一次，产生三个随机点
    public static void RandPoint(){
        Random r = new Random();
        list1 = map.get((r.nextInt(942)));
        list2 = map.get((r.nextInt(942)));
        list3 = map.get((r.nextInt(942)));
        System.out.print(list1.toString());
        System.out.print(list2.toString());
        System.out.println(list3.toString());
    }
    //给定一个map的value，判断他是哪个类,给数据分类
    public static void IsKM(List<Float> list,int index){

        float x1 = Math.abs(list1.get(0)-list.get(0))+Math.abs(list1.get(1)-list.get(1))
                +Math.abs(list1.get(2)-list.get(2));
        float x2 = Math.abs(list2.get(0)-list.get(0))+Math.abs(list2.get(1)-list.get(1))
                +Math.abs(list2.get(2)-list.get(2));
        float x3 = Math.abs(list3.get(0)-list.get(0))+Math.abs(list3.get(1)-list.get(1))
                +Math.abs(list3.get(2)-list.get(2));
        float min = (x1<x2)?x1:x2;
        min = (min<x3)?min:x3;
        if (min == x1){
            map1.put(index,list);
            //System.out.println(index + "属于第1类，中心点为"+list1.toString());
        }
        if(min == x2){
            map2.put(index,list);
            //System.out.println(index + "属于第2类，中心点为"+list2.toString());
        }
        if(min == x3){
            map3.put(index,list);
            //System.out.println(index + "属于第3类，中心点为"+list3.toString());
        }
    }
    //计算map中数据与中心点的距离
    public static void KMeans(int m) {
        for (int i = 0;i<m;i++){
            map1.clear();
            map2.clear();
            map3.clear();
            for (Map.Entry<Integer,List<Float>> entry : map.entrySet()) {
                IsKM(entry.getValue(),entry.getKey());
            }
            NewPoint();
            System.out.print(list1.toString());
            System.out.print(list2.toString());
            System.out.println(list3.toString());
        }
        System.out.println("第一个中心点"+map1);
        System.out.println("第二个中心点"+map2);
        System.out.println("第三个中心点"+map3);
    }
    //计算三个类的新中心
    public static void NewPoint(){
        //重置中心点
        list1.clear();
        list2.clear();
        list3.clear();
        //一列数据的和
        float sum1 = 0;
        float sum2 = 0;
        float sum3 = 0;
        for (Map.Entry<Integer,List<Float>> entry : map1.entrySet()) {
            //System.out.println(entry.getValue());
            //map最后一个value为空，要进行一波判断
            if (entry.getValue().size()>0) {
                sum1 = sum1 + entry.getValue().get(0);
                sum2 = sum2 + entry.getValue().get(1);
                sum3 = sum3 + entry.getValue().get(2);
            }
        }
        list1.add(sum1/map1.size());
        list1.add(sum2/map1.size());
        list1.add(sum3/map1.size());
        sum1=0;
        sum2=0;
        sum3=0;
        for (Map.Entry<Integer,List<Float>> entry : map2.entrySet()) {
            if (entry.getValue().size()>0){
                sum1 = sum1 + entry.getValue().get(0);
                sum2 = sum2 + entry.getValue().get(1);
                sum3 = sum3 + entry.getValue().get(2);
            }
        }
        list2.add(sum1/map2.size());
        list2.add(sum2/map2.size());
        list2.add(sum3/map2.size());
        sum1=0;
        sum2=0;
        sum3=0;
        for (Map.Entry<Integer,List<Float>> entry : map3.entrySet()) {
            if (entry.getValue().size()>0){
                sum1 = sum1 + entry.getValue().get(0);
                sum2 = sum2 + entry.getValue().get(1);
                sum3 = sum3 + entry.getValue().get(2);
            }
        }
        list3.add(sum1/map3.size());
        list3.add(sum2/map3.size());
        list3.add(sum3/map3.size());
    }

    public static void main(String[] args) {
        System.out.print("请输入迭代次数：");
        Scanner input = new Scanner(System.in);
        int m = input.nextInt();
        //读取数据
        ReadFile();
        //生成第一次的中心点
        System.out.print("第一次随机生成中心点：");
        RandPoint();
        //分类，求中心，再分类
        KMeans(m);
    }
}