python實現(xiàn)KNN近鄰算法
示例:《電影類型分類》
獲取數(shù)據(jù)來源
| 電影名稱 | 打斗次數(shù) | 接吻次數(shù) | 電影類型 |
|---|---|---|---|
| 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 |
數(shù)據(jù)顯示:肉眼判斷電影類型unknown是什么
from matplotlib import pyplot as plt
# 用來正常顯示中文標(biāo)簽
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"]
# 類型標(biāo)簽
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)
# 打斗次數(shù),接吻次數(shù)
X = [3, 8, 1, 111, 99, 88, 18]
Y = [104, 95, 81, 15, 2, 10, 88]
plt.title("通過打斗次數(shù)和接吻次數(shù)判斷電影類型", fontsize=18)
plt.xlabel("電影中打斗鏡頭出現(xiàn)的次數(shù)", fontsize=16)
plt.ylabel("電影中接吻鏡頭出現(xiàn)的次數(shù)", fontsize=16)
# 繪制數(shù)據(jù)
for i in range(len(X)):
# 散點圖繪制
plt.scatter(X[i], Y[i], color=colorDict[labels[i]])
# 每個點增加描述信息
for i in range(0, 7):
plt.text(X[i]+2, Y[i]-1, names[i], fontsize=14)
plt.show()
問題分析:根據(jù)已知信息分析電影類型unknown是什么
核心思想:
未標(biāo)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),也可以采用曼哈頓距離(水平上和垂直上的距離之和)、余弦值和相似度(這是距離的另一種表達(dá)方式)。相比于上述距離,馬氏距離更為精確,因為它能考慮很多因素,比如單位,由于在求協(xié)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,求解過程中極其復(fù)雜,故可不使用馬氏距離
知識擴展
- 馬氏距離概念:表示數(shù)據(jù)的協(xié)方差距離
- 方差:數(shù)據(jù)集中各個點到均值點的距離的平方的平均值
- 標(biāo)準(zhǔn)差:方差的開方
- 協(xié)方差cov(x, y):E表示均值,D表示方差,x,y表示不同的數(shù)據(jù)集,xy表示數(shù)據(jù)集元素對應(yīng)乘積組成數(shù)據(jù)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(xié)方差矩陣:根據(jù)維度組成的矩陣,假設(shè)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)]
算法實現(xiàn):歐氏距離
編碼實現(xiàn)
# 自定義實現(xiàn) mytest1.py
import numpy as np
# 創(chuàng)建數(shù)據(jù)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算法實現(xiàn),采用歐式距離
:param testFeature: 測試數(shù)據(jù)集,ndarray類型,一維數(shù)組
:param trainingSet: 訓(xùn)練數(shù)據(jù)集,ndarray類型,二維數(shù)組
:param labels: 訓(xùn)練集對應(yīng)標(biāo)簽,ndarray類型,一維數(shù)組
:param k: k值,int類型
:return: 預(yù)測結(jié)果,類型與標(biāo)簽中元素一致
"""
dataSetsize = trainingSet.shape[0]
"""
構(gòu)建一個由dataSet[i] - testFeature的新的數(shù)據(jù)集diffMat
diffMat中的每個元素都是dataSet中每個特征與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中各個數(shù)據(jù)的位置
如distance = [5, 9, 0, 2]
則sortedStance = [2, 3, 0, 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(jié)果進(jìn)行統(tǒng)計、排序,選取最終結(jié)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, labels, 3)
print(res)
# 使用python包實現(xiàn) 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(wǎng)站匹配效果預(yù)測》
數(shù)據(jù)來源:略
數(shù)據(jù)顯示
import pandas as pd
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# 數(shù)據(jù)加載
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圖顯示數(shù)據(jù)
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(shù)", fontsize=16)
plt.ylabel("視頻游戲耗時百分比", fontsize=16)
plt.clabel("冰淇凌消耗", fontsize=16)
plt.show()
datingData, datingTrainData, datingTrainLabel = loadDatingData(FILEPATH1)
datingView3D(datingTrainData, datingTrainLabel)
問題分析:抽取數(shù)據(jù)集的前10%在數(shù)據(jù)集的后90%進(jìn)行測試
編碼實現(xiàn)
# 自定義方法實現(xiàn)
import pandas as pd
import numpy as np
# 數(shù)據(jù)加載
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
# 數(shù)據(jù)歸一化
def autoNorm(datingTrainData):
# 獲取數(shù)據(jù)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, (m, 1))
normValuesData = (datingTrainData-minValuesData)/diffValuesData
return normValuesData
# 核心算法實現(xiàn)
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
# 對結(jié)果進(jìn)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]
# 數(shù)據(jù)測試
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 第三方包實現(xiàn)
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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