- 1. KNN算法原理
- 2. KNN算法特点
- 3. K值
- 4. 数据处理
- 4.1 KDTree
- 4.2 数据归一化
- 5. 算法流程
- 6. Java代码
- 6.1 训练集，测试集
- 6.2 KNN.java
- 6.3 预测
- "英文："
K-Nearest Neighbor
- "思想："
对于任意n维输入向量，分别对应于特征空间中的一个点，输出为该特征向量所对应的类别标签或预测值
- "原理："
1. 它的工作原理是利用训练数据对特征向量空间进行划分，并将划分结果作为最终算法模型
2. 输入没有标签的数据后，将这个没有标签的数据的每个特征与样本集中的数据对应的特征进行比较，
然后提取样本中特征最相近的数据（最近邻）的分类标签
1. 最基础、最简单
2. 我们只选择样本数据集中前k个最相似的数据，这就是KNN算法中K的由来（k<=20）
3. 优点：精度高、对异常值不敏感
4. 缺点：计算复杂度高、空间复杂度高
5. 也被称为惰性学习 lazy learning. 类似于开卷考试, 在已有数据中去找答案
6. 一般需要对数据归一化
- "K值选择："
1. k值过小，误差较小，但容易导致KNN算法的过拟合
2. k值过大，鲁棒性，模型容易发生欠拟合
3. 一般k值选得比较小，我们会在较小范围内选取k值，同时把测试集上准确率最高的那个确定为最终的算法超参数k
- "交叉验证："
1. 将样本数据按照一定比例，拆分出训练用的数据和验证用的数据（比如6：4拆分出部分训练数据和验证数据）
2. 从选取一个较小的K值开始不断增加K的值
3. 然后计算验证集合的方差，最终找到一个比较合适的K值。
- "目的："
为了快速查找到k个近邻，我们可以考虑使用特殊的数据结构存储训练数据，用来减少搜索次数。
其中，KDTree就是最著名的一种。
- 原因
1. 在距离计算中我们需要计算预测样本与训练数据集中多个特征的距离，但不同特征之间数据差异较大，会造成预测错误。
2. 可以类比：欧氏距离与标准化欧式距离
3. 目的：使特征等价
4. 数据归一化，使不同特征属于同一数量级，之间的差异性减弱，有利于KNN的分类
- 数据归一化
一般的数据归一化是将数据映射在 [0，1] 中，公式如下：
X = X − X m i n X m a x − X m i n X=\frac{X-X_{min}}{X_{max}-X_{min}} X=Xmax−XminX−Xmin
5. 算法流程 1. 计算待预测样本与训练数据集中样本特征之间的欧式距离。
2. 按照距离递增的顺序排序。
3. 选取距离最近的K个样本以及所属类别的次数。
4. 返回前k个点所出现频率最高的类别作为预测分类结果。
- iris.arff
@RELATION iris
@ATTRIBUTE sepallength REAL
@ATTRIBUTE sepalwidth REAL
@ATTRIBUTE petallength REAL
@ATTRIBUTE petalwidth REAL
@ATTRIBUTE class {Iris-setosa,Iris-versicolor,Iris-virginica}
@DATA
5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.0,1.4,0.2,Iris-setosa
4.7,3.2,1.3,0.2,Iris-setosa
4.6,3.1,1.5,0.2,Iris-setosa
5.0,3.6,1.4,0.2,Iris-setosa
5.4,3.9,1.7,0.4,Iris-setosa
4.6,3.4,1.4,0.3,Iris-setosa
5.0,3.4,1.5,0.2,Iris-setosa
4.4,2.9,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.4,3.7,1.5,0.2,Iris-setosa
4.8,3.4,1.6,0.2,Iris-setosa
4.8,3.0,1.4,0.1,Iris-setosa
4.3,3.0,1.1,0.1,Iris-setosa
5.8,4.0,1.2,0.2,Iris-setosa
5.7,4.4,1.5,0.4,Iris-setosa
5.4,3.9,1.3,0.4,Iris-setosa
5.1,3.5,1.4,0.3,Iris-setosa
5.7,3.8,1.7,0.3,Iris-setosa
5.1,3.8,1.5,0.3,Iris-setosa
5.4,3.4,1.7,0.2,Iris-setosa
5.1,3.7,1.5,0.4,Iris-setosa
4.6,3.6,1.0,0.2,Iris-setosa
5.1,3.3,1.7,0.5,Iris-setosa
4.8,3.4,1.9,0.2,Iris-setosa
5.0,3.0,1.6,0.2,Iris-setosa
5.0,3.4,1.6,0.4,Iris-setosa
5.2,3.5,1.5,0.2,Iris-setosa
5.2,3.4,1.4,0.2,Iris-setosa
4.7,3.2,1.6,0.2,Iris-setosa
4.8,3.1,1.6,0.2,Iris-setosa
5.4,3.4,1.5,0.4,Iris-setosa
5.2,4.1,1.5,0.1,Iris-setosa
5.5,4.2,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.0,3.2,1.2,0.2,Iris-setosa
5.5,3.5,1.3,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
4.4,3.0,1.3,0.2,Iris-setosa
5.1,3.4,1.5,0.2,Iris-setosa
5.0,3.5,1.3,0.3,Iris-setosa
4.5,2.3,1.3,0.3,Iris-setosa
4.4,3.2,1.3,0.2,Iris-setosa
5.0,3.5,1.6,0.6,Iris-setosa
5.1,3.8,1.9,0.4,Iris-setosa
4.8,3.0,1.4,0.3,Iris-setosa
5.1,3.8,1.6,0.2,Iris-setosa
4.6,3.2,1.4,0.2,Iris-setosa
5.3,3.7,1.5,0.2,Iris-setosa
5.0,3.3,1.4,0.2,Iris-setosa
7.0,3.2,4.7,1.4,Iris-versicolor
6.4,3.2,4.5,1.5,Iris-versicolor
6.9,3.1,4.9,1.5,Iris-versicolor
5.5,2.3,4.0,1.3,Iris-versicolor
6.5,2.8,4.6,1.5,Iris-versicolor
5.7,2.8,4.5,1.3,Iris-versicolor
6.3,3.3,4.7,1.6,Iris-versicolor
4.9,2.4,3.3,1.0,Iris-versicolor
6.6,2.9,4.6,1.3,Iris-versicolor
5.2,2.7,3.9,1.4,Iris-versicolor
5.0,2.0,3.5,1.0,Iris-versicolor
5.9,3.0,4.2,1.5,Iris-versicolor
6.0,2.2,4.0,1.0,Iris-versicolor
6.1,2.9,4.7,1.4,Iris-versicolor
5.6,2.9,3.6,1.3,Iris-versicolor
6.7,3.1,4.4,1.4,Iris-versicolor
5.6,3.0,4.5,1.5,Iris-versicolor
5.8,2.7,4.1,1.0,Iris-versicolor
6.2,2.2,4.5,1.5,Iris-versicolor
5.6,2.5,3.9,1.1,Iris-versicolor
5.9,3.2,4.8,1.8,Iris-versicolor
6.1,2.8,4.0,1.3,Iris-versicolor
6.3,2.5,4.9,1.5,Iris-versicolor
6.1,2.8,4.7,1.2,Iris-versicolor
6.4,2.9,4.3,1.3,Iris-versicolor
6.6,3.0,4.4,1.4,Iris-versicolor
6.8,2.8,4.8,1.4,Iris-versicolor
6.7,3.0,5.0,1.7,Iris-versicolor
6.0,2.9,4.5,1.5,Iris-versicolor
5.7,2.6,3.5,1.0,Iris-versicolor
5.5,2.4,3.8,1.1,Iris-versicolor
5.5,2.4,3.7,1.0,Iris-versicolor
5.8,2.7,3.9,1.2,Iris-versicolor
6.0,2.7,5.1,1.6,Iris-versicolor
5.4,3.0,4.5,1.5,Iris-versicolor
6.0,3.4,4.5,1.6,Iris-versicolor
6.7,3.1,4.7,1.5,Iris-versicolor
6.3,2.3,4.4,1.3,Iris-versicolor
5.6,3.0,4.1,1.3,Iris-versicolor
5.5,2.5,4.0,1.3,Iris-versicolor
5.5,2.6,4.4,1.2,Iris-versicolor
6.1,3.0,4.6,1.4,Iris-versicolor
5.8,2.6,4.0,1.2,Iris-versicolor
5.0,2.3,3.3,1.0,Iris-versicolor
5.6,2.7,4.2,1.3,Iris-versicolor
5.7,3.0,4.2,1.2,Iris-versicolor
5.7,2.9,4.2,1.3,Iris-versicolor
6.2,2.9,4.3,1.3,Iris-versicolor
5.1,2.5,3.0,1.1,Iris-versicolor
5.7,2.8,4.1,1.3,Iris-versicolor
6.3,3.3,6.0,2.5,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
7.1,3.0,5.9,2.1,Iris-virginica
6.3,2.9,5.6,1.8,Iris-virginica
6.5,3.0,5.8,2.2,Iris-virginica
7.6,3.0,6.6,2.1,Iris-virginica
4.9,2.5,4.5,1.7,Iris-virginica
7.3,2.9,6.3,1.8,Iris-virginica
6.7,2.5,5.8,1.8,Iris-virginica
7.2,3.6,6.1,2.5,Iris-virginica
6.5,3.2,5.1,2.0,Iris-virginica
6.4,2.7,5.3,1.9,Iris-virginica
6.8,3.0,5.5,2.1,Iris-virginica
5.7,2.5,5.0,2.0,Iris-virginica
5.8,2.8,5.1,2.4,Iris-virginica
6.4,3.2,5.3,2.3,Iris-virginica
6.5,3.0,5.5,1.8,Iris-virginica
7.7,3.8,6.7,2.2,Iris-virginica
7.7,2.6,6.9,2.3,Iris-virginica
6.0,2.2,5.0,1.5,Iris-virginica
6.9,3.2,5.7,2.3,Iris-virginica
5.6,2.8,4.9,2.0,Iris-virginica
7.7,2.8,6.7,2.0,Iris-virginica
6.3,2.7,4.9,1.8,Iris-virginica
6.7,3.3,5.7,2.1,Iris-virginica
7.2,3.2,6.0,1.8,Iris-virginica
6.2,2.8,4.8,1.8,Iris-virginica
6.1,3.0,4.9,1.8,Iris-virginica
6.4,2.8,5.6,2.1,Iris-virginica
7.2,3.0,5.8,1.6,Iris-virginica
7.4,2.8,6.1,1.9,Iris-virginica
7.9,3.8,6.4,2.0,Iris-virginica
6.4,2.8,5.6,2.2,Iris-virginica
6.3,2.8,5.1,1.5,Iris-virginica
6.1,2.6,5.6,1.4,Iris-virginica
7.7,3.0,6.1,2.3,Iris-virginica
6.3,3.4,5.6,2.4,Iris-virginica
6.4,3.1,5.5,1.8,Iris-virginica
6.0,3.0,4.8,1.8,Iris-virginica
6.9,3.1,5.4,2.1,Iris-virginica
6.7,3.1,5.6,2.4,Iris-virginica
6.9,3.1,5.1,2.3,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
6.8,3.2,5.9,2.3,Iris-virginica
6.7,3.3,5.7,2.5,Iris-virginica
6.7,3.0,5.2,2.3,Iris-virginica
6.3,2.5,5.0,1.9,Iris-virginica
6.5,3.0,5.2,2.0,Iris-virginica
6.2,3.4,5.4,2.3,Iris-virginica
5.9,3.0,5.1,1.8,Iris-virginica
- test.arff
@RELATION iris
@ATTRIBUTE sepallength REAL
@ATTRIBUTE sepalwidth REAL
@ATTRIBUTE petallength REAL
@ATTRIBUTE petalwidth REAL
@ATTRIBUTE class {Iris-setosa,Iris-versicolor,Iris-virginica}
@DATA
5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.0,1.4,0.2,Iris-setosa
package supervisedlearning;
import java.io.FileReader;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Set;
import weka.core.Instances;
public class KNN {
Instances trainDataset;
int k;
/**
* 读取训练集（参照集）
* @param trainingFile
* @param numNeighbors
*/
public KNN(String trainingFile, int numNeighbors) {
trainDataset = null;
k = numNeighbors;
try {
FileReader fileReader = new FileReader(trainingFile);
trainDataset = new Instances(fileReader);
fileReader.close();
} catch (Exception e) {
System.out.println("Cannot read the file: " + trainingFile + "\r\n" + e);
System.exit(0);
}
}
/**
* 从样本里面随机选num个样本下标
*
* @param length
* @param num
* @return
*/
public int[] getRandomIndices(int length, int num) {
// 1
Set<Integer> set = new HashSet<>(num);
// 2
while (set.size() != num) {
for (int i = 0; i < num; i++) {
set.add((int) (Math.random() * length));
}
}
// 3
int[] result = new int[num];
Iterator<Integer> it = set.iterator();
for (int i = 0; i < num; i++) {
result[i] = it.next();
}
return result;
}
/**
* 通过下标，来计算两个样本（原型样本---其余样本）的欧式距离
* @param testIndex
* @param trainIndex
* @return
*/
public double eudistance(int testIndex, int trainIndex) {
double result = 0.0;
for (int i = 0; i < trainDataset.numAttributes() - 1; i++) {
double temp;
double p1 = trainDataset.instance(testIndex).value(i);
double p2 = trainDataset.instance(trainIndex).value(i);
temp = Math.abs((p1 - p2)) * Math.abs((p1 - p2));
result += temp;
}
return Math.sqrt(result);
}
/**
* 读取测试集
* @param testingFile
* @return
*/
public Instances readTestingFile(String testingFile) {
Instances result = null;
try {
FileReader fileReader = new FileReader(testingFile);
result = new Instances(fileReader);
fileReader.close();
} catch (Exception e) {
System.out.println("Cannot read the file: " + testingFile + "\r\n" + e);
System.exit(0);
}
return result;
}
/**
* 测试样本（下标）到训练样本（下标）的欧式距离---->构成了二维矩阵
* @param testDataset
* @param trainDataset
* @return
*/
public double[][] getDistances(Instances testDataset, Instances trainDataset) {
int trainM = trainDataset.numInstances();
int testM = testDataset.numInstances();
double[][] distances = new double[testM][trainM];
for (int i = 0; i < testM; i++) {
for (int j = 0; j < trainM; j++) {
distances[i][j] = eudistance(i, j);
}
}
return distances;
}
public void bubbleSort(double[] arrs) {
int n = arrs.length;
for(int i=0; i<n; i++) {
for(int j=0; j<n-1-i; j++) {
if(arrs[j] > arrs[j+1]) {
swap(arrs, j, j+1);
}
}
}
} // bubbleSort
private void swap(double[] arrs, int i, int j) {
double temp = arrs[i];
arrs[i] = arrs[j];
arrs[j] = temp;
} // swap
public int[][] getIndexByDistances(double[][] distances) {
int len1 = distances.length;
int len2 = distances[0].length;
int[][] result = new int[len1][len2];
// 1
return result;
}
public void predict(String testingFile) {
Instances testDataset = readTestingFile(testingFile);
int trainM = trainDataset.numInstances();
int testM = testDataset.numInstances();
// 1
double[][] distances = new double[testM][trainM];
distances = getDistances(testDataset, trainDataset);
System.out.println("测试样本到训练样本的距离：" + Arrays.deepToString(distances));
int[][] indexOfTrains = getIndexByDistances(distances);
System.out.println("训练样本：" + Arrays.deepToString(indexOfTrains));
// 2
for(int i=0; i< testM; i++) {
bubbleSort(distances[i]);
}
System.out.println("排序后的距离：" + Arrays.deepToString(distances));
indexOfTrains = getIndexByDistances(distances);
System.out.println("训练样本：" + Arrays.deepToString(indexOfTrains));
// 3
double[][] kDistances = new double[testM][k];
for (int i = 0; i < testM; i++) {
for (int j = 0; j < k; j++) {
kDistances[i][j] = distances[i][j];
}
}
System.out.println(k + "个临近的距离：" + Arrays.deepToString(kDistances));
int[][] minIndex = getIndexByDistances(kDistances);
System.out.println("训练样本：" + Arrays.deepToString(minIndex));
// 4
}
public double getAccuracy() {
double result = 0.0;
// 1
return result;
}
public static void main(String args[]) {
KNN knn = new KNN("D:/data/iris.arff", 7);
knn.predict("D:/data/test.arff");
System.out.println("准确度：" + knn.getAccuracy()*100 + "%");
}
} // KNN
测试样本到训练样本的距离：[[0.0, 0.5385164807134502, 0.509901951359278, 0.648074069840786, 0.1414213562373093, 0.6164414002968979, 0.5196152422706632, 0.17320508075688762, 0.9219544457292882, 0.4690415759823426, 0.37416573867739483, 0.3741657386773941, 0.5916079783099616, 0.9949874371066197, 0.8831760866327848, 1.1045361017187267, 0.5477225575051664, 0.09999999999999998, 0.7416198487095667, 0.33166247903553986, 0.4358898943540679, 0.30000000000000016, 0.648074069840786, 0.46904157598234303, 0.5916079783099616, 0.5477225575051662, 0.316227766016838, 0.14142135623730995, 0.14142135623730995, 0.53851648071345, 0.5385164807134504, 0.3872983346207423, 0.6244997998398396, 0.8062257748298554, 0.4690415759823426, 0.37416573867739383, 0.41231056256176635, 0.4690415759823426, 0.866025403784438, 0.14142135623730964, 0.17320508075688743, 1.3490737563232043, 0.7681145747868601, 0.45825756949558394, 0.6164414002968975, 0.5916079783099616, 0.3605551275463989, 0.58309518948453, 0.30000000000000027, 0.22360679774997896, 4.003748243833521, 3.6166282640050254, 4.164132562731403, 3.093541659651604, 3.792097045171708, 3.416138170507745, 3.7854986461495406, 2.345207879911715, 3.749666651850535, 2.8879058156387303, 2.703701166919155, 3.228002478313795, 3.146426544510455, 3.7, 2.5806975801127883, 3.627671429443412, 3.4351128074635335, 3.009983388658482, 3.7682887362833544, 2.882707061079915, 3.8535697735995385, 3.0757112998459397, 4.047221268969613, 3.6578682316343767, 3.416138170507745, 3.59722114972099, 4.047221268969612, 4.244997055358225, 3.531288716601915, 2.4939927826679855, 2.8178005607210745, 2.7018512172212596, 2.8948229652260253, 4.135214625627066, 3.411744421846396, 3.5199431813596087, 3.9115214431215897, 3.6180105030251095, 2.9999999999999996, 3.0215889859476257, 3.3120990323358397, 3.59583091927304, 3.0099833886584824, 2.387467277262665, 3.1527765540868895, 3.07408522978788, 3.1256999216175574, 3.3451457367355464, 2.0904544960366875, 3.057776970284131, 5.2848841046895245, 4.208325082500163, 5.301886456724625, 4.690415759823429, 5.056678751908213, 6.0950799830683104, 3.591656999213594, 5.636488268416782, 5.047771785649585, 5.639148871948673, 4.356604182158392, 4.519955751995809, 4.853864439804639, 4.190465367951393, 4.417012565071555, 4.626013402488151, 4.645427859734774, 6.240192304729079, 6.498461356351979, 4.141255848169732, 5.121523210920752, 4.028647415696738, 6.211280061307815, 4.109744517606904, 4.969909455915672, 5.31224999411737, 3.9774363602702683, 4.007492981902776, 4.840454524112379, 5.0970579749498635, 5.546169849544818, 6.014149981501959, 4.880573736764972, 4.160528812542944, 4.570557952810575, 5.788782255362521, 4.891829923454003, 4.606517122512408, 3.8961519477556315, 4.796873982084583, 5.0199601592044525, 4.636809247747852, 4.208325082500163, 5.2573757712379665, 5.136146415358503, 4.654030511288039, 4.27668095606862, 4.459820624195552, 4.650806381693394, 4.1400483088968905], [0.5385164807134502, 0.0, 0.30000000000000016, 0.3316624790355407, 0.608276253029822, 1.0908712114635715, 0.5099019513592788, 0.42426406871192834, 0.5099019513592785, 0.17320508075688784, 0.8660254037844388, 0.4582575694955841, 0.1414213562373099, 0.6782329983125273, 1.360147050873544, 1.6278820596099708, 1.0535653752852738, 0.5477225575051659, 1.1747340124470729, 0.8366600265340752, 0.7071067811865475, 0.7615773105863909, 0.7810249675906658, 0.5567764362830019, 0.6480740698407861, 0.22360679774997896, 0.4999999999999999, 0.5916079783099616, 0.49999999999999983, 0.3464101615137758, 0.24494897427831822, 0.6782329983125268, 1.1489125293076055, 1.3416407864998738, 0.17320508075688784, 0.3, 0.7874007874011809, 0.17320508075688784, 0.5099019513592784, 0.4582575694955836, 0.529150262212918, 0.8185352771872454, 0.5477225575051662, 0.6782329983125268, 0.9848857801796101, 0.14142135623730986, 0.8485281374238567, 0.3605551275463996, 0.812403840463596, 0.31622776601683766, 4.096339829652808, 3.6864617182333523, 4.236744032862973, 2.9698484809834995, 3.811823710509183, 3.3911649915626345, 3.8600518131237567, 2.1470910553583886, 3.788139384975162, 2.8053520278211073, 2.4617067250182343, 3.2449961479175906, 3.0413812651491097, 3.712142238654117, 2.5592967784139455, 3.7000000000000006, 3.433656942677879, 2.971531591620725, 3.6918829883949464, 2.792848008753788, 3.893584466786357, 3.0740852297878796, 4.018706259482024, 3.6565010597564442, 3.4467375879228173, 3.651027252705737, 4.080441152620633, 4.295346318982906, 3.5383612025908264, 2.4186773244895647, 2.7, 2.5787593916455256, 2.8548204847240393, 4.11703777004778, 3.398529093593286, 3.59722114972099, 3.9786932528155523, 3.55808937493144, 2.9983328701129897, 2.929163703175362, 3.2434549480453714, 3.622154055254966, 2.9546573405388314, 2.179449471770337, 3.10322412983658, 3.0789608636681307, 3.1144823004794877, 3.3645207682521443, 1.9131126469708992, 3.029851481508623, 5.338539126015655, 4.180908992073374, 5.357238094391549, 4.708502946797421, 5.091168824543142, 6.159545437773796, 3.479942528261063, 5.686826883245173, 5.040833264451424, 5.747173218200404, 4.41927595879687, 4.521061822182926, 4.902040391510457, 4.134005321718878, 4.402272140611027, 4.68081189538738, 4.682947789587238, 6.369458375717672, 6.5314623171231725, 4.06201920231798, 5.1903757089443925, 4.0024992192379, 6.2617888817813085, 4.106093033529563, 5.042816673249187, 5.389805191284746, 3.9812058474788765, 4.031128874149275, 4.851803788283281, 5.158488150611572, 5.591958512006325, 6.154673021371647, 4.891829923454003, 4.168932717135165, 4.547526800360829, 5.860034129593443, 4.959838707054897, 4.650806381693394, 3.9153543900903784, 4.860041152089146, 5.072474741188959, 4.702127178203498, 4.180908992073374, 5.320714237769211, 5.206726418777926, 4.699999999999999, 4.249705872175156, 4.498888751680798, 4.718050444834179, 4.153311931459037]]
训练样本：[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 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, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 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, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149]]
排序后的距离：[[0.0, 0.09999999999999998, 0.1414213562373093, 0.14142135623730964, 0.14142135623730995, 0.14142135623730995, 0.17320508075688743, 0.17320508075688762, 0.22360679774997896, 0.30000000000000016, 0.30000000000000027, 0.316227766016838, 0.33166247903553986, 0.3605551275463989, 0.37416573867739383, 0.3741657386773941, 0.37416573867739483, 0.3872983346207423, 0.41231056256176635, 0.4358898943540679, 0.45825756949558394, 0.4690415759823426, 0.4690415759823426, 0.4690415759823426, 0.46904157598234303, 0.509901951359278, 0.5196152422706632, 0.53851648071345, 0.5385164807134502, 0.5385164807134504, 0.5477225575051662, 0.5477225575051664, 0.58309518948453, 0.5916079783099616, 0.5916079783099616, 0.5916079783099616, 0.6164414002968975, 0.6164414002968979, 0.6244997998398396, 0.648074069840786, 0.648074069840786, 0.7416198487095667, 0.7681145747868601, 0.8062257748298554, 0.866025403784438, 0.8831760866327848, 0.9219544457292882, 0.9949874371066197, 1.1045361017187267, 1.3490737563232043, 2.0904544960366875, 2.345207879911715, 2.387467277262665, 2.4939927826679855, 2.5806975801127883, 2.7018512172212596, 2.703701166919155, 2.8178005607210745, 2.882707061079915, 2.8879058156387303, 2.8948229652260253, 2.9999999999999996, 3.009983388658482, 3.0099833886584824, 3.0215889859476257, 3.057776970284131, 3.07408522978788, 3.0757112998459397, 3.093541659651604, 3.1256999216175574, 3.146426544510455, 3.1527765540868895, 3.228002478313795, 3.3120990323358397, 3.3451457367355464, 3.411744421846396, 3.416138170507745, 3.416138170507745, 3.4351128074635335, 3.5199431813596087, 3.531288716601915, 3.591656999213594, 3.59583091927304, 3.59722114972099, 3.6166282640050254, 3.6180105030251095, 3.627671429443412, 3.6578682316343767, 3.7, 3.749666651850535, 3.7682887362833544, 3.7854986461495406, 3.792097045171708, 3.8535697735995385, 3.8961519477556315, 3.9115214431215897, 3.9774363602702683, 4.003748243833521, 4.007492981902776, 4.028647415696738, 4.047221268969612, 4.047221268969613, 4.109744517606904, 4.135214625627066, 4.1400483088968905, 4.141255848169732, 4.160528812542944, 4.164132562731403, 4.190465367951393, 4.208325082500163, 4.208325082500163, 4.244997055358225, 4.27668095606862, 4.356604182158392, 4.417012565071555, 4.459820624195552, 4.519955751995809, 4.570557952810575, 4.606517122512408, 4.626013402488151, 4.636809247747852, 4.645427859734774, 4.650806381693394, 4.654030511288039, 4.690415759823429, 4.796873982084583, 4.840454524112379, 4.853864439804639, 4.880573736764972, 4.891829923454003, 4.969909455915672, 5.0199601592044525, 5.047771785649585, 5.056678751908213, 5.0970579749498635, 5.121523210920752, 5.136146415358503, 5.2573757712379665, 5.2848841046895245, 5.301886456724625, 5.31224999411737, 5.546169849544818, 5.636488268416782, 5.639148871948673, 5.788782255362521, 6.014149981501959, 6.0950799830683104, 6.211280061307815, 6.240192304729079, 6.498461356351979], [0.0, 0.14142135623730986, 0.1414213562373099, 0.17320508075688784, 0.17320508075688784, 0.17320508075688784, 0.22360679774997896, 0.24494897427831822, 0.3, 0.30000000000000016, 0.31622776601683766, 0.3316624790355407, 0.3464101615137758, 0.3605551275463996, 0.42426406871192834, 0.4582575694955836, 0.4582575694955841, 0.49999999999999983, 0.4999999999999999, 0.5099019513592784, 0.5099019513592785, 0.5099019513592788, 0.529150262212918, 0.5385164807134502, 0.5477225575051659, 0.5477225575051662, 0.5567764362830019, 0.5916079783099616, 0.608276253029822, 0.6480740698407861, 0.6782329983125268, 0.6782329983125268, 0.6782329983125273, 0.7071067811865475, 0.7615773105863909, 0.7810249675906658, 0.7874007874011809, 0.812403840463596, 0.8185352771872454, 0.8366600265340752, 0.8485281374238567, 0.8660254037844388, 0.9848857801796101, 1.0535653752852738, 1.0908712114635715, 1.1489125293076055, 1.1747340124470729, 1.3416407864998738, 1.360147050873544, 1.6278820596099708, 1.9131126469708992, 2.1470910553583886, 2.179449471770337, 2.4186773244895647, 2.4617067250182343, 2.5592967784139455, 2.5787593916455256, 2.7, 2.792848008753788, 2.8053520278211073, 2.8548204847240393, 2.929163703175362, 2.9546573405388314, 2.9698484809834995, 2.971531591620725, 2.9983328701129897, 3.029851481508623, 3.0413812651491097, 3.0740852297878796, 3.0789608636681307, 3.10322412983658, 3.1144823004794877, 3.2434549480453714, 3.2449961479175906, 3.3645207682521443, 3.3911649915626345, 3.398529093593286, 3.433656942677879, 3.4467375879228173, 3.479942528261063, 3.5383612025908264, 3.55808937493144, 3.59722114972099, 3.622154055254966, 3.651027252705737, 3.6565010597564442, 3.6864617182333523, 3.6918829883949464, 3.7000000000000006, 3.712142238654117, 3.788139384975162, 3.811823710509183, 3.8600518131237567, 3.893584466786357, 3.9153543900903784, 3.9786932528155523, 3.9812058474788765, 4.0024992192379, 4.018706259482024, 4.031128874149275, 4.06201920231798, 4.080441152620633, 4.096339829652808, 4.106093033529563, 4.11703777004778, 4.134005321718878, 4.153311931459037, 4.168932717135165, 4.180908992073374, 4.180908992073374, 4.236744032862973, 4.249705872175156, 4.295346318982906, 4.402272140611027, 4.41927595879687, 4.498888751680798, 4.521061822182926, 4.547526800360829, 4.650806381693394, 4.68081189538738, 4.682947789587238, 4.699999999999999, 4.702127178203498, 4.708502946797421, 4.718050444834179, 4.851803788283281, 4.860041152089146, 4.891829923454003, 4.902040391510457, 4.959838707054897, 5.040833264451424, 5.042816673249187, 5.072474741188959, 5.091168824543142, 5.158488150611572, 5.1903757089443925, 5.206726418777926, 5.320714237769211, 5.338539126015655, 5.357238094391549, 5.389805191284746, 5.591958512006325, 5.686826883245173, 5.747173218200404, 5.860034129593443, 6.154673021371647, 6.159545437773796, 6.2617888817813085, 6.369458375717672, 6.5314623171231725]]
训练样本：[[0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 31, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
7个临近的距离：[[0.0, 0.09999999999999998, 0.1414213562373093, 0.14142135623730964, 0.14142135623730995, 0.14142135623730995, 0.17320508075688743], [0.0, 0.14142135623730986, 0.1414213562373099, 0.17320508075688784, 0.17320508075688784, 0.17320508075688784, 0.22360679774997896]]
训练样本：[[0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0]]
准确度：0.0%
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