机器学习——k近邻

6.2 距离计算

任务

• 构建自定义函数cal_eculidean(array_a, array_b)函数，计算欧式距离。输入变量为ndarray类型数组，返回结果为二者之间的欧式距离；

• 针对测试集test_data中的每个数据样本，使用自定义函数计算其和训练集每个样本的欧式距离，保存在变量distances中。

预期结果

待补全代码

import pandas as pd
import numpy as np
import math
train_data = pd.read_table('gender.csv', sep = ',')
test_data = pd.read_table('test.csv', sep = ',')

# 请在下方作答 #

def cal_eculidean(array_a, array_b):
    import numpy as np
    
    ## 计算变量各个维度的差的平方
    array_square = (array_a-array_b)**2
    
    ## 计算差的平方和array_square_sum
    array_square_sum = sum(array_square)
    
    ## 开根号
    sum_root = math.sqrt(array_square_sum)
    
    return sum_root

## 声储存距离的变量
distances = []

## 遍历`test_data`中的每个数据样本, 样本的储存格式为ndarray
for item in test_data.iloc[:,:-1].values:
    
    ## 储存数据样本和训练集中每个样本的距离，dist格式为字典类型，形如{index: distance}
    dist = {}
    
    for index, train_item in enumerate(train_data.iloc[:,:-1].values):
        
        ## 使用自定义函数计算item和train_item之间的举例distance
        distance = cal_eculidean(item,train_item)
        ## 将distance，和train_item的index存入字典变量dist中
        dist[index]= distance
    
    #将dist加入到distances中
    distances.append(dist)
print(distances)

[{0: 32.449961479175904, 1: 27.294688127912362, 2: 19.697715603592208, 3: 29.206163733020468, 4: 35.608987629529715, 5: 27.459060435491963, 6: 22.20360331117452, 7: 23.430749027719962, 8: 31.064449134018133, 9: 31.622776601683793, 10: 31.622776601683793, 11: 30.805843601498726, 12: 26.570660511172846, 13: 31.622776601683793, 14: 26.419689627245813, 15: 22.20360331117452, 16: 10.295630140987, 17: 18.973665961010276, 18: 29.206163733020468, 19: 29.206163733020468, 20: 26.92582403567252, 21: 33.28663395418648, 22: 26.40075756488817, 23: 28.319604517012593, 24: 21.633307652783937, 25: 34.0, 26: 26.90724809414742, 27: 29.154759474226502, 28: 30.4138126514911, 29: 33.12099032335839, 30: 33.97057550292606, 31: 19.6468827043885, 32: 22.360679774997898, 33: 21.93171219946131, 34: 33.97057550292606, 35: 40.22437072223753, 36: 30.886890422961002, 37: 39.408120990476064, 38: 21.095023109728988, 39: 22.80350850198276, 40: 32.7566787083184, 41: 22.20360331117452, 42: 32.55764119219941, 43: 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23.853720883753127, 214: 36.6742416417845, 215: 40.24922359499622, 216: 16.15549442140351, 217: 27.80287754891569, 218: 26.40075756488817, 219: 27.65863337187866, 220: 37.8021163428716, 221: 16.0312195418814, 222: 21.95449840010015, 223: 32.202484376209235, 224: 29.698484809834994, 225: 29.5296461204668, 226: 21.95449840010015, 227: 31.064449134018133, 228: 42.720018726587654, 229: 53.75872022286245, 230: 31.304951684997057, 231: 15.231546211727817, 232: 26.1725046566048, 233: 77.87810988975015, 234: 26.076809620810597, 235: 16.15549442140351, 236: 10.816653826391969, 237: 41.400483088968905, 238: 23.345235059857504, 239: 17.029386365926403, 240: 13.341664064126334, 241: 17.804493814764857, 242: 30.479501308256342, 243: 25.612496949731394, 244: 25.495097567963924, 245: 18.681541692269406, 246: 23.345235059857504, 247: 22.02271554554524, 248: 27.202941017470888, 249: 29.206163733020468, 250: 30.528675044947494, 251: 18.35755975068582, 252: 41.72529209005013, 253: 6.082762530298219, 254: 9.219544457292887, 255: 39.698866482558415, 256: 46.52956049652737, 257: 30.30264014900352, 258: 21.2602916254693, 259: 35.84689665786984, 260: 38.91015291668744, 261: 24.758836806279895, 262: 23.47871376374779, 263: 7.615773105863909, 264: 25.80697580112788, 265: 28.319604517012593, 266: 14.7648230602334, 267: 24.596747752497688, 268: 18.027756377319946, 269: 36.124783736376884, 270: 19.1049731745428, 271: 27.294688127912362, 272: 29.154759474226502, 273: 9.604686356149273, 274: 29.068883707497267, 275: 27.202941017470888, 276: 13.892443989449804, 277: 18.384776310850235, 278: 26.92582403567252, 279: 38.600518131237564, 280: 29.5296461204668, 281: 25.612496949731394, 282: 28.319604517012593, 283: 27.202941017470888, 284: 33.97057550292606, 285: 30.01666203960727, 286: 26.40075756488817, 287: 21.95449840010015, 288: 16.64331697709324, 289: 34.9463875100131, 290: 24.20743687382041, 291: 20.248456731316587, 292: 26.40075756488817, 293: 26.40075756488817, 294: 34.713109915419565, 295: 26.40075756488817, 296: 22.847319317591726, 297: 21.95449840010015, 298: 26.870057685088806, 299: 22.02271554554524}, {0: 5.0, 1: 2.23606797749979, 2: 8.602325267042627, 3: 3.0, 4: 8.602325267042627, 5: 0.0, 6: 10.44030650891055, 7: 5.0, 8: 3.605551275463989, 9: 4.242640687119285, 10: 4.242640687119285, 11: 3.605551275463989, 12: 6.324555320336759, 13: 4.242640687119285, 14: 12.806248474865697, 15: 10.44030650891055, 16: 17.204650534085253, 17: 17.26267650163207, 18: 9.433981132056603, 19: 3.0, 20: 5.385164807134504, 21: 5.830951894845301, 22: 2.23606797749979, 23: 7.211102550927978, 24: 5.830951894845301, 25: 7.0710678118654755, 26: 4.242640687119285, 27: 2.0, 28: 4.123105625617661, 29: 6.082762530298219, 30: 8.246211251235321, 31: 10.770329614269007, 32: 5.830951894845301, 33: 7.0, 34: 8.246211251235321, 35: 12.806248474865697, 36: 4.0, 37: 12.041594578792296, 38: 6.4031242374328485, 39: 5.0990195135927845, 40: 5.385164807134504, 41: 10.44030650891055, 42: 7.0710678118654755, 43: 0.0, 44: 4.242640687119285, 45: 8.602325267042627, 46: 3.0, 47: 2.5, 48: 6.0, 49: 1.0, 50: 37.16180835212409, 51: 19.72308292331602, 52: 54.62600113499065, 53: 15.132745950421556, 54: 22.360679774997898, 55: 19.209372712298546, 56: 17.204650534085253, 57: 17.327723451163457, 58: 8.602325267042627, 59: 7.0710678118654755, 60: 7.0, 61: 10.63014581273465, 62: 22.20360331117452, 63: 33.54101966249684, 64: 17.804493814764857, 65: 15.620499351813308, 66: 23.323807579381203, 67: 19.849433241279208, 68: 18.439088914585774, 69: 34.17601498127012, 70: 26.1725046566048, 71: 10.0, 72: 14.142135623730951, 73: 13.892443989449804, 74: 23.430749027719962, 75: 38.07886552931954, 76: 21.18962010041709, 77: 18.027756377319946, 78: 5.385164807134504, 79: 27.459060435491963, 80: 21.18962010041709, 81: 18.439088914585774, 82: 21.02379604162864, 83: 23.323807579381203, 84: 22.360679774997898, 85: 34.48187929913333, 86: 8.54400374531753, 87: 14.142135623730951, 88: 33.60059523282288, 89: 18.601075237738275, 90: 17.69180601295413, 91: 33.97057550292606, 92: 10.63014581273465, 93: 16.55294535724685, 94: 18.027756377319946, 95: 25.495097567963924, 96: 23.323807579381203, 97: 17.0, 98: 21.18962010041709, 99: 16.55294535724685, 100: 16.76305461424021, 101: 21.633307652783937, 102: 20.0, 103: 22.67156809750927, 104: 21.93171219946131, 105: 23.345235059857504, 106: 19.72308292331602, 107: 17.0, 108: 20.808652046684813, 109: 16.278820596099706, 110: 15.811388300841896, 111: 47.43416490252569, 112: 18.027756377319946, 113: 12.165525060596439, 114: 5.0, 115: 19.4164878389476, 116: 16.55294535724685, 117: 20.615528128088304, 118: 29.154759474226502, 119: 19.697715603592208, 120: 18.867962264113206, 121: 24.698178070456937, 122: 24.758836806279895, 123: 19.849433241279208, 124: 11.40175425099138, 125: 15.620499351813308, 126: 10.198039027185569, 127: 21.93171219946131, 128: 37.83186487605389, 129: 8.54400374531753, 130: 15.811388300841896, 131: 8.06225774829855, 132: 3.605551275463989, 133: 31.827660925679098, 134: 17.204650534085253, 135: 8.602325267042627, 136: 23.021728866442675, 137: 19.209372712298546, 138: 23.021728866442675, 139: 30.805843601498726, 140: 52.81098370604357, 141: 29.95413160150032, 142: 18.027756377319946, 143: 27.459060435491963, 144: 11.180339887498949, 145: 27.018512172212592, 146: 16.1245154965971, 147: 24.20743687382041, 148: 25.238858928247925, 149: 34.48187929913333, 150: 23.853720883753127, 151: 16.15549442140351, 152: 12.206555615733702, 153: 25.553864678361276, 154: 36.87817782917155, 155: 28.178005607210743, 156: 26.627053911388696, 157: 29.154759474226502, 158: 14.212670403551895, 159: 38.91015291668744, 160: 44.41846462902562, 161: 4.0, 162: 27.313000567495326, 163: 12.206555615733702, 164: 36.05551275463989, 165: 18.027756377319946, 166: 17.72004514666935, 167: 25.0, 168: 33.54101966249684, 169: 21.213203435596427, 170: 14.866068747318506, 171: 19.697715603592208, 172: 12.206555615733702, 173: 14.142135623730951, 174: 14.142135623730951, 175: 22.360679774997898, 176: 15.620499351813308, 177: 26.90724809414742, 178: 24.041630560342615, 179: 19.209372712298546, 180: 27.459060435491963, 181: 44.204072210600685, 182: 28.30194339616981, 183: 13.92838827718412, 184: 15.811388300841896, 185: 24.758836806279895, 186: 34.058772731852805, 187: 33.24154027718932, 188: 11.661903789690601, 189: 42.720018726587654, 190: 25.0, 191: 15.264337522473747, 192: 21.095023109728988, 193: 18.027756377319946, 194: 25.553864678361276, 195: 22.67156809750927, 196: 19.209372712298546, 197: 21.470910553583888, 198: 17.4928556845359, 199: 16.55294535724685, 200: 5.830951894845301, 201: 18.601075237738275, 202: 23.430749027719962, 203: 22.80350850198276, 204: 16.278820596099706, 205: 19.209372712298546, 206: 33.24154027718932, 207: 50.0, 208: 30.083217912982647, 209: 21.213203435596427, 210: 12.083045973594572, 211: 25.612496949731394, 212: 38.2099463490856, 213: 17.69180601295413, 214: 33.24154027718932, 215: 36.68787265568828, 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6.3 选择最近邻样本

任务

• 对于distances中的每个字典元素的值进行递增排序，选择距离最小的K个样本，将样本的索引保存在变量index_list中。

预期结果

待补全代码

• 此代码中用到的数据 distances 来自上一实验的结果

## 声明储存K个邻居的index的列表
index_list = []

## 遍历每个测试样本的与训练集的举例，item类型为dict
for item in distances:

  
    ## item的类型为dict，即{'index': distance}
    ## 使用sorted函数对item按照diatance进行升序排列,并取前10个距离最小的样本
    sorted_item = sorted(item.items(), key =lambda d: d[1])[0:10]
    
    ## sorted_item形如[(index, distance),(index, distance)...(index, distance)]
    ## 使用zip函数从sorted_items中获取对应的index
    indexes,_ = zip(*sorted_item)
    ## 将获取的indexes加入到index_list中
    index_list.append(indexes)

index_list

[(143, 180, 182, 284, 118, 157, 153, 194, 242, 141),
 (181, 160, 207, 212, 154, 252, 164, 128, 159, 186),
 (182, 118, 143, 157, 180, 284, 141, 155, 153, 194),
 (183, 170, 239, 73, 151, 270, 93, 99, 116, 199),
 (110, 130, 184, 247, 299, 16, 56, 146, 158, 198),
 (185, 178, 257, 70, 105, 122, 249, 103, 195, 250),
 (186, 91, 255, 88, 187, 252, 154, 133, 269, 220),
 (187, 91, 255, 133, 220, 186, 237, 269, 252, 154),
 (188, 152, 163, 172, 241, 71, 61, 73, 92, 270),
 (189, 256, 75, 111, 228, 159, 50, 215, 260, 128),
 (190, 147, 211, 224, 74, 150, 202, 274, 121, 136),
 (191, 296, 262, 65, 125, 134, 176, 222, 226, 287),
 (192, 232, 101, 298, 51, 106, 108, 62, 115, 219),
 (94, 193, 267, 120, 134, 262, 55, 137, 286, 296),
 (153, 194, 242, 121, 150, 66, 83, 96, 143, 180),
 (103, 195, 105, 169, 178, 209, 248, 250, 275, 283),
 (179, 196, 205, 68, 81, 89, 102, 123, 201, 243),
 (197, 272, 286, 119, 120, 138, 94, 193, 267, 278),
 (198, 77, 97, 107, 112, 142, 165, 238, 246, 16),
 (93, 99, 116, 199, 258, 97, 107, 151, 146, 198),
 (29, 25, 40, 21, 36, 0, 28, 8, 9, 10),
 (30, 34, 42, 48, 4, 11, 9, 10, 13, 0),
 (31, 144, 245, 268, 210, 277, 129, 216, 235, 131),
 (32, 200, 78, 240, 38, 131, 2, 24, 58, 59),
 (33, 273, 7, 254, 39, 236, 86, 24, 126, 6),
 (30, 34, 42, 48, 4, 11, 9, 10, 13, 0),
 (35, 37, 4, 21, 25, 0, 40, 30, 34, 29),
 (36, 28, 47, 27, 8, 29, 40, 0, 9, 10),
 (37, 35, 4, 21, 30, 34, 0, 40, 25, 29),
 (38, 24, 276, 236, 32, 45, 200, 266, 132, 2),
 (39, 7, 236, 254, 24, 33, 132, 273, 38, 263),
 (40, 21, 0, 29, 8, 9, 10, 13, 25, 36),
 (6, 15, 41, 273, 33, 14, 126, 113, 7, 254),
 (42, 30, 34, 48, 4, 3, 11, 19, 46, 9),
 (5, 43, 49, 253, 27, 263, 1, 22, 47, 3)]

6.4 确定样本预测类别

任务

• 按照index_list，对train_data进行切片，获取测试数据集中每个样本的K个邻居的数据记录neighbor_df；
• 针对每个测试样本，查看neighbor_df的特征gender的取值，获取出现频率最高的值，存入到数组pred_label中；
• 根据pred_label和test_data的特征gender取值，计算K近邻算法的正确率accuracy_rate。

预期实验结果

待补全代码

• 此代码中用到的数据 index_list 是基于上一节中的输出数据

import numpy as np
## 声明预测类别数组
pred_label = []

## 遍历索引数组
for indexes in index_list:
    
    ## 获取测试样本K个邻居的数据记录neighbor_df,类型为Dataframe
    neighbor_df=pd.DataFrame(train_data,index=indexes)
    mylist=neighbor_df['gender'].tolist()

    ## 找到出现频率最高的类别mode_value，类型为str
    mode_value=str(max(mylist,key=mylist.count))
    
    ## 将mode_value保存在pred_label
    pred_label.append(mode_value)

## 将取值作变换 ‘M’:1  ‘F’:0
pred_label = [1 if item == 'M' else 0 for item in pred_label]

## 预测值与真实值相减，获得结果diff
truelist=pd.DataFrame(test_data,columns=['gender'])['gender'].tolist()
diff = [pred_label[i]-truelist[i] for i in range(0,len(pred_label))]
## 计算正确率
accuracy_rate = sum(i==0 for i in diff)/len(diff)
print(accuracy_rate)

0.9428571428571428

6.5 K值的选择

任务：

• 在训练集train_data和测试集test_data上运行K近邻算法，可以使用自定义函数knn_classify(train_data, test_data, k)；
• 算法K的取值范围为[3, 20]，针对每个K，计算预测错误样本的个数error_num；
• 绘制折线图， x轴为K的取值范围，y轴为正确率。

预期结果

• 可以把图画的更完善，比如添加坐标轴说明
  

待补全代码

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
train_data = pd.read_table('gender.csv', sep = ',')
test_data = pd.read_table('test.csv', sep = ',')

# 自定义函数 knn_classify(train_data, test_data, k)；
def knn_classify(train_data, test_data, k):
    ## 声储存距离的变量
    distances = []

    ## 遍历`test_data`中的每个数据样本, 样本的储存格式为ndarray
    for item in test_data.iloc[:,:-1].values:
        
        ## 储存数据样本和训练集中每个样本的距离，dist格式为字典类型，形如{index: distance}
        dist = {}
        
        for index, train_item in enumerate(train_data.iloc[:,:-1].values):
            
            ## 使用自定义函数计算item和train_item之间的举例distance
            distance = cal_eculidean(item,train_item)
            ## 将distance，和train_item的index存入字典变量dist中
            dist[index]= distance
        
        #将dist加入到distances中
        distances.append(dist)

    ## 声明储存K个邻居的index的列表
    index_list = []

    ## 遍历每个测试样本的与训练集的举例，item类型为dict
    for item in distances:

    
        ## item的类型为dict，即{'index': distance}
        ## 使用sorted函数对item按照diatance进行升序排列,并取前10个距离最小的样本
        sorted_item = sorted(item.items(), key =lambda d: d[1])[0:k+1]
        
        ## sorted_item形如[(index, distance),(index, distance)...(index, distance)]
        ## 使用zip函数从sorted_items中获取对应的index
        indexes,_ = zip(*sorted_item)
        ## 将获取的indexes加入到index_list中
        index_list.append(indexes)

    ## 声明预测类别数组
    pred_label = []

    ## 遍历索引数组
    for indexes in index_list:
        
        ## 获取测试样本K个邻居的数据记录neighbor_df,类型为Dataframe
        neighbor_df=pd.DataFrame(train_data,index=indexes)
        mylist=neighbor_df['gender'].tolist()

        ## 找到出现频率最高的类别mode_value，类型为str
        mode_value=str(max(mylist,key=mylist.count))
        
        ## 将mode_value保存在pred_label
        pred_label.append(mode_value)
    
    return pred_label
## 声明保存预测错误样本个数列表
error = []

## K的取值范围
k_value = range(3, 20, 1)

truelist=pd.DataFrame(test_data,columns=['gender'])['gender'].tolist()
## 遍历K = 3，4，5，6 ... 20
for num in k_value:
    
    ## 调用knn_classify函数，返回预测结果pred
    pred = knn_classify(train_data,test_data,num)
    
    ## 预测结果转换 ‘M’:1 'F':0
    pred = [1 if item == 'M' else 0 for item in pred]

    ## 预测值与真实值之查
    diff = [pred[i]-truelist[i] for i in range(0,len(pred))]

    ## 统计预测错误的样本个数
    error_num = sum(i!=0 for i in diff)
    ## 将具体的K值对应的样本个数保存到列表error
    error.append(error_num)
    
## 计算正确率
rate_list = [1-(i/len(truelist)) for i in error]

## 绘制折线图
plt.plot(k_value, rate_list,  '--r*')
plt.title('KNN')
plt.xlabel('value(k)')
plt.ylabel('accuracy_rate')
## 输出图像
plt.show()

赏

谢谢你请我吃糖果