示例：《电影类型分类》
获取数据来源
| 电影名称 | 打斗次数 | 接吻次数 | 电影类型 |
|---|---|---|---|
| california man | 3 | 104 | romance |
| he’s not really into dudes | 8 | 95 | romance |
| beautiful woman | 1 | 81 | romance |
| kevin longblade | 111 | 15 | action |
| roob slayer 3000 | 99 | 2 | action |
| amped ii | 88 | 10 | action |
| unknown | 18 | 90 | unknown |
数据显示：肉眼判断电影类型unknown是什么
from matplotlib import pyplot as plt
# 用来正常显示中文标签
plt.rcparams["font.sans-serif"] = ["simhei"]
# 电影名称
names = ["california man", "he's not really into dudes", "beautiful woman",
"kevin longblade", "robo slayer 3000", "amped ii", "unknown"]
# 类型标签
labels = ["romance", "romance", "romance", "action", "action", "action", "unknown"]
colors = ["darkblue", "red", "green"]
colordict = {label: color for (label, color) in zip(set(labels), colors)}
print(colordict)
# 打斗次数，接吻次数
x = [3, 8, 1, 111, 99, 88, 18]
y = [104, 95, 81, 15, 2, 10, 88]
plt.title("通过打斗次数和接吻次数判断电影类型", fontsize=18)
plt.xlabel("电影中打斗镜头出现的次数", fontsize=16)
plt.ylabel("电影中接吻镜头出现的次数", fontsize=16)
# 绘制数据
for i in range(len(x)):
# 散点图绘制
plt.scatter(x[i], y[i], color=colordict[labels[i]])
# 每个点增加描述信息
for i in range(0, 7):
plt.text(x[i]+2, y[i]-1, names[i], fontsize=14)
plt.show()
问题分析：根据已知信息分析电影类型unknown是什么
核心思想：
未标记样本的类别由距离其最近的k个邻居的类别决定
距离度量：
一般距离计算使用欧式距离（用勾股定理计算距离），也可以采用曼哈顿距离（水平上和垂直上的距离之和）、余弦值和相似度（这是距离的另一种表达方式）。相比于上述距离，马氏距离更为精确，因为它能考虑很多因素，比如单位，由于在求协方差矩阵逆矩阵的过程中，可能不存在，而且若碰见3维及3维以上，求解过程中极其复杂，故可不使用马氏距离
知识扩展
- 马氏距离概念：表示数据的协方差距离
- 方差：数据集中各个点到均值点的距离的平方的平均值
- 标准差：方差的开方
- 协方差cov(x, y)：e表示均值，d表示方差，x，y表示不同的数据集，xy表示数据集元素对应乘积组成数据集
cov(x, y) = e(xy) – e(x)*e(y)
cov(x, x) = d(x)
cov(x1+x2, y) = cov(x1, y) + cov(x2, y)
cov(ax, by) = abcov(x, y)
- 协方差矩阵：根据维度组成的矩阵，假设有三个维度，a，b，c
∑ij = [cov(a, a) cov(a, b) cov(a, c) cov(b, a) cov(b,b) cov(b, c) cov(c, a) cov(c, b) cov(c, c)]
算法实现：欧氏距离
编码实现
# 自定义实现 mytest1.py
import numpy as np
# 创建数据集
def createdataset():
features = np.array([[3, 104], [8, 95], [1, 81], [111, 15],
[99, 2], [88, 10]])
labels = ["romance", "romance", "romance", "action", "action", "action"]
return features, labels
def knnclassify(testfeature, trainingset, labels, k):
"""
knn算法实现，采用欧式距离
:param testfeature: 测试数据集，ndarray类型，一维数组
:param trainingset: 训练数据集，ndarray类型，二维数组
:param labels: 训练集对应标签，ndarray类型，一维数组
:param k: k值，int类型
:return: 预测结果，类型与标签中元素一致
"""
datasetsize = trainingset.shape[0]
"""
构建一个由dataset[i] - testfeature的新的数据集diffmat
diffmat中的每个元素都是dataset中每个特征与testfeature的差值（欧式距离中差）
"""
testfeaturearray = np.tile(testfeature, (datasetsize, 1))
diffmat = testfeaturearray - trainingset
# 对每个差值求平方
sqdiffmat = diffmat ** 2
# 计算dataset中每个属性与testfeature的差的平方的和
sqdistances = sqdiffmat.sum(axis=1)
# 计算每个feature与testfeature之间的欧式距离
distances = sqdistances ** 0.5
"""
排序，按照从小到大的顺序记录distances中各个数据的位置
如distance = [5, 9, 0, 2]
则sortedstance = [2, 3, 0, 1]
"""
sorteddistances = distances.argsort()
# 选择距离最小的k个点
classcount = {}
for i in range(k):
voteilabel = labels[list(sorteddistances).index(i)]
classcount[voteilabel] = classcount.get(voteilabel, 0) + 1
# 对k个结果进行统计、排序，选取最终结果，将字典按照value值从大到小排序
sortedclasscount = sorted(classcount.items(), key=lambda x: x[1], reverse=true)
return sortedclasscount[0][0]
testfeature = np.array([100, 200])
features, labels = createdataset()
res = knnclassify(testfeature, features, labels, 3)
print(res)
# 使用python包实现 mytest2.py
from sklearn.neighbors import kneighborsclassifier
from .mytest1 import createdataset
features, labels = createdataset()
k = 5
clf = kneighborsclassifier(k_neighbors=k)
clf.fit(features, labels)
# 样本值
my_sample = [[18, 90]]
res = clf.predict(my_sample)
print(res)
示例：《交友网站匹配效果预测》
数据来源：略
数据显示
import pandas as pd
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import axes3d
# 数据加载
def loaddatingdata(file):
datingdata = pd.read_table(file, header=none)
datingdata.columns = ["flightdistance", "playtimepreweek", "icecreamcostpreweek", "label"]
datingtraindata = np.array(datingdata[["flightdistance", "playtimepreweek", "icecreamcostpreweek"]])
datingtrainlabel = np.array(datingdata["label"])
return datingdata, datingtraindata, datingtrainlabel
# 3d图显示数据
def dataview3d(datingtraindata, datingtrainlabel):
plt.figure(1, figsize=(8, 3))
plt.subplot(111, projection="3d")
plt.scatter(np.array([datingtraindata[x][0]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "smalldoses"]),
np.array([datingtraindata[x][1]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "smalldoses"]),
np.array([datingtraindata[x][2]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "smalldoses"]), c="red")
plt.scatter(np.array([datingtraindata[x][0]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "didntlike"]),
np.array([datingtraindata[x][1]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "didntlike"]),
np.array([datingtraindata[x][2]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "didntlike"]), c="green")
plt.scatter(np.array([datingtraindata[x][0]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "largedoses"]),
np.array([datingtraindata[x][1]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "largedoses"]),
np.array([datingtraindata[x][2]
for x in range(len(datingtrainlabel))
if datingtrainlabel[x] == "largedoses"]), c="blue")
plt.xlabel("飞行里程数", fontsize=16)
plt.ylabel("视频游戏耗时百分比", fontsize=16)
plt.clabel("冰淇凌消耗", fontsize=16)
plt.show()
datingdata, datingtraindata, datingtrainlabel = loaddatingdata(filepath1)
datingview3d(datingtraindata, datingtrainlabel)
问题分析：抽取数据集的前10%在数据集的后90%进行测试
编码实现
# 自定义方法实现
import pandas as pd
import numpy as np
# 数据加载
def loaddatingdata(file):
datingdata = pd.read_table(file, header=none)
datingdata.columns = ["flightdistance", "playtimepreweek", "icecreamcostpreweek", "label"]
datingtraindata = np.array(datingdata[["flightdistance", "playtimepreweek", "icecreamcostpreweek"]])
datingtrainlabel = np.array(datingdata["label"])
return datingdata, datingtraindata, datingtrainlabel
# 数据归一化
def autonorm(datingtraindata):
# 获取数据集每一列的最值
minvalues, maxvalues = datingtraindata.min(0), datingtraindata.max(0)
diffvalues = maxvalues - minvalues
# 定义形状和datingtraindata相似的最小值矩阵和差值矩阵
m = datingtraindata.shape(0)
minvaluesdata = np.tile(minvalues, (m, 1))
diffvaluesdata = np.tile(diffvalues, (m, 1))
normvaluesdata = (datingtraindata-minvaluesdata)/diffvaluesdata
return normvaluesdata
# 核心算法实现
def knnclassifier(testdata, traindata, trainlabel, k):
m = traindata.shape(0)
testdataarray = np.tile(testdata, (m, 1))
diffdataarray = (testdataarray - traindata) ** 2
sumdataarray = diffdataarray.sum(axis=1) ** 0.5
# 对结果进行排序
sumdatasortedarray = sumdataarray.argsort()
classcount = {}
for i in range(k):
labelname = trainlabel[list(sumdatasortedarray).index(i)]
classcount[labelname] = classcount.get(labelname, 0)+1
classcount = sorted(classcount.items(), key=lambda x: x[1], reversed=true)
return classcount[0][0]
# 数据测试
def datingtest(file):
datingdata, datingtraindata, datingtrainlabel = loaddatingdata(file)
normvaluesdata = autonorm(datingtraindata)
errorcount = 0
ratio = 0.10
total = datingtraindata.shape(0)
numbertest = int(total * ratio)
for i in range(numbertest):
res = knnclassifier(normvaluesdata[i], normvaluesdata[numbertest:m], datingtrainlabel, 5)
if res != datingtrainlabel[i]:
errorcount += 1
print("the total error rate is : {}\n".format(error/float(numbertest)))
if __name__ == "__main__":
filepath = "./datingtestset1.txt"
datingtest(filepath)
# python 第三方包实现
import pandas as pd
import numpy as np
from sklearn.neighbors import kneighborsclassifier
if __name__ == "__main__":
filepath = "./datingtestset1.txt"
datingdata, datingtraindata, datingtrainlabel = loaddatingdata(filepath)
normvaluesdata = autonorm(datingtraindata)
errorcount = 0
ratio = 0.10
total = normvaluesdata.shape[0]
numbertest = int(total * ratio)
k = 5
clf = kneighborsclassifier(n_neighbors=k)
clf.fit(normvaluesdata[numbertest:total], datingtrainlabel[numbertest:total])
for i in range(numbertest):
res = clf.predict(normvaluesdata[i].reshape(1, -1))
if res != datingtrainlabel[i]:
errorcount += 1
print("the total error rate is : {}\n".format(errorcount/float(numbertest)))
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