分類算法KNN(K Nearest Neighbor)
示例：《電影類型分類》

獲取數據來源

電影名稱 打斗次數 接吻次數 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
數據顯示：肉眼判斷python基礎教程電影類型unknown是什么

from matplotlib import pyplot as plt ? # 用來正常顯示中文標簽 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，接吻次數 X = [3, 8, 1, 111, 99, 88, 18] Y = [104, 95, 81, 15, 2, 10, 88] ? plt.title("通過打斗次數和接吻次數判斷電影類型", fontsize=18) plt.xlabel("電影中打斗鏡頭出現的次數", fontsize=16) plt.ylabel("電影中接吻鏡頭出現的次數", fontsize=16) ? # 繪制數據 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：根據已知信息分析電影類型unknown是什么

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，求解過程中極其復雜，故可不使用馬氏距離

知識擴展

馬氏距離概念：表示數據的協方差距離

方差：數據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表示不同的數據集，xy表示數據集元素對應乘積組成數據集

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)]

算法實現：歐氏距離

編碼實現

# 自定義實現 mytest1.py import numpy as np ? # 創建數據集 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，采用歐式距離:param testFeature: 測試數據集，ndarray類型，一維數組:param trainingSet: 訓練數據集，ndarray類型，二維數組:param labels: 訓練集對應標簽，ndarray類型，一維數組:param k: k值，int類型:return: 預測結果，類型與標簽中元素一致"""dataSetsize = trainingSet.shape[0]"""構建一個由dataSet[i] - testFeature的新的數據集diffMatdiffMat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中各個數據的位置如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, labels, 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》

數據來源：略

數據顯示

import pandas as pd import numpy as np from matplotlib import pyplot as plt from mpl_toolkits.mplot3d import Axes3D ? # 數據加載 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圖顯示數據 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：抽取數據集的前10%在數據集的后90%進行測試

編碼實現

# 自定義方法實現 import pandas as pd import numpy as np ? # 數據加載 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 ? # 數據歸一化 def autoNorm(datingTrainData):# 獲取數據集每一列的最值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)/diffValuesDatareturn normValuesData ? # 核心算法實現 def KNNClassifier(testData, trainData, trainLabel, k):m = trainData.shape(0)testDataArray = np.tile(testData, (m, 1))diffDataArray = (testDataArray - trainData) ** 2sumDataArray = 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)+1classCount = sorted(classCount.items(), key=lambda x: x[1], reversed=True)return classCount[0][0]? # 數據測試 def datingTest(file):datingData, datingTrainData, datingTrainLabel = loadDatingData(file)normValuesData = autoNorm(datingTrainData)errorCount = 0ratio = 0.10total = 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 += 1print("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, datingTrainData, datingTrainLabel = loadDatingData(FILEPATH)normValuesData = autoNorm(datingTrainData)errorCount = 0ratio = 0.10total = normValuesData.shape[0]numberTest = int(total * ratio)k = 5clf = 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 += 1print("The total error rate is : {}\n".format(errorCount/float(numberTest)))

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