python實現KNN近鄰算法
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.pyimport 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, labelsdef 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.pyfrom sklearn.neighbors import KNeighborsClassifierfrom .mytest1 import createDataSetfeatures, labels = createDataSet()k = 5clf = 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 pdimport numpy as npfrom matplotlib import pyplot as pltfrom 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 pdimport 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)/diffValuesData return 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) ** 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(), 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 = 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 pdimport numpy as npfrom sklearn.neighbors import KNeighborsClassifierif __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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