描述
算法接受参数 k ；然后将事先输入的n个数据对象划分为 k个聚类以便使得所获得的聚类满足：同一聚类中的对象相似度较高；而不同聚类中的对象相似度较小。聚类相似度是利用各聚类中对象的均值所获得一个“中心对象”（引力中心）来进行计算的。
K-means算法是最为经典的基于划分的聚类方法，是十大经典数据挖掘算法之一。K-means算法的基本思想是：以空间中k个点为中心进行聚类，对最靠近他们的对象归类。通过迭代的方法，逐次更新各聚类中心的值，直至得到最好的聚类结果。 该算法的最大优势在于简洁和快速。算法的关键在于初始中心的选择和距离公式。
聚类
聚类分析是一种静态数据分析方法，常被用于机器学习，模式识别，数据挖掘等领域。通常认为，聚类是一种无监督式的机器学习方法，它的过程是这样的：在未知样本类别的情况下，通过计算样本彼此间的距离（欧式距离,马式距离，汉明距离，余弦距离等）来估计样本所属类别。从结构性来划分，聚类方法分为自上而下和自下而上两种方法，前者的算法是先把所有样本视为一类，然后不断从这个大类中分离出小类，直到不能再分为止；后者则相反，首先所有样本自成一类，然后不断两两合并，直到最终形成几个大类。
聚类算法
常用的聚类方法主要有以下四种：
- Connectivity based clustering （如hierarchical clustering 层次聚类法)
- Centroid-based clustering (如kmeans)
- Distribution-based clustering
- Density-based clustering
优缺点
Kmeans聚类是一种自下而上的聚类方法，它的优点是简单、速度快；缺点是聚类结果与初始中心的选择有关系，且必须提供聚类的数目。Kmeans的第二个缺点是致命的，因为在有些时候，我们不知道样本集将要聚成多少个类别，这种时候kmeans是不适合的，推荐使用hierarchical 或meanshift来聚类。第一个缺点可以通过多次聚类取最佳结果来解决。
算法流程
首先从n个数据对象任意选择 k 个对象作为初始聚类中心；
而对于所剩下其它对象，则根据它们与这些聚类中心的相似度（距离），分别将它们分配给与其最相似的（聚类中心所代表的）聚类；
然后再计算每个所获新聚类的聚类中心（该聚类中所有对象的均值）；
不断重复这一过程直到标准测度函数开始收敛为止。
一般都采用均方差作为标准测度函数.
k个聚类具有以下特点：各聚类本身尽可能的紧凑，而各聚类之间尽可能的分开。
输入：k, data[n];
- 选择k个初始中心点，例如c[0]=data[0],…c[k-1]=data[k-1];
- 对于data[0]….data[n], 分别与c[0]…c[k-1]比较，假定与c[i]差值最少，就标记为i;
- 对于所有标记为i点，重新计算c[i]={ 所有标记为i的data[j]之和}/标记为i的个数；
- 重复(2)(3),直到所有c[i]值的变化小于给定阈值。
源码示例
python
自编
# coding=utf-8
'''
* k-Means算法，聚类算法；
* 实现步骤：1. 首先是随机获取总体中的K个元素作为总体的K个中心；
* 2. 接下来对总体中的元素进行分类，每个元素都去判断自己到K个中心的距离，并归类到最近距离中心去；
* 3. 计算每个聚类的平均值，并作为新的中心点
* 4. 重复2，3步骤，直到这k个中线点不再变化（收敛了），或执行了足够多的迭代
'''
from numpy import linalg as ll
import numpy as np
import random
from sklearn import cluster as sc
# train data
srcdata = [ [ 5.1, 3.5, 1.4, 0.2],
[ 4.9, 3.0, 1.4, 0.2 ],[ 4.7, 3.2, 1.3, 0.2 ],
[ 4.6, 3.1, 1.5, 0.2 ],[ 5.0, 3.6, 1.4, 0.2 ],
[ 7.0, 3.2, 4.7, 1.4 ],[ 6.4, 3.2, 4.5, 1.5 ],
[ 6.9, 3.1, 4.9, 1.5 ],[ 5.5, 2.3, 4.0, 1.3 ],
[ 6.5, 2.8, 4.6, 1.5 ],[ 5.7, 2.8, 4.5, 1.3 ],
[ 6.5, 3.0, 5.8, 2.2 ],[ 7.6, 3.0, 6.6, 2.1 ],
[ 4.9, 2.5, 4.5, 1.7 ],[ 7.3, 2.9, 6.3, 1.8 ],
[ 6.7, 2.5, 5.8, 1.8 ],[ 6.9, 3.1, 5.1, 2.3 ] ]
#print srcdata
srclen = len(srcdata)
len0 = len(srcdata[0])
# set k = 5
k = 5
# step 1
# index = range(k) -- use first k
# use random to get index.
index = random.sample( range( srclen ) , k)
#print index
c = np.arange(k*len0,dtype=float).reshape(k,len0)
for i in range(k):
for j in range(len0):
c[i][j] = srcdata[index[i]][j]
print c
# set stop threshold
delta = 0.001
dis = np.arange(k,dtype=float)
calindex = np.arange(srclen)
norm = 10.0
# step 4
while norm>delta:
# step 2
for i in range( srclen ):
for m in range(k):
dis[m] = 0.0
for j in range(len0):
for m in range(k):
dis[m] += (srcdata[i][j] - c[m][j])*(srcdata[i][j] - c[m][j])
calindex[i] = np.where(dis == np.min(dis) )[0][0]
# step 3
newc = np.zeros(k*len0).reshape(k,len0)
for xx in range(srclen):
for j in range(len0):
newc[calindex[xx]][j] += srcdata[xx][j]
for i in range(k):
size = len(np.where(calindex == i)[0])
#print size
for j in range(len0):
newc[i][j]/=size
norm = ll.norm(c-newc)
#print norm
c = newc.copy()
print c
print calindex
## sklearn -> k-means++
cc = sc.k_means(srcdata,k)
print cc
Java
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
public class Kmeans {
/**
* @param args
* @throws IOException
*/
public static List<ArrayList<ArrayList<Double>>>
initHelpCenterList(List<ArrayList<ArrayList<Double>>> helpCenterList,int k){
for(int i=0;i<k;i++){
helpCenterList.add(new ArrayList<ArrayList<Double>>());
}
return helpCenterList;
}
/**
* @param args
* @throws IOException
*/
public static void main(String[] args) throws IOException{
List<ArrayList<Double>> centers = new ArrayList<ArrayList<Double>>();
List<ArrayList<Double>> newCenters = new ArrayList<ArrayList<Double>>();
List<ArrayList<ArrayList<Double>>> helpCenterList = new ArrayList<ArrayList<ArrayList<Double>>>();
//读入原始数据
BufferedReader br=new BufferedReader(new InputStreamReader(new FileInputStream("wine.txt")));
String data = null;
List<ArrayList<Double>> dataList = new ArrayList<ArrayList<Double>>();
while((data=br.readLine())!=null){
//System.out.println(data);
String []fields = data.split(",");
List<Double> tmpList = new ArrayList<Double>();
for(int i=0; i<fields.length;i++)
tmpList.add(Double.parseDouble(fields[i]));
dataList.add((ArrayList<Double>) tmpList);
}
br.close();
//随机确定K个初始聚类中心
Random rd = new Random();
int k=3;
int [] initIndex={59,71,48};
int [] helpIndex = {0,59,130};
int [] givenIndex = {0,1,2};
System.out.println("random centers' index");
for(int i=0;i<k;i++){
int index = rd.nextInt(initIndex[i]) + helpIndex[i];
//int index = givenIndex[i];
System.out.println("index "+index);
centers.add(dataList.get(index));
helpCenterList.add(new ArrayList<ArrayList<Double>>());
}
/*
//注释掉的这部分目的是，取测试数据集最后稳定的三个类簇的聚类中心作为初始聚类中心
centers = new ArrayList<ArrayList<Double>>();
for(int i=0;i<59;i++)
helpCenterList.get(0).add(dataList.get(i));
for(int i=59;i<130;i++)
helpCenterList.get(1).add(dataList.get(i));
for(int i=130;i<178;i++)
helpCenterList.get(2).add(dataList.get(i));
for(int i=0;i<k;i++){
ArrayList<Double> tmp = new ArrayList<Double>();
for(int j=0;j<dataList.get(0).size();j++){
double sum=0;
for(int t=0;t<helpCenterList.get(i).size();t++)
sum+=helpCenterList.get(i).get(t).get(j);
tmp.add(sum/helpCenterList.get(i).size());
}
centers.add(tmp);
}
*/
//输出k个初始中心
System.out.println("original centers:");
for(int i=0;i<k;i++)
System.out.println(centers.get(i));
while(true)
{//进行若干次迭代，直到聚类中心稳定
for(int i=0;i<dataList.size();i++){//标注每一条记录所属于的中心
double minDistance=99999999;
int centerIndex=-1;
for(int j=0;j<k;j++){//离0~k之间哪个中心最近
double currentDistance=0;
for(int t=1;t<centers.get(0).size();t++){//计算两点之间的欧式距离
currentDistance += ((centers.get(j).get(t)-dataList.get(i).get(t))/(centers.get(j).get(t)+dataList.get(i).get(t))) * ((centers.get(j).get(t)-dataList.get(i).get(t))/(centers.get(j).get(t)+dataList.get(i).get(t)));
}
if(minDistance>currentDistance){
minDistance=currentDistance;
centerIndex=j;
}
}
helpCenterList.get(centerIndex).add(dataList.get(i));
}
// System.out.println(helpCenterList);
//计算新的k个聚类中心
for(int i=0;i<k;i++){
ArrayList<Double> tmp = new ArrayList<Double>();
for(int j=0;j<centers.get(0).size();j++){
double sum=0;
for(int t=0;t<helpCenterList.get(i).size();t++)
sum+=helpCenterList.get(i).get(t).get(j);
tmp.add(sum/helpCenterList.get(i).size());
}
newCenters.add(tmp);
}
System.out.println("\nnew clusters' centers:\n");
for(int i=0;i<k;i++)
System.out.println(newCenters.get(i));
//计算新旧中心之间的距离，当距离小于阈值时，聚类算法结束
double distance=0;
for(int i=0;i<k;i++){
for(int j=1;j<centers.get(0).size();j++){//计算两点之间的欧式距离
distance += ((centers.get(i).get(j)-newCenters.get(i).get(j))/(centers.get(i).get(j)+newCenters.get(i).get(j))) * ((centers.get(i).get(j)-newCenters.get(i).get(j))/(centers.get(i).get(j)+newCenters.get(i).get(j)));
}
//System.out.println(i+" "+distance);
}
System.out.println("\ndistance: "+distance+"\n\n");
if(distance==0)//小于阈值时，结束循环
break;
else//否则，新的中心来代替旧的中心，进行下一轮迭代
{
centers = new ArrayList<ArrayList<Double>>(newCenters);
//System.out.println(newCenters);
newCenters = new ArrayList<ArrayList<Double>>();
helpCenterList = new ArrayList<ArrayList<ArrayList<Double>>>();
helpCenterList=initHelpCenterList(helpCenterList,k);
}
}
//输出最后聚类结果
for(int i=0;i<k;i++){
System.out.println("\n\nCluster: "+(i+1)+" size: "+helpCenterList.get(i).size()+" :\n\n");
for(int j=0;j<helpCenterList.get(i).size();j++)
{
System.out.println(helpCenterList.get(i).get(j));
}
}
}
}
test
测试数据集来源：wine数据集from UCI
以下是某次的运行结果，可以看出聚类结果与参考结果比较吻合
random centers' index
index 4
index 102
index 166
original centers:
[1.0, 13.744745762711865, 2.0106779661016954, 2.455593220338984, 17.037288135593222, 106.33898305084746, 2.8401694915254234, 2.982372881355932, 0.29, 1.8993220338983055, 5.528305084745763, 1.0620338983050848, 3.1577966101694916, 1115.7118644067796]
[2.0, 12.278732394366198, 1.932676056338028, 2.244788732394365, 20.238028169014086, 94.54929577464789, 2.2588732394366198, 2.080845070422536, 0.363661971830986, 1.6302816901408452, 3.08661971830986, 1.0562816901408452, 2.785352112676055, 519.5070422535211]
[3.0, 13.153749999999997, 3.3337500000000007, 2.4370833333333333, 21.416666666666668, 99.3125, 1.6787500000000002, 0.7814583333333331, 0.44749999999999995, 1.1535416666666667, 7.396249979166668, 0.6827083333333334, 1.6835416666666658, 629.8958333333334]
new clusters' centers:
[1.040983606557377, 13.695245901639344, 1.9844262295081967, 2.446475409836067, 17.199999999999996, 106.13934426229508, 2.8595901639344263, 3.0022950819672127, 0.28737704918032797, 1.900901639344262, 5.5009836065573765, 1.062131147540984, 3.1613934426229497, 1101.0]
[2.0, 12.272352941176464, 1.9286764705882358, 2.2503676470588228, 20.209558823529413, 94.72058823529412, 2.229705882352941, 2.0449999999999995, 0.3635294117647058, 1.6292647058823533, 3.0122794117647054, 1.0586176470588233, 2.7795588235294093, 517.6102941176471]
[2.9693877551020407, 13.146530612244899, 3.3402040816326526, 2.428163265306121, 21.360204081632656, 98.74489795918367, 1.6831632653061233, 0.7961224489795918, 0.4522448979591836, 1.151734693877551, 7.34581630612245, 0.6867346938775512, 1.6943877551020412, 624.2551020408164]
distance: 6.251918634057867E-4
new clusters' centers:
[1.0793650793650793, 13.648888888888889, 1.9598412698412708, 2.4379365079365085, 17.352380952380955, 105.95238095238095, 2.8777777777777778, 3.0209523809523806, 0.2849206349206349, 1.9023809523809527, 5.475396825396826, 1.0622222222222224, 3.164761904761905, 1087.2222222222222]
[2.0, 12.265384615384615, 1.9243076923076925, 2.256461538461538, 20.17846153846154, 94.9076923076923, 2.1978461538461547, 2.0058461538461545, 0.3633846153846154, 1.628153846153846, 2.931076923076924, 1.0611692307692309, 2.7732307692307687, 515.5384615384615]
[2.94, 13.1396, 3.3464000000000005, 2.4195999999999995, 21.305999999999997, 98.2, 1.6874, 0.8101999999999998, 0.45679999999999993, 1.15, 7.29739998, 0.6906000000000002, 1.7047999999999994, 618.84]
distance: 6.566946236291001E-4
new clusters' centers:
[1.0793650793650793, 13.648888888888889, 1.9598412698412708, 2.4379365079365085, 17.352380952380955, 105.95238095238095, 2.8777777777777778, 3.0209523809523806, 0.2849206349206349, 1.9023809523809527, 5.475396825396826, 1.0622222222222224, 3.164761904761905, 1087.2222222222222]
[2.0, 12.265384615384615, 1.9243076923076925, 2.256461538461538, 20.17846153846154, 94.9076923076923, 2.1978461538461547, 2.0058461538461545, 0.3633846153846154, 1.628153846153846, 2.931076923076924, 1.0611692307692309, 2.7732307692307687, 515.5384615384615]
[2.94, 13.1396, 3.3464000000000005, 2.4195999999999995, 21.305999999999997, 98.2, 1.6874, 0.8101999999999998, 0.45679999999999993, 1.15, 7.29739998, 0.6906000000000002, 1.7047999999999994, 618.84]
distance: 0.0
Cluster: 1 size: 63 :
[1.0, 14.23, 1.71, 2.43, 15.6, 127.0, 2.8, 3.06, 0.28, 2.29, 5.64, 1.04, 3.92, 1065.0]
[1.0, 13.2, 1.78, 2.14, 11.2, 100.0, 2.65, 2.76, 0.26, 1.28, 4.38, 1.05, 3.4, 1050.0]
[1.0, 13.16, 2.36, 2.67, 18.6, 101.0, 2.8, 3.24, 0.3, 2.81, 5.68, 1.03, 3.17, 1185.0]
[1.0, 14.37, 1.95, 2.5, 16.8, 113.0, 3.85, 3.49, 0.24, 2.18, 7.8, 0.86, 3.45, 1480.0]
[1.0, 13.24, 2.59, 2.87, 21.0, 118.0, 2.8, 2.69, 0.39, 1.82, 4.32, 1.04, 2.93, 735.0]
[1.0, 14.2, 1.76, 2.45, 15.2, 112.0, 3.27, 3.39, 0.34, 1.97, 6.75, 1.05, 2.85, 1450.0]
[1.0, 14.39, 1.87, 2.45, 14.6, 96.0, 2.5, 2.52, 0.3, 1.98, 5.25, 1.02, 3.58, 1290.0]
[1.0, 14.06, 2.15, 2.61, 17.6, 121.0, 2.6, 2.51, 0.31, 1.25, 5.05, 1.06, 3.58, 1295.0]
[1.0, 14.83, 1.64, 2.17, 14.0, 97.0, 2.8, 2.98, 0.29, 1.98, 5.2, 1.08, 2.85, 1045.0]
[1.0, 13.86, 1.35, 2.27, 16.0, 98.0, 2.98, 3.15, 0.22, 1.85, 7.22, 1.01, 3.55, 1045.0]
[1.0, 14.1, 2.16, 2.3, 18.0, 105.0, 2.95, 3.32, 0.22, 2.38, 5.75, 1.25, 3.17, 1510.0]
[1.0, 14.12, 1.48, 2.32, 16.8, 95.0, 2.2, 2.43, 0.26, 1.57, 5.0, 1.17, 2.82, 1280.0]
[1.0, 13.75, 1.73, 2.41, 16.0, 89.0, 2.6, 2.76, 0.29, 1.81, 5.6, 1.15, 2.9, 1320.0]
[1.0, 14.75, 1.73, 2.39, 11.4, 91.0, 3.1, 3.69, 0.43, 2.81, 5.4, 1.25, 2.73, 1150.0]
[1.0, 14.38, 1.87, 2.38, 12.0, 102.0, 3.3, 3.64, 0.29, 2.96, 7.5, 1.2, 3.0, 1547.0]
[1.0, 13.63, 1.81, 2.7, 17.2, 112.0, 2.85, 2.91, 0.3, 1.46, 7.3, 1.28, 2.88, 1310.0]
[1.0, 14.3, 1.92, 2.72, 20.0, 120.0, 2.8, 3.14, 0.33, 1.97, 6.2, 1.07, 2.65, 1280.0]
[1.0, 13.83, 1.57, 2.62, 20.0, 115.0, 2.95, 3.4, 0.4, 1.72, 6.6, 1.13, 2.57, 1130.0]
[1.0, 14.19, 1.59, 2.48, 16.5, 108.0, 3.3, 3.93, 0.32, 1.86, 8.7, 1.23, 2.82, 1680.0]
[1.0, 13.64, 3.1, 2.56, 15.2, 116.0, 2.7, 3.03, 0.17, 1.66, 5.1, 0.96, 3.36, 845.0]
[1.0, 14.06, 1.63, 2.28, 16.0, 126.0, 3.0, 3.17, 0.24, 2.1, 5.65, 1.09, 3.71, 780.0]
[1.0, 12.93, 3.8, 2.65, 18.6, 102.0, 2.41, 2.41, 0.25, 1.98, 4.5, 1.03, 3.52, 770.0]
[1.0, 13.71, 1.86, 2.36, 16.6, 101.0, 2.61, 2.88, 0.27, 1.69, 3.8, 1.11, 4.0, 1035.0]
[1.0, 12.85, 1.6, 2.52, 17.8, 95.0, 2.48, 2.37, 0.26, 1.46, 3.93, 1.09, 3.63, 1015.0]
[1.0, 13.5, 1.81, 2.61, 20.0, 96.0, 2.53, 2.61, 0.28, 1.66, 3.52, 1.12, 3.82, 845.0]
[1.0, 13.39, 1.77, 2.62, 16.1, 93.0, 2.85, 2.94, 0.34, 1.45, 4.8, 0.92, 3.22, 1195.0]
[1.0, 13.3, 1.72, 2.14, 17.0, 94.0, 2.4, 2.19, 0.27, 1.35, 3.95, 1.02, 2.77, 1285.0]
[1.0, 13.87, 1.9, 2.8, 19.4, 107.0, 2.95, 2.97, 0.37, 1.76, 4.5, 1.25, 3.4, 915.0]
[1.0, 14.02, 1.68, 2.21, 16.0, 96.0, 2.65, 2.33, 0.26, 1.98, 4.7, 1.04, 3.59, 1035.0]
[1.0, 13.73, 1.5, 2.7, 22.5, 101.0, 3.0, 3.25, 0.29, 2.38, 5.7, 1.19, 2.71, 1285.0]
[1.0, 13.58, 1.66, 2.36, 19.1, 106.0, 2.86, 3.19, 0.22, 1.95, 6.9, 1.09, 2.88, 1515.0]
[1.0, 13.68, 1.83, 2.36, 17.2, 104.0, 2.42, 2.69, 0.42, 1.97, 3.84, 1.23, 2.87, 990.0]
[1.0, 13.76, 1.53, 2.7, 19.5, 132.0, 2.95, 2.74, 0.5, 1.35, 5.4, 1.25, 3.0, 1235.0]
[1.0, 13.51, 1.8, 2.65, 19.0, 110.0, 2.35, 2.53, 0.29, 1.54, 4.2, 1.1, 2.87, 1095.0]
[1.0, 13.48, 1.81, 2.41, 20.5, 100.0, 2.7, 2.98, 0.26, 1.86, 5.1, 1.04, 3.47, 920.0]
[1.0, 13.28, 1.64, 2.84, 15.5, 110.0, 2.6, 2.68, 0.34, 1.36, 4.6, 1.09, 2.78, 880.0]
[1.0, 13.05, 1.65, 2.55, 18.0, 98.0, 2.45, 2.43, 0.29, 1.44, 4.25, 1.12, 2.51, 1105.0]
[1.0, 13.07, 1.5, 2.1, 15.5, 98.0, 2.4, 2.64, 0.28, 1.37, 3.7, 1.18, 2.69, 1020.0]
[1.0, 14.22, 3.99, 2.51, 13.2, 128.0, 3.0, 3.04, 0.2, 2.08, 5.1, 0.89, 3.53, 760.0]
[1.0, 13.56, 1.71, 2.31, 16.2, 117.0, 3.15, 3.29, 0.34, 2.34, 6.13, 0.95, 3.38, 795.0]
[1.0, 13.41, 3.84, 2.12, 18.8, 90.0, 2.45, 2.68, 0.27, 1.48, 4.28, 0.91, 3.0, 1035.0]
[1.0, 13.88, 1.89, 2.59, 15.0, 101.0, 3.25, 3.56, 0.17, 1.7, 5.43, 0.88, 3.56, 1095.0]
[1.0, 13.24, 3.98, 2.29, 17.5, 103.0, 2.64, 2.63, 0.32, 1.66, 4.36, 0.82, 3.0, 680.0]
[1.0, 13.05, 1.77, 2.1, 17.0, 107.0, 3.0, 3.0, 0.28, 2.03, 5.04, 0.88, 3.35, 885.0]
[1.0, 14.21, 4.04, 2.44, 18.9, 111.0, 2.85, 2.65, 0.3, 1.25, 5.24, 0.87, 3.33, 1080.0]
[1.0, 14.38, 3.59, 2.28, 16.0, 102.0, 3.25, 3.17, 0.27, 2.19, 4.9, 1.04, 3.44, 1065.0]
[1.0, 13.9, 1.68, 2.12, 16.0, 101.0, 3.1, 3.39, 0.21, 2.14, 6.1, 0.91, 3.33, 985.0]
[1.0, 14.1, 2.02, 2.4, 18.8, 103.0, 2.75, 2.92, 0.32, 2.38, 6.2, 1.07, 2.75, 1060.0]
[1.0, 13.94, 1.73, 2.27, 17.4, 108.0, 2.88, 3.54, 0.32, 2.08, 8.9, 1.12, 3.1, 1260.0]
[1.0, 13.05, 1.73, 2.04, 12.4, 92.0, 2.72, 3.27, 0.17, 2.91, 7.2, 1.12, 2.91, 1150.0]
[1.0, 13.83, 1.65, 2.6, 17.2, 94.0, 2.45, 2.99, 0.22, 2.29, 5.6, 1.24, 3.37, 1265.0]
[1.0, 13.82, 1.75, 2.42, 14.0, 111.0, 3.88, 3.74, 0.32, 1.87, 7.05, 1.01, 3.26, 1190.0]
[1.0, 13.77, 1.9, 2.68, 17.1, 115.0, 3.0, 2.79, 0.39, 1.68, 6.3, 1.13, 2.93, 1375.0]
[1.0, 13.74, 1.67, 2.25, 16.4, 118.0, 2.6, 2.9, 0.21, 1.62, 5.85, 0.92, 3.2, 1060.0]
[1.0, 13.56, 1.73, 2.46, 20.5, 116.0, 2.96, 2.78, 0.2, 2.45, 6.25, 0.98, 3.03, 1120.0]
[1.0, 14.22, 1.7, 2.3, 16.3, 118.0, 3.2, 3.0, 0.26, 2.03, 6.38, 0.94, 3.31, 970.0]
[1.0, 13.29, 1.97, 2.68, 16.8, 102.0, 3.0, 3.23, 0.31, 1.66, 6.0, 1.07, 2.84, 1270.0]
[1.0, 13.72, 1.43, 2.5, 16.7, 108.0, 3.4, 3.67, 0.19, 2.04, 6.8, 0.89, 2.87, 1285.0]
[2.0, 13.11, 1.01, 1.7, 15.0, 78.0, 2.98, 3.18, 0.26, 2.28, 5.3, 1.12, 3.18, 502.0]
[2.0, 12.99, 1.67, 2.6, 30.0, 139.0, 3.3, 2.89, 0.21, 1.96, 3.35, 1.31, 3.5, 985.0]
[2.0, 11.96, 1.09, 2.3, 21.0, 101.0, 3.38, 2.14, 0.13, 1.65, 3.21, 0.99, 3.13, 886.0]
[2.0, 12.37, 1.07, 2.1, 18.5, 88.0, 3.52, 3.75, 0.24, 1.95, 4.5, 1.04, 2.77, 660.0]
[2.0, 11.56, 2.05, 3.23, 28.5, 119.0, 3.18, 5.08, 0.47, 1.87, 6.0, 0.93, 3.69, 465.0]
Cluster: 2 size: 65 :
[1.0, 13.05, 2.05, 3.22, 25.0, 124.0, 2.63, 2.68, 0.47, 1.92, 3.58, 1.13, 3.2, 830.0]
[2.0, 12.37, 0.94, 1.36, 10.6, 88.0, 1.98, 0.57, 0.28, 0.42, 1.95, 1.05, 1.82, 520.0]
[2.0, 12.33, 1.1, 2.28, 16.0, 101.0, 2.05, 1.09, 0.63, 0.41, 3.27, 1.25, 1.67, 680.0]
[2.0, 13.67, 1.25, 1.92, 18.0, 94.0, 2.1, 1.79, 0.32, 0.73, 3.8, 1.23, 2.46, 630.0]
[2.0, 12.37, 1.13, 2.16, 19.0, 87.0, 3.5, 3.1, 0.19, 1.87, 4.45, 1.22, 2.87, 420.0]
[2.0, 12.17, 1.45, 2.53, 19.0, 104.0, 1.89, 1.75, 0.45, 1.03, 2.95, 1.45, 2.23, 355.0]
[2.0, 12.37, 1.21, 2.56, 18.1, 98.0, 2.42, 2.65, 0.37, 2.08, 4.6, 1.19, 2.3, 678.0]
[2.0, 12.37, 1.17, 1.92, 19.6, 78.0, 2.11, 2.0, 0.27, 1.04, 4.68, 1.12, 3.48, 510.0]
[2.0, 13.34, 0.94, 2.36, 17.0, 110.0, 2.53, 1.3, 0.55, 0.42, 3.17, 1.02, 1.93, 750.0]
[2.0, 12.21, 1.19, 1.75, 16.8, 151.0, 1.85, 1.28, 0.14, 2.5, 2.85, 1.28, 3.07, 718.0]
[2.0, 12.29, 1.61, 2.21, 20.4, 103.0, 1.1, 1.02, 0.37, 1.46, 3.05, 0.906, 1.82, 870.0]
[2.0, 13.86, 1.51, 2.67, 25.0, 86.0, 2.95, 2.86, 0.21, 1.87, 3.38, 1.36, 3.16, 410.0]
[2.0, 13.49, 1.66, 2.24, 24.0, 87.0, 1.88, 1.84, 0.27, 1.03, 3.74, 0.98, 2.78, 472.0]
[2.0, 11.66, 1.88, 1.92, 16.0, 97.0, 1.61, 1.57, 0.34, 1.15, 3.8, 1.23, 2.14, 428.0]
[2.0, 13.03, 0.9, 1.71, 16.0, 86.0, 1.95, 2.03, 0.24, 1.46, 4.6, 1.19, 2.48, 392.0]
[2.0, 11.84, 2.89, 2.23, 18.0, 112.0, 1.72, 1.32, 0.43, 0.95, 2.65, 0.96, 2.52, 500.0]
[2.0, 12.33, 0.99, 1.95, 14.8, 136.0, 1.9, 1.85, 0.35, 2.76, 3.4, 1.06, 2.31, 750.0]
[2.0, 12.7, 3.87, 2.4, 23.0, 101.0, 2.83, 2.55, 0.43, 1.95, 2.57, 1.19, 3.13, 463.0]
[2.0, 12.0, 0.92, 2.0, 19.0, 86.0, 2.42, 2.26, 0.3, 1.43, 2.5, 1.38, 3.12, 278.0]
[2.0, 12.72, 1.81, 2.2, 18.8, 86.0, 2.2, 2.53, 0.26, 1.77, 3.9, 1.16, 3.14, 714.0]
[2.0, 12.08, 1.13, 2.51, 24.0, 78.0, 2.0, 1.58, 0.4, 1.4, 2.2, 1.31, 2.72, 630.0]
[2.0, 11.84, 0.89, 2.58, 18.0, 94.0, 2.2, 2.21, 0.22, 2.35, 3.05, 0.79, 3.08, 520.0]
[2.0, 12.67, 0.98, 2.24, 18.0, 99.0, 2.2, 1.94, 0.3, 1.46, 2.62, 1.23, 3.16, 450.0]
[2.0, 12.16, 1.61, 2.31, 22.8, 90.0, 1.78, 1.69, 0.43, 1.56, 2.45, 1.33, 2.26, 495.0]
[2.0, 11.65, 1.67, 2.62, 26.0, 88.0, 1.92, 1.61, 0.4, 1.34, 2.6, 1.36, 3.21, 562.0]
[2.0, 11.64, 2.06, 2.46, 21.6, 84.0, 1.95, 1.69, 0.48, 1.35, 2.8, 1.0, 2.75, 680.0]
[2.0, 12.08, 1.33, 2.3, 23.6, 70.0, 2.2, 1.59, 0.42, 1.38, 1.74, 1.07, 3.21, 625.0]
[2.0, 12.08, 1.83, 2.32, 18.5, 81.0, 1.6, 1.5, 0.52, 1.64, 2.4, 1.08, 2.27, 480.0]
[2.0, 12.0, 1.51, 2.42, 22.0, 86.0, 1.45, 1.25, 0.5, 1.63, 3.6, 1.05, 2.65, 450.0]
[2.0, 12.69, 1.53, 2.26, 20.7, 80.0, 1.38, 1.46, 0.58, 1.62, 3.05, 0.96, 2.06, 495.0]
[2.0, 12.29, 2.83, 2.22, 18.0, 88.0, 2.45, 2.25, 0.25, 1.99, 2.15, 1.15, 3.3, 290.0]
[2.0, 11.62, 1.99, 2.28, 18.0, 98.0, 3.02, 2.26, 0.17, 1.35, 3.25, 1.16, 2.96, 345.0]
[2.0, 12.47, 1.52, 2.2, 19.0, 162.0, 2.5, 2.27, 0.32, 3.28, 2.6, 1.16, 2.63, 937.0]
[2.0, 11.81, 2.12, 2.74, 21.5, 134.0, 1.6, 0.99, 0.14, 1.56, 2.5, 0.95, 2.26, 625.0]
[2.0, 12.29, 1.41, 1.98, 16.0, 85.0, 2.55, 2.5, 0.29, 1.77, 2.9, 1.23, 2.74, 428.0]
[2.0, 12.29, 3.17, 2.21, 18.0, 88.0, 2.85, 2.99, 0.45, 2.81, 2.3, 1.42, 2.83, 406.0]
[2.0, 12.08, 2.08, 1.7, 17.5, 97.0, 2.23, 2.17, 0.26, 1.4, 3.3, 1.27, 2.96, 710.0]
[2.0, 12.6, 1.34, 1.9, 18.5, 88.0, 1.45, 1.36, 0.29, 1.35, 2.45, 1.04, 2.77, 562.0]
[2.0, 12.34, 2.45, 2.46, 21.0, 98.0, 2.56, 2.11, 0.34, 1.31, 2.8, 0.8, 3.38, 438.0]
[2.0, 11.82, 1.72, 1.88, 19.5, 86.0, 2.5, 1.64, 0.37, 1.42, 2.06, 0.94, 2.44, 415.0]
[2.0, 12.51, 1.73, 1.98, 20.5, 85.0, 2.2, 1.92, 0.32, 1.48, 2.94, 1.04, 3.57, 672.0]
[2.0, 12.42, 2.55, 2.27, 22.0, 90.0, 1.68, 1.84, 0.66, 1.42, 2.7, 0.86, 3.3, 315.0]
[2.0, 12.25, 1.73, 2.12, 19.0, 80.0, 1.65, 2.03, 0.37, 1.63, 3.4, 1.0, 3.17, 510.0]
[2.0, 12.72, 1.75, 2.28, 22.5, 84.0, 1.38, 1.76, 0.48, 1.63, 3.3, 0.88, 2.42, 488.0]
[2.0, 12.22, 1.29, 1.94, 19.0, 92.0, 2.36, 2.04, 0.39, 2.08, 2.7, 0.86, 3.02, 312.0]
[2.0, 11.61, 1.35, 2.7, 20.0, 94.0, 2.74, 2.92, 0.29, 2.49, 2.65, 0.96, 3.26, 680.0]
[2.0, 11.46, 3.74, 1.82, 19.5, 107.0, 3.18, 2.58, 0.24, 3.58, 2.9, 0.75, 2.81, 562.0]
[2.0, 12.52, 2.43, 2.17, 21.0, 88.0, 2.55, 2.27, 0.26, 1.22, 2.0, 0.9, 2.78, 325.0]
[2.0, 11.76, 2.68, 2.92, 20.0, 103.0, 1.75, 2.03, 0.6, 1.05, 3.8, 1.23, 2.5, 607.0]
[2.0, 11.41, 0.74, 2.5, 21.0, 88.0, 2.48, 2.01, 0.42, 1.44, 3.08, 1.1, 2.31, 434.0]
[2.0, 12.08, 1.39, 2.5, 22.5, 84.0, 2.56, 2.29, 0.43, 1.04, 2.9, 0.93, 3.19, 385.0]
[2.0, 11.03, 1.51, 2.2, 21.5, 85.0, 2.46, 2.17, 0.52, 2.01, 1.9, 1.71, 2.87, 407.0]
[2.0, 11.82, 1.47, 1.99, 20.8, 86.0, 1.98, 1.6, 0.3, 1.53, 1.95, 0.95, 3.33, 495.0]
[2.0, 12.42, 1.61, 2.19, 22.5, 108.0, 2.0, 2.09, 0.34, 1.61, 2.06, 1.06, 2.96, 345.0]
[2.0, 12.0, 3.43, 2.0, 19.0, 87.0, 2.0, 1.64, 0.37, 1.87, 1.28, 0.93, 3.05, 564.0]
[2.0, 11.45, 2.4, 2.42, 20.0, 96.0, 2.9, 2.79, 0.32, 1.83, 3.25, 0.8, 3.39, 625.0]
[2.0, 12.42, 4.43, 2.73, 26.5, 102.0, 2.2, 2.13, 0.43, 1.71, 2.08, 0.92, 3.12, 365.0]
[2.0, 13.05, 5.8, 2.13, 21.5, 86.0, 2.62, 2.65, 0.3, 2.01, 2.6, 0.73, 3.1, 380.0]
[2.0, 11.87, 4.31, 2.39, 21.0, 82.0, 2.86, 3.03, 0.21, 2.91, 2.8, 0.75, 3.64, 380.0]
[2.0, 12.07, 2.16, 2.17, 21.0, 85.0, 2.6, 2.65, 0.37, 1.35, 2.76, 0.86, 3.28, 378.0]
[2.0, 12.43, 1.53, 2.29, 21.5, 86.0, 2.74, 3.15, 0.39, 1.77, 3.94, 0.69, 2.84, 352.0]
[2.0, 11.79, 2.13, 2.78, 28.5, 92.0, 2.13, 2.24, 0.58, 1.76, 3.0, 0.97, 2.44, 466.0]
[2.0, 12.37, 1.63, 2.3, 24.5, 88.0, 2.22, 2.45, 0.4, 1.9, 2.12, 0.89, 2.78, 342.0]
[2.0, 12.04, 4.3, 2.38, 22.0, 80.0, 2.1, 1.75, 0.42, 1.35, 2.6, 0.79, 2.57, 580.0]
[3.0, 12.86, 1.35, 2.32, 18.0, 122.0, 1.51, 1.25, 0.21, 0.94, 4.1, 0.76, 1.29, 630.0]
Cluster: 3 size: 50 :
[2.0, 12.64, 1.36, 2.02, 16.8, 100.0, 2.02, 1.41, 0.53, 0.62, 5.75, 0.98, 1.59, 450.0]
[2.0, 13.05, 3.86, 2.32, 22.5, 85.0, 1.65, 1.59, 0.61, 1.62, 4.8, 0.84, 2.01, 515.0]
[2.0, 12.77, 3.43, 1.98, 16.0, 80.0, 1.63, 1.25, 0.43, 0.83, 3.4, 0.7, 2.12, 372.0]
[3.0, 12.88, 2.99, 2.4, 20.0, 104.0, 1.3, 1.22, 0.24, 0.83, 5.4, 0.74, 1.42, 530.0]
[3.0, 12.81, 2.31, 2.4, 24.0, 98.0, 1.15, 1.09, 0.27, 0.83, 5.7, 0.66, 1.36, 560.0]
[3.0, 12.7, 3.55, 2.36, 21.5, 106.0, 1.7, 1.2, 0.17, 0.84, 5.0, 0.78, 1.29, 600.0]
[3.0, 12.51, 1.24, 2.25, 17.5, 85.0, 2.0, 0.58, 0.6, 1.25, 5.45, 0.75, 1.51, 650.0]
[3.0, 12.6, 2.46, 2.2, 18.5, 94.0, 1.62, 0.66, 0.63, 0.94, 7.1, 0.73, 1.58, 695.0]
[3.0, 12.25, 4.72, 2.54, 21.0, 89.0, 1.38, 0.47, 0.53, 0.8, 3.85, 0.75, 1.27, 720.0]
[3.0, 12.53, 5.51, 2.64, 25.0, 96.0, 1.79, 0.6, 0.63, 1.1, 5.0, 0.82, 1.69, 515.0]
[3.0, 13.49, 3.59, 2.19, 19.5, 88.0, 1.62, 0.48, 0.58, 0.88, 5.7, 0.81, 1.82, 580.0]
[3.0, 12.84, 2.96, 2.61, 24.0, 101.0, 2.32, 0.6, 0.53, 0.81, 4.92, 0.89, 2.15, 590.0]
[3.0, 12.93, 2.81, 2.7, 21.0, 96.0, 1.54, 0.5, 0.53, 0.75, 4.6, 0.77, 2.31, 600.0]
[3.0, 13.36, 2.56, 2.35, 20.0, 89.0, 1.4, 0.5, 0.37, 0.64, 5.6, 0.7, 2.47, 780.0]
[3.0, 13.52, 3.17, 2.72, 23.5, 97.0, 1.55, 0.52, 0.5, 0.55, 4.35, 0.89, 2.06, 520.0]
[3.0, 13.62, 4.95, 2.35, 20.0, 92.0, 2.0, 0.8, 0.47, 1.02, 4.4, 0.91, 2.05, 550.0]
[3.0, 12.25, 3.88, 2.2, 18.5, 112.0, 1.38, 0.78, 0.29, 1.14, 8.21, 0.65, 2.0, 855.0]
[3.0, 13.16, 3.57, 2.15, 21.0, 102.0, 1.5, 0.55, 0.43, 1.3, 4.0, 0.6, 1.68, 830.0]
[3.0, 13.88, 5.04, 2.23, 20.0, 80.0, 0.98, 0.34, 0.4, 0.68, 4.9, 0.58, 1.33, 415.0]
[3.0, 12.87, 4.61, 2.48, 21.5, 86.0, 1.7, 0.65, 0.47, 0.86, 7.65, 0.54, 1.86, 625.0]
[3.0, 13.32, 3.24, 2.38, 21.5, 92.0, 1.93, 0.76, 0.45, 1.25, 8.42, 0.55, 1.62, 650.0]
[3.0, 13.08, 3.9, 2.36, 21.5, 113.0, 1.41, 1.39, 0.34, 1.14, 9.4, 0.57, 1.33, 550.0]
[3.0, 13.5, 3.12, 2.62, 24.0, 123.0, 1.4, 1.57, 0.22, 1.25, 8.6, 0.59, 1.3, 500.0]
[3.0, 12.79, 2.67, 2.48, 22.0, 112.0, 1.48, 1.36, 0.24, 1.26, 10.8, 0.48, 1.47, 480.0]
[3.0, 13.11, 1.9, 2.75, 25.5, 116.0, 2.2, 1.28, 0.26, 1.56, 7.1, 0.61, 1.33, 425.0]
[3.0, 13.23, 3.3, 2.28, 18.5, 98.0, 1.8, 0.83, 0.61, 1.87, 10.52, 0.56, 1.51, 675.0]
[3.0, 12.58, 1.29, 2.1, 20.0, 103.0, 1.48, 0.58, 0.53, 1.4, 7.6, 0.58, 1.55, 640.0]
[3.0, 13.17, 5.19, 2.32, 22.0, 93.0, 1.74, 0.63, 0.61, 1.55, 7.9, 0.6, 1.48, 725.0]
[3.0, 13.84, 4.12, 2.38, 19.5, 89.0, 1.8, 0.83, 0.48, 1.56, 9.01, 0.57, 1.64, 480.0]
[3.0, 12.45, 3.03, 2.64, 27.0, 97.0, 1.9, 0.58, 0.63, 1.14, 7.5, 0.67, 1.73, 880.0]
[3.0, 14.34, 1.68, 2.7, 25.0, 98.0, 2.8, 1.31, 0.53, 2.7, 13.0, 0.57, 1.96, 660.0]
[3.0, 13.48, 1.67, 2.64, 22.5, 89.0, 2.6, 1.1, 0.52, 2.29, 11.75, 0.57, 1.78, 620.0]
[3.0, 12.36, 3.83, 2.38, 21.0, 88.0, 2.3, 0.92, 0.5, 1.04, 7.65, 0.56, 1.58, 520.0]
[3.0, 13.69, 3.26, 2.54, 20.0, 107.0, 1.83, 0.56, 0.5, 0.8, 5.88, 0.96, 1.82, 680.0]
[3.0, 12.85, 3.27, 2.58, 22.0, 106.0, 1.65, 0.6, 0.6, 0.96, 5.58, 0.87, 2.11, 570.0]
[3.0, 12.96, 3.45, 2.35, 18.5, 106.0, 1.39, 0.7, 0.4, 0.94, 5.28, 0.68, 1.75, 675.0]
[3.0, 13.78, 2.76, 2.3, 22.0, 90.0, 1.35, 0.68, 0.41, 1.03, 9.58, 0.7, 1.68, 615.0]
[3.0, 13.73, 4.36, 2.26, 22.5, 88.0, 1.28, 0.47, 0.52, 1.15, 6.62, 0.78, 1.75, 520.0]
[3.0, 13.45, 3.7, 2.6, 23.0, 111.0, 1.7, 0.92, 0.43, 1.46, 10.68, 0.85, 1.56, 695.0]
[3.0, 12.82, 3.37, 2.3, 19.5, 88.0, 1.48, 0.66, 0.4, 0.97, 10.26, 0.72, 1.75, 685.0]
[3.0, 13.58, 2.58, 2.69, 24.5, 105.0, 1.55, 0.84, 0.39, 1.54, 8.66, 0.74, 1.8, 750.0]
[3.0, 13.4, 4.6, 2.86, 25.0, 112.0, 1.98, 0.96, 0.27, 1.11, 8.5, 0.67, 1.92, 630.0]
[3.0, 12.2, 3.03, 2.32, 19.0, 96.0, 1.25, 0.49, 0.4, 0.73, 5.5, 0.66, 1.83, 510.0]
[3.0, 12.77, 2.39, 2.28, 19.5, 86.0, 1.39, 0.51, 0.48, 0.64, 9.899999, 0.57, 1.63, 470.0]
[3.0, 14.16, 2.51, 2.48, 20.0, 91.0, 1.68, 0.7, 0.44, 1.24, 9.7, 0.62, 1.71, 660.0]
[3.0, 13.71, 5.65, 2.45, 20.5, 95.0, 1.68, 0.61, 0.52, 1.06, 7.7, 0.64, 1.74, 740.0]
[3.0, 13.4, 3.91, 2.48, 23.0, 102.0, 1.8, 0.75, 0.43, 1.41, 7.3, 0.7, 1.56, 750.0]
[3.0, 13.27, 4.28, 2.26, 20.0, 120.0, 1.59, 0.69, 0.43, 1.35, 10.2, 0.59, 1.56, 835.0]
[3.0, 13.17, 2.59, 2.37, 20.0, 120.0, 1.65, 0.68, 0.53, 1.46, 9.3, 0.6, 1.62, 840.0]
[3.0, 14.13, 4.1, 2.74, 24.5, 96.0, 2.05, 0.76, 0.56, 1.35, 9.2, 0.61, 1.6, 560.0]