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# 1.6. 最近邻
校验者:
        [@DataMonk2017](https://github.com/DataMonk2017)
        [@Veyron C](https://github.com/caopeirui)
        [@舞空](https://github.com/pan8664716)
        [@Loopy](https://github.com/loopyme)
[@qinhanmin2014](https://github.com/qinhanmin2014)
翻译者:
        [@那伊抹微笑](https://github.com/wangyangting)
[`sklearn.neighbors`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.neighbors) 提供了 neighbors-based (基于邻居的) 无监督学习以及监督学习方法的功能。 无监督的最近邻是许多其它学习方法的基础,尤其是 manifold learning (流形学习) 和 spectral clustering (谱聚类)。 neighbors-based (基于邻居的) 监督学习分为两种: [classification](#162-最近邻分类) (分类)针对的是具有离散标签的数据,[regression](#163-最近邻回归) (回归)针对的是具有连续标签的数据。
最近邻方法背后的原理是从训练样本中找到与新点在距离上最近的预定数量的几个点,然后从这些点中预测标签。 这些点的数量可以是用户自定义的常量K-最近邻学习), 也可以根据不同的点的局部密度(基于半径的最近邻学习)确定。距离通常可以通过任何度量来衡量: standard Euclidean distance标准欧式距离是最常见的选择。Neighbors-based基于邻居的方法被称为 *非泛化* 机器学习方法, 因为它们只是简单地”记住”了其所有的训练数据(可能转换为一个快速索引结构,如 [Ball Tree](#1643-ball-树) 或 [KD Tree](#1642-k-d-树))。
尽管它简单,但最近邻算法已经成功地适用于很多的分类和回归问题,例如手写数字或卫星图像的场景。 作为一个 non-parametric非参数化方法它经常成功地应用于决策边界非常不规则的分类情景下。
尽管它简单,但最近邻算法已经成功地适用于很多的分类和回归问题,例如手写数字或卫星图像的场景。 作为一个 **non-parametric非参数化** 方法,它经常成功地应用于决策边界非常不规则的分类情景下。
[`sklearn.neighbors`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.neighbors) 可以处理 Numpy 数组或 `scipy.sparse` 矩阵作为其输入。 对于密集矩阵,大多数可能的距离度量都是支持的。对于稀疏矩阵,支持搜索任意的 Minkowski 度量。

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适用数据范围: 数值型和标称型
```
### KNN 算法设计
* 对位置类别属性的数据集中的每个点一次执行以下操作:
1. 计算一致类别数据集中点与当前带点之间的距离;
2. 按照距离递增次序排序
3. 选取与当前点距离最小的k个点
4. 确定前k个点所在的类别出现的频率
5. 返回前k个点出现频率最高的类别作为当前点的预测类别
* 算法的伪代码如下
```
def classify(inX,dataset,labels,k):
dataSetSize = dataSet.shap[0];
diffMat = tile(inX,dataSetSize,1)) - dataSet
sqDiffMat = difMat**2
sqDistances = sqDifMat.sum(axis = 1)
distaces = sqDistances**0.5
sortedDistaIndicies = distances.argsort()
classCount={}
for i in range (k):
voteIlabel = labels[sortedDistIndicies[i]]
classCount[voteIlabel] = classCount.get(voteIlabel,0)+1
sortedClassCount = sorted(classCount.iteritems(),
key=operator.itermgetter(1),reverse=True)
return sortedClassCount[0][0]
```
## 4 KNN 项目案例
### 项目案例1: 优化约会网站的配对效果
## 4.1 项目案例1: 优化约会网站的配对效果
* [源码](../源代码/ml/2.KNN/kNN.py)
@@ -119,7 +93,7 @@ def classify(inX,dataset,labels,k):
> 收集数据: 提供文本文件
海伦把这些约会对象的数据存放在文本文件 [datingTestSet2.txt](/data/2.KNN/datingTestSet2.txt) 中,总共有 1000 行。海伦约会的对象主要包含以下 3 种特征:
海伦把这些约会对象的数据存放在文本文件 [datingTestSet2.txt]() 中,总共有 1000 行。海伦约会的对象主要包含以下 3 种特征:
* 每年获得的飞行常客里程数
* 玩视频游戏所耗时间百分比
@@ -199,7 +173,7 @@ $$\sqrt{(0-67)^2 + (20000-32000)^2 + (1.1-0.1)^2 }$$
归一化特征值,消除特征之间量级不同导致的影响
**归一化定义: ** 我是这样认为的,归一化就是要把你需要处理的数据经过处理后(通过某种算法)限制在你需要的一定范围内。首先归一化是为了后面数据处理的方便,其次是保正程序运行时收敛加快。 方法有如下:
**归一化定义** 我是这样认为的,归一化就是要把你需要处理的数据经过处理后(通过某种算法)限制在你需要的一定范围内。首先归一化是为了后面数据处理的方便,其次是保正程序运行时收敛加快。 方法有如下:
1) 线性函数转换,表达式如下:   
@@ -356,9 +330,9 @@ You will probably like this person: in small doses
### 项目案例2: 手写数字识别系统
## 4.2 项目案例2: 手写数字识别系统
[完整代码地址](/src/py2.x/ml/2.KNN/kNN.py): <https://github.com/apachecn/AiLearning/blob/master/src/py2.x/ml/2.KNN/kNN.py>
[完整代码地址](/src/py2.x/ml/2.KNN/kNN.py)
#### 项目概述
@@ -453,7 +427,7 @@ def handwritingClassTest():
> 使用算法: 本例没有完成此步骤,若你感兴趣可以构建完整的应用程序,从图像中提取数字,并完成数字识别,美国的邮件分拣系统就是一个实际运行的类似系统。
## KNN 小结
## 5 KNN 小结
KNN 是什么?定义: 监督学习? 非监督学习?
@@ -461,129 +435,84 @@ KNN 是一个简单的无显示学习过程,非泛化学习的监督学习模
### 基本原理
简单来说: 通过距离度量来计算查询点query point与每个训练数据点的距离然后选出与查询点query point相近的K个最邻点K nearest neighbors使用分类决策来选出对应的标签来作为该查询点的标签。
* 简单来说: 通过距离度量来计算查询点query point与每个训练数据点的距离然后选出与查询点query point相近的K个最邻点K nearest neighbors使用分类决策来选出对应的标签来作为该查询点的标签。
### KNN 三要素
>K, K的取值
>>>>对查询点标签影响显著效果拔群。k值小的时候 近似误差小,估计误差大。 k值大 近似误差大,估计误差小
>>>>如果选择较小的 k 值就相当于用较小的邻域中的训练实例进行预测“学习”的近似误差approximation error会减小只有与输入实例较近的相似的训练实例才会对预测结果起作用。但缺点是“学习”的估计误差estimation error会增大预测结果会对近邻的实例点非常敏感。如果邻近的实例点恰巧是噪声预测就会出错。换句话说k 值的减小就意味着整体模型变得复杂,容易发生过拟合
* K, K的取值
* 对查询点标签影响显著效果拔群。k值小的时候 近似误差小,估计误差大。 k值大 近似误差大,估计误差小。
* 如果选择较小的 k 值就相当于用较小的邻域中的训练实例进行预测“学习”的近似误差approximation error会减小只有与输入实例较近的相似的训练实例才会对预测结果起作用。但缺点是“学习”的估计误差estimation error会增大预测结果会对近邻的实例点非常敏感。如果邻近的实例点恰巧是噪声预测就会出错。换句话说k 值的减小就意味着整体模型变得复杂,容易发生过拟合
* 如果选择较大的 k 值,就相当于用较大的邻域中的训练实例进行预测。其优点是可以减少学习的估计误差。但缺点是学习的近似误差会增大。这时与输入实例较远的(不相似的)训练实例也会对预测起作用,使预测发生错误。 k 值的增大就意味着整体的模型变得简单。
* 太大太小都不太好可以用交叉验证cross validation来选取适合的k值
* 近似误差和估计误差,请看这里: https://www.zhihu.com/question/60793482
>>>>如果选择较大的 k 值,就相当于用较大的邻域中的训练实例进行预测。其优点是可以减少学习的估计误差。但缺点是学习的近似误差会增大。这时与输入实例较远的(不相似的)训练实例也会对预测起作用,使预测发生错误。 k 值的增大就意味着整体的模型变得简单。
* 距离度量 Metric/Distance Measure
* 距离度量 通常为 欧式距离Euclidean distance还可以是 Minkowski 距离 或者 曼哈顿距离。也可以是 地理空间中的一些距离公式。(更多细节可以参看 sklearn 中 valid_metric 部分)
* 分类决策 decision rule
* 分类决策 在 分类问题中 通常为通过少数服从多数 来选取票数最多的标签,在回归问题中通常为 K个最邻点的标签的平均值。
### 算法:
* sklearn 上有三种
* Brute Force 暴力计算/线性扫描
* KD Tree 使用二叉树根据数据维度来平分参数空间。
* Ball Tree 使用一系列的超球体来平分训练数据集。
* 树结构的算法都有建树和查询两个过程。Brute Force 没有建树的过程。
* 算法特点:
>>>>太大太小都不太好可以用交叉验证cross validation来选取适合的k值。
* 优点: High Accuracy No Assumption on data not sensitive to outliers
* 缺点: 时间和空间复杂度 高
* 适用范围: continuous values and nominal values
* 相似同源产物:
* radius neighbors 根据制定的半径来找寻邻点
* 影响算法因素:
* N 数据集样本数量(number of samples) D 数据维度 (number of features)
* 总消耗:
* Brute Force: O[DN^2]
* 此处考虑的是最蠢的方法: 把所有训练的点之间的距离都算一遍。当然有更快的实现方式, 比如 O(ND + kN) 和 O(NDK) , 最快的是 O[DN] 。感兴趣的可以阅读这个链接: [k-NN computational complexity](https://stats.stackexchange.com/questions/219655/k-nn-computational-complexity)
* KD Tree: O[DN log(N)]
* Ball Tree: O[DN log(N)] 跟 KD Tree 处于相同的数量级,虽然建树时间会比 KD Tree 久一点,但是在高结构的数据,甚至是高纬度的数据中,查询速度有很大的提升。
* 查询所需消耗:
* Brute Force: O[DN]
* KD Tree: 当维度比较小的时候, 比如 D<20, O[Dlog(N)] 。相反,将会趋向于 O[DN]
* Ball Tree: O[Dlog(N)]
* 当数据集比较小的时候,比如 N<30的时候Brute Force 更有优势。
* Intrinsic Dimensionality(本征维数) 和 Sparsity稀疏度
* 数据的 intrinsic dimensionality 是指数据所在的流形的维数 d < D , 在参数空间可以是线性或非线性的。稀疏度指的是数据填充参数空间的程度(这与“稀疏”矩阵中使用的概念不同, 数据矩阵可能没有零项, 但是从这个意义上来讲,它的结构 仍然是 "稀疏" 的)。
* Brute Force 的查询时间不受影响。
* 对于 KD Tree 和 Ball Tree的查询时间, 较小本征维数且更稀疏的数据集的查询时间更快。KD Tree 的改善由于通过坐标轴来平分参数空间的自身特性 没有Ball Tree 显著。
* k的取值 (k 个邻点)
* Brute Force 的查询时间基本不受影响。
* 但是对于 KD Tree 和 Ball Tree , k越大查询时间越慢。
* k 在N的占比较大的时候使用 Brute Force 比较好。
* Number of Query Points (查询点数量, 即测试数据的数量)
* 查询点较少的时候用Brute Force。查询点较多的时候可以使用树结构算法。
* 关于 sklearn 中模型的一些额外干货:
* 如果KD TreeBall Tree 和Brute Force 应用场景傻傻分不清楚,可以直接使用 含有algorithm='auto'的模组。 algorithm='auto' 自动为您选择最优算法。
* 有 regressor 和 classifier 可以来选择。
* metric/distance measure 可以选择。 另外距离 可以通过weight 来加权。
* leaf size 对KD Tree 和 Ball Tree 的影响
* 建树时间: leaf size 比较大的时候,建树时间也就快点。
* 查询时间: leaf size 太大太小都不太好。如果leaf size 趋向于 N训练数据的样本数量算法其实就是 brute force了。如果leaf size 太小了趋向于1那查询的时候 遍历树的时间就会大大增加。leaf size 建议的数值是 30也就是默认值。
* 内存: leaf size 变大,存树结构的内存变小。
>>>>近似误差和估计误差,请看这里: https://www.zhihu.com/question/60793482
>距离度量 Metric/Distance Measure
>>>>距离度量 通常为 欧式距离Euclidean distance还可以是 Minkowski 距离 或者 曼哈顿距离。也可以是 地理空间中的一些距离公式。(更多细节可以参看 sklearn 中 valid_metric 部分)
* Nearest Centroid Classifier
* 分类决策是哪个标签的质心与测试点最近,就选哪个标签。
* 该模型假设在所有维度中方差相同。 是一个很好的base line。
>分类决策 decision rule
>>>>分类决策 在 分类问题中 通常为通过少数服从多数 来选取票数最多的标签,在回归问题中通常为 K个最邻点的标签的平均值。
### 算法: sklearn 上有三种)
>Brute Force 暴力计算/线性扫描
>KD Tree 使用二叉树根据数据维度来平分参数空间。
>Ball Tree 使用一系列的超球体来平分训练数据集。
>树结构的算法都有建树和查询两个过程。Brute Force 没有建树的过程。
>算法特点:
>>>>优点: High Accuracy No Assumption on data not sensitive to outliers
>>>>缺点: 时间和空间复杂度 高
>>>>适用范围: continuous values and nominal values
>相似同源产物:
>>>>radius neighbors 根据制定的半径来找寻邻点
>影响算法因素:
>>>>N 数据集样本数量(number of samples) D 数据维度 (number of features)
>总消耗:
>>>>Brute Force: O[DN^2]
>>>>此处考虑的是最蠢的方法: 把所有训练的点之间的距离都算一遍。当然有更快的实现方式, 比如 O(ND + kN) 和 O(NDK) , 最快的是 O[DN] 。感兴趣的可以阅读这个链接: [k-NN computational complexity](https://stats.stackexchange.com/questions/219655/k-nn-computational-complexity)
>>>>KD Tree: O[DN log(N)]
>>>>Ball Tree: O[DN log(N)] 跟 KD Tree 处于相同的数量级,虽然建树时间会比 KD Tree 久一点,但是在高结构的数据,甚至是高纬度的数据中,查询速度有很大的提升。
>查询所需消耗:
>>>>Brute Force: O[DN]
>>>>KD Tree: 当维度比较小的时候, 比如 D<20, O[Dlog(N)] 。相反,将会趋向于 O[DN]
>>>>Ball Tree: O[Dlog(N)]
>>>>当数据集比较小的时候,比如 N<30的时候Brute Force 更有优势。
>Intrinsic Dimensionality(本征维数) 和 Sparsity稀疏度
>>>>数据的 intrinsic dimensionality 是指数据所在的流形的维数 d < D , 在参数空间可以是线性或非线性的。稀疏度指的是数据填充参数空间的程度(这与“稀疏”矩阵中使用的概念不同, 数据矩阵可能没有零项, 但是从这个意义上来讲,它的结构 仍然是 "稀疏" 的)。
>>>>Brute Force 的查询时间不受影响。
>>>>对于 KD Tree 和 Ball Tree的查询时间, 较小本征维数且更稀疏的数据集的查询时间更快。KD Tree 的改善由于通过坐标轴来平分参数空间的自身特性 没有Ball Tree 显著。
>k的取值 (k 个邻点)
>>>>Brute Force 的查询时间基本不受影响。
>>>>但是对于 KD Tree 和 Ball Tree , k越大查询时间越慢。
>>>>k 在N的占比较大的时候使用 Brute Force 比较好。
>Number of Query Points (查询点数量, 即测试数据的数量)
>>>>查询点较少的时候用Brute Force。查询点较多的时候可以使用树结构算法。
>关于 sklearn 中模型的一些额外干货:
>>>>如果KD TreeBall Tree 和Brute Force 应用场景傻傻分不清楚,可以直接使用 含有algorithm='auto'的模组。 algorithm='auto' 自动为您选择最优算法。
>>>>有 regressor 和 classifier 可以来选择。
>>>>metric/distance measure 可以选择。 另外距离 可以通过weight 来加权。
>leaf size 对KD Tree 和 Ball Tree 的影响
>>>>建树时间: leaf size 比较大的时候,建树时间也就快点。
>>>>查询时间: leaf size 太大太小都不太好。如果leaf size 趋向于 N训练数据的样本数量算法其实就是 brute force了。如果leaf size 太小了趋向于1那查询的时候 遍历树的时间就会大大增加。leaf size 建议的数值是 30也就是默认值。
>>>>内存: leaf size 变大,存树结构的内存变小。
>Nearest Centroid Classifier
>>>>分类决策是哪个标签的质心与测试点最近,就选哪个标签。
>>>>该模型假设在所有维度中方差相同。 是一个很好的base line。
>进阶版: Nearest Shrunken Centroid
>>>>可以通过shrink_threshold来设置。
>>>>作用: 可以移除某些影响分类的特征,例如移除噪音特征的影响
* * *
* **作者: [羊三](http://cwiki.apachecn.org/display/~xuxin) [小瑶](http://cwiki.apachecn.org/display/~chenyao)**
* [GitHub地址](https://github.com/apachecn/AiLearning): <https://github.com/apachecn/AiLearning>
* **版权声明: 欢迎转载学习 => 请标注信息来源于 [ApacheCN](http://www.apachecn.org/)**
* 进阶版: Nearest Shrunken Centroid
* 可以通过shrink_threshold来设置。
* 作用: 可以移除某些影响分类的特征,例如移除噪音特征的影响

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@@ -1,6 +1,5 @@
# 第3章 决策树
## 1 决策树 概述
`决策树Decision Tree算法是一种基本的分类与回归方法是最经常使用的数据挖掘算法之一。我们这章节只讨论用于分类的决策树。`

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@@ -241,7 +241,7 @@ def datingClassTest():
# 设置测试数据的的一个比例(训练数据集比例=1-hoRatio
hoRatio = 0.1 # 测试范围,一部分测试一部分作为样本
# 从文件中加载数据
datingDataMat, datingLabels = file2matrix("data/2.KNN/datingTestSet2.txt") # load data setfrom file
datingDataMat, datingLabels = file2matrix("datingTestSet2.txt") # load data setfrom file
# 归一化数据
normMat, ranges, minVals = autoNorm(datingDataMat)
# m 表示数据的行数,即矩阵的第一维
@@ -291,7 +291,7 @@ def handwritingClassTest():
"""
# 1. 导入数据
hwLabels = []
trainingFileList = os.listdir("data/2.KNN/trainingDigits") # load the training set
trainingFileList = os.listdir("trainingDigits") # load the training set
m = len(trainingFileList)
trainingMat = zeros((m, 1024))
# hwLabels存储09对应的index位置 trainingMat存放的每个位置对应的图片向量
@@ -301,17 +301,17 @@ def handwritingClassTest():
classNumStr = int(fileStr.split('_')[0])
hwLabels.append(classNumStr)
# 将 32*32的矩阵->1*1024的矩阵
trainingMat[i] = img2vector('data/2.KNN/trainingDigits/%s' % fileNameStr)
trainingMat[i] = img2vector('trainingDigits/%s' % fileNameStr)
# 2. 导入测试数据
testFileList = os.listdir('data/2.KNN/testDigits') # iterate through the test set
testFileList = os.listdir('testDigits') # iterate through the test set
errorCount = 0
mTest = len(testFileList)
for i in range(mTest):
fileNameStr = testFileList[i]
fileStr = fileNameStr.split('.')[0] # take off .txt
classNumStr = int(fileStr.split('_')[0])
vectorUnderTest = img2vector('data/2.KNN/testDigits/%s' % fileNameStr)
vectorUnderTest = img2vector('testDigits/%s' % fileNameStr)
classifierResult = classify0(vectorUnderTest, trainingMat, hwLabels, 3)
print("the classifier came back with: %d, the real answer is: %d" % (classifierResult, classNumStr))
errorCount += classifierResult != classNumStr
@@ -322,6 +322,4 @@ def handwritingClassTest():
if __name__ == '__main__':
# test1()
# datingClassTest()
handwritingClassTest()
# %%
handwritingClassTest()

View File

@@ -1,69 +0,0 @@
#!/usr/bin/python
# -*- coding: UTF-8 -*-
"""
Created on 2017-06-28
Updated on 2017-06-28
KNN: k近邻算法
Author: 小瑶
GitHub: https://github.com/apachecn/AiLearning
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from numpy import *
from matplotlib.colors import ListedColormap
from sklearn import neighbors, datasets
n_neighbors = 3
# 导入一些要玩的数据
iris = datasets.load_iris()
X = iris.data[:, :2] # 我们只采用前两个feature. 我们可以使用二维数据集避免这个丑陋的切片
y = iris.target
# print 'X=', type(X), X
# print 'y=', type(y), y
# X = array([[-1.0, -1.1], [-1.0, -1.0], [0, 0], [1.0, 1.1], [2.0, 2.0], [2.0, 2.1]])
# y = array([0, 0, 0, 1, 1, 1])
# print 'X=', type(X), X
# print 'y=', type(y), y
h = .02 # 网格中的步长
# 创建彩色的图
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
# cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA'])
# cmap_bold = ListedColormap(['#FF0000', '#00FF00'])
for weights in ['uniform', 'distance']:
# 我们创建了一个knn分类器的实例并拟合数据。
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# 绘制决策边界。为此,我们将为每个分配一个颜色
# 来绘制网格中的点 [x_min, x_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# 将结果放入一个彩色图中
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# 绘制训练点
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
plt.show()

View File

@@ -0,0 +1,108 @@
#!/usr/bin/python
# -*- coding: UTF-8 -*-
"""
Created on 2017-06-28
Updated on 2017-06-28
KNN: k近邻算法
Author: 小瑶
GitHub: https://github.com/apachecn/AiLearning
"""
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
import kNN as knn
from numpy import *
from matplotlib.colors import ListedColormap
from sklearn import neighbors, datasets
def test_knn_dating():
#%% 利用knn模块的数据读取函数
x,y = knn.file2matrix('datingTestSet2.txt')
norm_x, ranges, minVals = knn.autoNorm(x)
norm_x=np.array(norm_x)
y = np.array(y)
#%% 生成测试数据的比例
train_ratio = 0.9
test_ratio = 0.1
size_data = len(norm_x)
indices = np.random.permutation(size_data)
x_train = norm_x[indices[:int(train_ratio*size_data)]]
y_train = y[indices[:int(train_ratio*size_data)]]
x_test = norm_x[indices[int(test_ratio*size_data):]]
y_test = y[indices[int(test_ratio*size_data):]]
#%%
# 设置分类器,并填充训练数据
knn_classfier = neighbors.KNeighborsClassifier()
knn_classfier.fit(x_train,y_train)
#%%
# 按比例进行测试数据
result = knn_classfier.predict(x_test)
for i in range(100):
if result[i]==y_test[i]:
print(True)
else:
print(False)
# np.sum(error_count)
# print(error_count)
#%%
def test_knn_digits():
pass
def test_knn_iris():
n_neighbors = 3
# 导入一些要玩的数据
iris = datasets.load_iris()
X = iris.data[:, :2] # 我们只采用前两个feature. 我们可以使用二维数据集避免这个丑陋的切片
y = iris.target
# print 'X=', type(X), X
# print 'y=', type(y), y
# X = array([[-1.0, -1.1], [-1.0, -1.0], [0, 0], [1.0, 1.1], [2.0, 2.0], [2.0, 2.1]])
# y = array([0, 0, 0, 1, 1, 1])
# print 'X=', type(X), X
# print 'y=', type(y), y
h = .02 # 网格中的步长
# 创建彩色的图
cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
# cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA'])
# cmap_bold = ListedColormap(['#FF0000', '#00FF00'])
for weights in ['uniform', 'distance']:
# 我们创建了一个knn分类器的实例并拟合数据。
clf = neighbors.KNeighborsClassifier(n_neighbors, weights=weights)
clf.fit(X, y)
# 绘制决策边界。为此,我们将为每个分配一个颜色
# 来绘制网格中的点 [x_min, x_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# 将结果放入一个彩色图中
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# 绘制训练点
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = %i, weights = '%s')"
% (n_neighbors, weights))
plt.show()
# %%

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