聚类-K均值

数据来源:http://archive.ics.uci.edu/ml/datasets/seeds

15.26    14.84    0.871    5.763    3.312    2.221    5.22    Kama
14.88 14.57 0.8811 5.554 3.333 1.018 4.956 Kama
14.29 14.09 0.905 5.291 3.337 2.699 4.825 Kama
13.84 13.94 0.8955 5.324 3.379 2.259 4.805 Kama
16.14 14.99 0.9034 5.658 3.562 1.355 5.175 Kama
14.38 14.21 0.8951 5.386 3.312 2.462 4.956 Kama
14.69 14.49 0.8799 5.563 3.259 3.586 5.219 Kama
14.11 14.1 0.8911 5.42 3.302 2.7 5.0 Kama
16.63 15.46 0.8747 6.053 3.465 2.04 5.877 Kama
16.44 15.25 0.888 5.884 3.505 1.969 5.533 Kama
15.26 14.85 0.8696 5.714 3.242 4.543 5.314 Kama
14.03 14.16 0.8796 5.438 3.201 1.717 5.001 Kama
13.89 14.02 0.888 5.439 3.199 3.986 4.738 Kama
13.78 14.06 0.8759 5.479 3.156 3.136 4.872 Kama
13.74 14.05 0.8744 5.482 3.114 2.932 4.825 Kama
14.59 14.28 0.8993 5.351 3.333 4.185 4.781 Kama
13.99 13.83 0.9183 5.119 3.383 5.234 4.781 Kama
15.69 14.75 0.9058 5.527 3.514 1.599 5.046 Kama
14.7 14.21 0.9153 5.205 3.466 1.767 4.649 Kama
12.72 13.57 0.8686 5.226 3.049 4.102 4.914 Kama
14.16 14.4 0.8584 5.658 3.129 3.072 5.176 Kama
14.11 14.26 0.8722 5.52 3.168 2.688 5.219 Kama
15.88 14.9 0.8988 5.618 3.507 0.7651 5.091 Kama
12.08 13.23 0.8664 5.099 2.936 1.415 4.961 Kama
15.01 14.76 0.8657 5.789 3.245 1.791 5.001 Kama
16.19 15.16 0.8849 5.833 3.421 0.903 5.307 Kama
13.02 13.76 0.8641 5.395 3.026 3.373 4.825 Kama
12.74 13.67 0.8564 5.395 2.956 2.504 4.869 Kama
14.11 14.18 0.882 5.541 3.221 2.754 5.038 Kama
13.45 14.02 0.8604 5.516 3.065 3.531 5.097 Kama
13.16 13.82 0.8662 5.454 2.975 0.8551 5.056 Kama
15.49 14.94 0.8724 5.757 3.371 3.412 5.228 Kama
14.09 14.41 0.8529 5.717 3.186 3.92 5.299 Kama
13.94 14.17 0.8728 5.585 3.15 2.124 5.012 Kama
15.05 14.68 0.8779 5.712 3.328 2.129 5.36 Kama
16.12 15.0 0.9 5.709 3.485 2.27 5.443 Kama
16.2 15.27 0.8734 5.826 3.464 2.823 5.527 Kama
17.08 15.38 0.9079 5.832 3.683 2.956 5.484 Kama
14.8 14.52 0.8823 5.656 3.288 3.112 5.309 Kama
14.28 14.17 0.8944 5.397 3.298 6.685 5.001 Kama
13.54 13.85 0.8871 5.348 3.156 2.587 5.178 Kama
13.5 13.85 0.8852 5.351 3.158 2.249 5.176 Kama
13.16 13.55 0.9009 5.138 3.201 2.461 4.783 Kama
15.5 14.86 0.882 5.877 3.396 4.711 5.528 Kama
15.11 14.54 0.8986 5.579 3.462 3.128 5.18 Kama
13.8 14.04 0.8794 5.376 3.155 1.56 4.961 Kama
15.36 14.76 0.8861 5.701 3.393 1.367 5.132 Kama
14.99 14.56 0.8883 5.57 3.377 2.958 5.175 Kama
14.79 14.52 0.8819 5.545 3.291 2.704 5.111 Kama
14.86 14.67 0.8676 5.678 3.258 2.129 5.351 Kama
14.43 14.4 0.8751 5.585 3.272 3.975 5.144 Kama
15.78 14.91 0.8923 5.674 3.434 5.593 5.136 Kama
14.49 14.61 0.8538 5.715 3.113 4.116 5.396 Kama
14.33 14.28 0.8831 5.504 3.199 3.328 5.224 Kama
14.52 14.6 0.8557 5.741 3.113 1.481 5.487 Kama
15.03 14.77 0.8658 5.702 3.212 1.933 5.439 Kama
14.46 14.35 0.8818 5.388 3.377 2.802 5.044 Kama
14.92 14.43 0.9006 5.384 3.412 1.142 5.088 Kama
15.38 14.77 0.8857 5.662 3.419 1.999 5.222 Kama
12.11 13.47 0.8392 5.159 3.032 1.502 4.519 Kama
11.42 12.86 0.8683 5.008 2.85 2.7 4.607 Kama
11.23 12.63 0.884 4.902 2.879 2.269 4.703 Kama
12.36 13.19 0.8923 5.076 3.042 3.22 4.605 Kama
13.22 13.84 0.868 5.395 3.07 4.157 5.088 Kama
12.78 13.57 0.8716 5.262 3.026 1.176 4.782 Kama
12.88 13.5 0.8879 5.139 3.119 2.352 4.607 Kama
14.34 14.37 0.8726 5.63 3.19 1.313 5.15 Kama
14.01 14.29 0.8625 5.609 3.158 2.217 5.132 Kama
14.37 14.39 0.8726 5.569 3.153 1.464 5.3 Kama
12.73 13.75 0.8458 5.412 2.882 3.533 5.067 Kama
17.63 15.98 0.8673 6.191 3.561 4.076 6.06 Rosa
16.84 15.67 0.8623 5.998 3.484 4.675 5.877 Rosa
17.26 15.73 0.8763 5.978 3.594 4.539 5.791 Rosa
19.11 16.26 0.9081 6.154 3.93 2.936 6.079 Rosa
16.82 15.51 0.8786 6.017 3.486 4.004 5.841 Rosa
16.77 15.62 0.8638 5.927 3.438 4.92 5.795 Rosa
17.32 15.91 0.8599 6.064 3.403 3.824 5.922 Rosa
20.71 17.23 0.8763 6.579 3.814 4.451 6.451 Rosa
18.94 16.49 0.875 6.445 3.639 5.064 6.362 Rosa
17.12 15.55 0.8892 5.85 3.566 2.858 5.746 Rosa
16.53 15.34 0.8823 5.875 3.467 5.532 5.88 Rosa
18.72 16.19 0.8977 6.006 3.857 5.324 5.879 Rosa
20.2 16.89 0.8894 6.285 3.864 5.173 6.187 Rosa
19.57 16.74 0.8779 6.384 3.772 1.472 6.273 Rosa
19.51 16.71 0.878 6.366 3.801 2.962 6.185 Rosa
18.27 16.09 0.887 6.173 3.651 2.443 6.197 Rosa
18.88 16.26 0.8969 6.084 3.764 1.649 6.109 Rosa
18.98 16.66 0.859 6.549 3.67 3.691 6.498 Rosa
21.18 17.21 0.8989 6.573 4.033 5.78 6.231 Rosa
20.88 17.05 0.9031 6.45 4.032 5.016 6.321 Rosa
20.1 16.99 0.8746 6.581 3.785 1.955 6.449 Rosa
18.76 16.2 0.8984 6.172 3.796 3.12 6.053 Rosa
18.81 16.29 0.8906 6.272 3.693 3.237 6.053 Rosa
18.59 16.05 0.9066 6.037 3.86 6.001 5.877 Rosa
18.36 16.52 0.8452 6.666 3.485 4.933 6.448 Rosa
16.87 15.65 0.8648 6.139 3.463 3.696 5.967 Rosa
19.31 16.59 0.8815 6.341 3.81 3.477 6.238 Rosa
18.98 16.57 0.8687 6.449 3.552 2.144 6.453 Rosa
18.17 16.26 0.8637 6.271 3.512 2.853 6.273 Rosa
18.72 16.34 0.881 6.219 3.684 2.188 6.097 Rosa
16.41 15.25 0.8866 5.718 3.525 4.217 5.618 Rosa
17.99 15.86 0.8992 5.89 3.694 2.068 5.837 Rosa
19.46 16.5 0.8985 6.113 3.892 4.308 6.009 Rosa
19.18 16.63 0.8717 6.369 3.681 3.357 6.229 Rosa
18.95 16.42 0.8829 6.248 3.755 3.368 6.148 Rosa
18.83 16.29 0.8917 6.037 3.786 2.553 5.879 Rosa
18.85 16.17 0.9056 6.152 3.806 2.843 6.2 Rosa
17.63 15.86 0.88 6.033 3.573 3.747 5.929 Rosa
19.94 16.92 0.8752 6.675 3.763 3.252 6.55 Rosa
18.55 16.22 0.8865 6.153 3.674 1.738 5.894 Rosa
18.45 16.12 0.8921 6.107 3.769 2.235 5.794 Rosa
19.38 16.72 0.8716 6.303 3.791 3.678 5.965 Rosa
19.13 16.31 0.9035 6.183 3.902 2.109 5.924 Rosa
19.14 16.61 0.8722 6.259 3.737 6.682 6.053 Rosa
20.97 17.25 0.8859 6.563 3.991 4.677 6.316 Rosa
19.06 16.45 0.8854 6.416 3.719 2.248 6.163 Rosa
18.96 16.2 0.9077 6.051 3.897 4.334 5.75 Rosa
19.15 16.45 0.889 6.245 3.815 3.084 6.185 Rosa
18.89 16.23 0.9008 6.227 3.769 3.639 5.966 Rosa
20.03 16.9 0.8811 6.493 3.857 3.063 6.32 Rosa
20.24 16.91 0.8897 6.315 3.962 5.901 6.188 Rosa
18.14 16.12 0.8772 6.059 3.563 3.619 6.011 Rosa
16.17 15.38 0.8588 5.762 3.387 4.286 5.703 Rosa
18.43 15.97 0.9077 5.98 3.771 2.984 5.905 Rosa
15.99 14.89 0.9064 5.363 3.582 3.336 5.144 Rosa
18.75 16.18 0.8999 6.111 3.869 4.188 5.992 Rosa
18.65 16.41 0.8698 6.285 3.594 4.391 6.102 Rosa
17.98 15.85 0.8993 5.979 3.687 2.257 5.919 Rosa
20.16 17.03 0.8735 6.513 3.773 1.91 6.185 Rosa
17.55 15.66 0.8991 5.791 3.69 5.366 5.661 Rosa
18.3 15.89 0.9108 5.979 3.755 2.837 5.962 Rosa
18.94 16.32 0.8942 6.144 3.825 2.908 5.949 Rosa
15.38 14.9 0.8706 5.884 3.268 4.462 5.795 Rosa
16.16 15.33 0.8644 5.845 3.395 4.266 5.795 Rosa
15.56 14.89 0.8823 5.776 3.408 4.972 5.847 Rosa
15.38 14.66 0.899 5.477 3.465 3.6 5.439 Rosa
17.36 15.76 0.8785 6.145 3.574 3.526 5.971 Rosa
15.57 15.15 0.8527 5.92 3.231 2.64 5.879 Rosa
15.6 15.11 0.858 5.832 3.286 2.725 5.752 Rosa
16.23 15.18 0.885 5.872 3.472 3.769 5.922 Rosa
13.07 13.92 0.848 5.472 2.994 5.304 5.395 Canadian
13.32 13.94 0.8613 5.541 3.073 7.035 5.44 Canadian
13.34 13.95 0.862 5.389 3.074 5.995 5.307 Canadian
12.22 13.32 0.8652 5.224 2.967 5.469 5.221 Canadian
11.82 13.4 0.8274 5.314 2.777 4.471 5.178 Canadian
11.21 13.13 0.8167 5.279 2.687 6.169 5.275 Canadian
11.43 13.13 0.8335 5.176 2.719 2.221 5.132 Canadian
12.49 13.46 0.8658 5.267 2.967 4.421 5.002 Canadian
12.7 13.71 0.8491 5.386 2.911 3.26 5.316 Canadian
10.79 12.93 0.8107 5.317 2.648 5.462 5.194 Canadian
11.83 13.23 0.8496 5.263 2.84 5.195 5.307 Canadian
12.01 13.52 0.8249 5.405 2.776 6.992 5.27 Canadian
12.26 13.6 0.8333 5.408 2.833 4.756 5.36 Canadian
11.18 13.04 0.8266 5.22 2.693 3.332 5.001 Canadian
11.36 13.05 0.8382 5.175 2.755 4.048 5.263 Canadian
11.19 13.05 0.8253 5.25 2.675 5.813 5.219 Canadian
11.34 12.87 0.8596 5.053 2.849 3.347 5.003 Canadian
12.13 13.73 0.8081 5.394 2.745 4.825 5.22 Canadian
11.75 13.52 0.8082 5.444 2.678 4.378 5.31 Canadian
11.49 13.22 0.8263 5.304 2.695 5.388 5.31 Canadian
12.54 13.67 0.8425 5.451 2.879 3.082 5.491 Canadian
12.02 13.33 0.8503 5.35 2.81 4.271 5.308 Canadian
12.05 13.41 0.8416 5.267 2.847 4.988 5.046 Canadian
12.55 13.57 0.8558 5.333 2.968 4.419 5.176 Canadian
11.14 12.79 0.8558 5.011 2.794 6.388 5.049 Canadian
12.1 13.15 0.8793 5.105 2.941 2.201 5.056 Canadian
12.44 13.59 0.8462 5.319 2.897 4.924 5.27 Canadian
12.15 13.45 0.8443 5.417 2.837 3.638 5.338 Canadian
11.35 13.12 0.8291 5.176 2.668 4.337 5.132 Canadian
11.24 13.0 0.8359 5.09 2.715 3.521 5.088 Canadian
11.02 13.0 0.8189 5.325 2.701 6.735 5.163 Canadian
11.55 13.1 0.8455 5.167 2.845 6.715 4.956 Canadian
11.27 12.97 0.8419 5.088 2.763 4.309 5.0 Canadian
11.4 13.08 0.8375 5.136 2.763 5.588 5.089 Canadian
10.83 12.96 0.8099 5.278 2.641 5.182 5.185 Canadian
10.8 12.57 0.859 4.981 2.821 4.773 5.063 Canadian
11.26 13.01 0.8355 5.186 2.71 5.335 5.092 Canadian
10.74 12.73 0.8329 5.145 2.642 4.702 4.963 Canadian
11.48 13.05 0.8473 5.18 2.758 5.876 5.002 Canadian
12.21 13.47 0.8453 5.357 2.893 1.661 5.178 Canadian
11.41 12.95 0.856 5.09 2.775 4.957 4.825 Canadian
12.46 13.41 0.8706 5.236 3.017 4.987 5.147 Canadian
12.19 13.36 0.8579 5.24 2.909 4.857 5.158 Canadian
11.65 13.07 0.8575 5.108 2.85 5.209 5.135 Canadian
12.89 13.77 0.8541 5.495 3.026 6.185 5.316 Canadian
11.56 13.31 0.8198 5.363 2.683 4.062 5.182 Canadian
11.81 13.45 0.8198 5.413 2.716 4.898 5.352 Canadian
10.91 12.8 0.8372 5.088 2.675 4.179 4.956 Canadian
11.23 12.82 0.8594 5.089 2.821 7.524 4.957 Canadian
10.59 12.41 0.8648 4.899 2.787 4.975 4.794 Canadian
10.93 12.8 0.839 5.046 2.717 5.398 5.045 Canadian
11.27 12.86 0.8563 5.091 2.804 3.985 5.001 Canadian
11.87 13.02 0.8795 5.132 2.953 3.597 5.132 Canadian
10.82 12.83 0.8256 5.18 2.63 4.853 5.089 Canadian
12.11 13.27 0.8639 5.236 2.975 4.132 5.012 Canadian
12.8 13.47 0.886 5.16 3.126 4.873 4.914 Canadian
12.79 13.53 0.8786 5.224 3.054 5.483 4.958 Canadian
13.37 13.78 0.8849 5.32 3.128 4.67 5.091 Canadian
12.62 13.67 0.8481 5.41 2.911 3.306 5.231 Canadian
12.76 13.38 0.8964 5.073 3.155 2.828 4.83 Canadian
12.38 13.44 0.8609 5.219 2.989 5.472 5.045 Canadian
12.67 13.32 0.8977 4.984 3.135 2.3 4.745 Canadian
11.18 12.72 0.868 5.009 2.81 4.051 4.828 Canadian
12.7 13.41 0.8874 5.183 3.091 8.456 5.0 Canadian
12.37 13.47 0.8567 5.204 2.96 3.919 5.001 Canadian
12.19 13.2 0.8783 5.137 2.981 3.631 4.87 Canadian
11.23 12.88 0.8511 5.14 2.795 4.325 5.003 Canadian
13.2 13.66 0.8883 5.236 3.232 8.315 5.056 Canadian
11.84 13.21 0.8521 5.175 2.836 3.598 5.044 Canadian
12.3 13.34 0.8684 5.243 2.974 5.637 5.063 Canadian

聚类方法:K-均值

实现语言:java

输入:样本集seed={X1,X2...Xn}

聚类数目:k =3;

过程:

首先用zscore()函数对数据集进行标准化 Xi = (Xi - μ)/σ (μ 为算数均值, σ 为标准差;

从样本中随机抽取k个数据作为初始均值向量{μ12,...,μk}

repeat:

  令C=Φ (1 ≤ i ≤ k )

  for i=1,2,...,n do

    计算样本 Xi 与各均值向量的距离,并把它加入到离它最近的均值向量所在的集合中;

  end for

  for i =1,2,...,k do

    计算每个集合中所有元素的均值向量 μ′i;

    if  μ′≠ μ

       μi  =  μ′i

    else

      不用更新;

    end if

  end for

until 当前均值向量均未更新

输出:簇分类 C = {C1,C2,...Ck}

程序代码:

import java.io.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Set;
import java.util.HashSet; public class KCluster{
static float[][] seed;
static String[] kind;
static int n;
static float e = (float) 1.0E-20;//0.000000001;-17
KCluster() throws IOException{
File file = new File("seeds.txt");
n = countLines(file);
seed = new float[n][7];
kind = new String[n];
Scanner sc=new Scanner(file);
for(int i=0;i<n;i++){
for(int j=0;j<7;j++){
seed[i][j] = sc.nextFloat();
}
kind[i] = sc.next();
}
sc.close();
zscore(seed);//标准化
}
public static void main(String[] args) throws FileNotFoundException,IOException{
new KCluster();
int k=3;
float [][] sample =new float[k][]; //存放初始均值向量
ArrayList<Set<Integer>> set = new ArrayList<Set<Integer>>();
for(int i=0;i<k;i++){ //从n组数据随机取出k组
sample[i] = seed[(int)(Math.random()*(n))];
set.add(new HashSet<Integer>());
}
float d;
int tag; //簇标记
Boolean flag; //标记均值向量是否更新
do{
flag =true;
for(int i=0;i<k;i++){
set.get(i).clear();
}
for(int i=0;i<n;i++){ //按距离最近确定每组数据的簇标记
d = distance(seed[i],sample[0]);
tag =0;
for(int j =1;j<k;j++){
if(distance(seed[i],sample[j])<d){
d=distance(seed[i],sample[j]);
tag=j;
}
}
set.get(tag).add(i);
}
//计算新的均值向量
for(int i=0;i<k;i++){
float[] sam = new float[7];
for(int j=0;j<7;j++){
sam[j] = sample[i][j];
sample[i][j]=0;
}
int size = set.get(i).size();
for(Integer each:set.get(i)){
float[] temp = seed[each];
for(int l=0;l<7;l++){
sample[i][l] +=temp[l];
}
}
for(int j =0;j<7;j++){
sample[i][j] /= size;
}
for(int j=0;j<7;j++){
if(sam[j] - sample[i][j] > e){
flag = false;
break;
}
}
}
}while(!flag);
showset(set);
show(set);
}
public static int countLines(File file)throws IOException{
byte[] buff = new byte[1024];
InputStream in =new BufferedInputStream(new FileInputStream(file));
int count =0;
int num=0;
Boolean flag =false;
while((num=in.read(buff))!=-1){
flag = true;
for(int i=0;i<num;i++){
if(buff[i]=='\n'){
count++;
}
}
}
in.close();
count = (count==0&&!flag)?0:count+1;
return count;
}
public static float distance(float[] a,float[] b){
if(a.length!=b.length){
return -1;
}
float s=0 ;
for(int i=0;i<a.length;i++){
s += (a[i]-b[i])*(a[i]-b[i]);
}
s = (float)Math.sqrt(s);
return s;
}
public static void show(ArrayList<Set<Integer>> set){
for(int i=0;i<set.size();i++){
for(Integer each:set.get(i)){
for(int j=0;j<7;j++){
System.out.print(seed[each][j]+"\t");
}
System.out.println(kind[each]);
}
System.out.println();
}
}
public static void showset(ArrayList<Set<Integer>> set){
for(int i=0;i<set.size();i++){
System.out.println("|C"+(i+1)+"| = "+set.get(i).size());
System.out.print("C"+(i+1)+" = { ");
for(Integer each:set.get(i)){
System.out.print(each+",");
}
System.out.println(" }");
}
}
public static void zscore(float[][] a){
float[] x = new float[7];
float[] s = new float[7];
for(int i=0;i<n;i++){
for(int j =0;j<7;j++){
x[j] += seed[i][j];
}
}
for(int i=0;i<7;i++){
x[i] /= n;
}
for(int i=0;i<n;i++){
for(int j=0;j<7;j++){
s[j] += (seed[i][j] - x[j])*(seed[i][j] - x[j]);
}
}
for(int i=0;i<7;i++){
s[i] = (float)Math.sqrt(s[i]/n);
}
for(int i=0;i<n;i++){
for(int j=0;j<7;j++){
seed[i][j] = (seed[i][j] - x[j])/s[j];
}
}
}
}

 运行结果:

|C1| = 79
C1 = { 10,140,141,142,143,144,145,146,19,147,148,149,150,151,152,153,26,154,27,155,156,29,157,158,159,32,160,161,162,163,164,166,39,167,168,169,170,171,172,173,174,175,176,177,178,179,52,180,181,182,183,184,185,186,59,187,60,188,189,190,63,191,192,193,194,195,196,69,197,198,200,202,203,204,205,206,207,208,209, }
|C2| = 74
C2 = { 128,129,130,131,132,133,134,8,136,9,137,138,139,36,37,43,51,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,125,126,127, }
|C3| = 57
C3 = { 0,1,2,3,4,5,6,7,11,12,13,14,15,16,17,18,20,21,22,23,24,25,28,30,31,33,34,35,38,40,41,42,44,45,46,47,48,49,50,53,54,55,56,57,58,61,62,64,65,66,67,68,124,135,165,199,201, }
0.14209792 0.22313938 -0.059333883 0.19336289 -0.04406783 0.5618759 -0.19185953 Kama
-0.61235595 -0.49068293 -0.9756335 -0.35413957 -0.7022178 1.0692182 -0.026657853 Canadian
-0.5262311 -0.4753323 -0.41143063 -0.1980341 -0.4925653 2.2232387 0.065121174 Canadian
-0.51934093 -0.4676566 -0.3817359 -0.54191965 -0.48991168 1.529893 -0.20613618 Canadian
-0.9051803 -0.95121354 -0.24598807 -0.91521657 -0.77387106 1.1792201 -0.38153574 Canadian
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0.18343781 0.16173539 0.623648 0.07571768 0.4256594 -1.1341548 -0.37949634 Kama
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0.3935823 0.25384137 1.5017698 -0.6007423 0.8582338 -0.24280539 -0.5385799 Rosa
0.18343781 0.07730435 1.1878508 -0.3428273 0.5477355 -0.06680227 0.06308179 Rosa
-0.94652015 -1.0816972 0.35215238 -1.1844428 -0.84287065 -0.9994857 -0.71805817 Canadian
-0.7191506 -0.9051602 1.077555 -1.2568399 -0.2749513 -0.58147806 -1.1789927 Canadian
-0.75015557 -0.95121354 1.1327043 -1.4581934 -0.3280278 -0.9334845 -1.3523529 Canadian
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