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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