示例：《電影型別分類》

獲取資料來源

電影名稱	打鬥次數	接吻次數	電影型別
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

資料顯示：肉眼判斷電影型別unknown是什麼

from matplotlib import pyplot as plt
​
# 用來正常顯示中文標籤
plt.rcParams["font.sans-serif"] = ["SimHei"]
# 電影名稱
names = ["California Man","He's Not Really into Dudes","Beautiful Woman","Kevin Longblade","Robo Slayer 3000","Amped II","Unknown"]
# 型別標籤
labels = ["Romance","Romance","Action","Unknown"]
colors = ["darkblue","red","green"]
colorDict = {label: color for (label,color) in zip(set(labels),colors)}
print(colorDict)
# 打鬥次數，接吻次數
X = [3,8,1,111,99,88,18]
Y = [104,95,81,15,2,10,88]
​
plt.title("通過打鬥次數和接吻次數判斷電影型別",fontsize=18)
plt.xlabel("電影中打鬥鏡頭出現的次數",fontsize=16)
plt.ylabel("電影中接吻鏡頭出現的次數",fontsize=16)
​
# 繪製資料
for i in range(len(X)):
 # 散點圖繪製
 plt.scatter(X[i],Y[i],color=colorDict[labels[i]])
​
# 每個點增加描述資訊
for i in range(0,7):
 plt.text(X[i]+2,Y[i]-1,names[i],fontsize=14)
​
plt.show()

問題分析：根據已知資訊分析電影型別unknown是什麼

核心思想：

未標記樣本的類別由距離其最近的K個鄰居的類別決定

距離度量：

一般距離計算使用歐式距離（用勾股定理計算距離），也可以採用曼哈頓距離（水平上和垂直上的距離之和）、餘弦值和相似度（這是距離的另一種表達方式）。相比於上述距離，馬氏距離更為精確，因為它能考慮很多因素，比如單位，由於在求協方差矩陣逆矩陣的過程中，可能不存在，而且若碰見3維及3維以上，求解過程中極其複雜，故可不使用馬氏距離

知識擴充套件

• 馬氏距離概念：表示資料的協方差距離
• 方差：資料集中各個點到均值點的距離的平方的平均值
• 標準差：方差的開方
• 協方差cov(x,y)：E表示均值，D表示方差，x，y表示不同的資料集，xy表示資料集元素對應乘積組成資料集

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)

• 協方差矩陣：根據維度組成的矩陣，假設有三個維度，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)]

演算法實現：歐氏距離

編碼實現

# 自定義實現 mytest1.py
import numpy as np
​
# 建立資料集
def createDataSet():
 features = np.array([[3,104],[8,95],[1,81],[111,15],[99,2],[88,10]])
 labels = ["Romance","Action"]
 return features,labels
​
def knnClassify(testFeature,trainingSet,labels,k):
 """
 KNN演算法實現，採用歐式距離
 :param testFeature: 測試資料集，ndarray型別，一維陣列
 :param trainingSet: 訓練資料集，ndarray型別，二維陣列
 :param labels: 訓練集對應標籤，ndarray型別，一維陣列
 :param k: k值，int型別
 :return: 預測結果，型別與標籤中元素一致
 """
 dataSetsize = trainingSet.shape[0]
 """
 構建一個由dataSet[i] - testFeature的新的資料集diffMat
 diffMat中的每個元素都是dataSet中每個特徵與testFeature的差值（歐式距離中差）
 """
 testFeatureArray = np.tile(testFeature,(dataSetsize,1))
 diffMat = testFeatureArray - trainingSet
 # 對每個差值求平方
 sqDiffMat = diffMat ** 2
 # 計算dataSet中每個屬性與testFeature的差的平方的和
 sqDistances = sqDiffMat.sum(axis=1)
 # 計算每個feature與testFeature之間的歐式距離
 distances = sqDistances ** 0.5
​
 """
 排序，按照從小到大的順序記錄distances中各個資料的位置
 如distance = [5,9,2]
 則sortedStance = [2,3,1]
 """
 sortedDistances = distances.argsort()
​
 # 選擇距離最小的k個點
 classCount = {}
 for i in range(k):
  voteiLabel = labels[list(sortedDistances).index(i)]
  classCount[voteiLabel] = classCount.get(voteiLabel,0) + 1
 # 對k個結果進行統計、排序，選取最終結果，將字典按照value值從大到小排序
 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,3)
print(res)
# 使用python包實現 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)
​
# 樣本值
my_sample = [[18,90]]
res = clf.predict(my_sample)
print(res)

示例：《交友網站匹配效果預測》

資料來源：略

資料顯示

import pandas as pd
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
​
# 資料載入
def loadDatingData(file):
 datingData = pd.read_table(file,header=None)
 datingData.columns = ["FlightDistance","PlaytimePreweek","IcecreamCostPreweek","label"]
 datingTrainData = np.array(datingData[["FlightDistance","IcecreamCostPreweek"]])
 datingTrainLabel = np.array(datingData["label"])
 return datingData,datingTrainData,datingTrainLabel
​
# 3D圖顯示資料
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("飛行里程數",fontsize=16)
 plt.ylabel("視訊遊戲耗時百分比",fontsize=16)
 plt.clabel("冰淇凌消耗",fontsize=16)
 plt.show()
 
datingData,datingTrainLabel = loadDatingData(FILEPATH1)
datingView3D(datingTrainData,datingTrainLabel)

問題分析：抽取資料集的前10%在資料集的後90%進行測試

編碼實現

# 自定義方法實現
import pandas as pd
import numpy as np
​
# 資料載入
def loadDatingData(file):
 datingData = pd.read_table(file,datingTrainLabel
​
# 資料歸一化
def autoNorm(datingTrainData):
 # 獲取資料集每一列的最值
 minValues,maxValues = datingTrainData.min(0),datingTrainData.max(0)
 diffValues = maxValues - minValues
 
 # 定義形狀和datingTrainData相似的最小值矩陣和差值矩陣
 m = datingTrainData.shape(0)
 minValuesData = np.tile(minValues,(m,1))
 diffValuesData = np.tile(diffValues,1))
 normValuesData = (datingTrainData-minValuesData)/diffValuesData
 return normValuesData
​
# 核心演算法實現
def KNNClassifier(testData,trainData,trainLabel,k):
 m = trainData.shape(0)
 testDataArray = np.tile(testData,1))
 diffDataArray = (testDataArray - trainData) ** 2
 sumDataArray = diffDataArray.sum(axis=1) ** 0.5
 # 對結果進行排序
 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(),reversed=True)
 return classCount[0][0]
 
​
# 資料測試
def datingTest(file):
 datingData,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 第三方包實現
import pandas as pd
import numpy as np
from sklearn.neighbors import KNeighborsClassifier
​
if __name__ == "__main__":
 FILEPATH = "./datingTestSet1.txt"
 datingData,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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