K-近邻算法（KNN）概述
邻近算法，或者说K最近邻(kNN，k-NearestNeighbor)分类算法是数据挖掘分类技术中最简单的方法之一。所谓K最近邻，就是k个最近的邻居的意思，说的是每个样本都可以用它最接近的k个邻居来代表。Cover和Hart在1968年提出了最初的邻近算法。KNN是一种分类(classification)算法，它输入基于实例的学习（instance-based learning），属于懒惰学习（lazy learning）即KNN没有显式的学习过程，也就是说没有训练阶段，数据集事先已有了分类和特征值，待收到新样本后直接进行处理。
KNN是通过测量不同特征值之间的距离进行分类。它的的思路是：如果一个样本在特征空间中的k个最相似(即特征空间中最邻近)的样本中的大多数属于某一个类别，则该样本也属于这个类别。K通常是不大于20的整数。KNN算法中，所选择的邻居都是已经正确分类的对象。该方法在定类决策上只依据最邻近的一个或者几个样本的类别来决定待分样本所属的类别。
下面通过一个简单的例子说明一下：如下图，绿色圆要被决定赋予哪个类，是红色三角形还是蓝色四方形？如果K=3，由于红色三角形所占比例为2/3，绿色圆将被赋予红色三角形那个类，如果K=5，由于蓝色四方形比例为3/5，因此绿色圆被赋予蓝色四方形类。
由此也说明了KNN算法的结果很大程度取决于K的选择。
在KNN中，通过计算对象间距离来作为各个对象之间的非相似性指标，避免了对象之间的匹配问题，在这里距离一般使用欧氏距离或曼哈顿距离：
同时，KNN通过依据k个对象中占优的类别进行决策，而不是单一的对象类别决策。这两点就是KNN算法的优势。
接下来对KNN算法的思想总结一下：就是在训练集中数据和标签已知的情况下，输入测试数据，将测试数据的特征与训练集中对应的特征进行相互比较，找到训练集中与之最为相似的前K个数据，则该测试数据对应的类别就是K个数据中出现次数最多的那个分类，其算法的描述为：
1）计算测试数据与各个训练数据之间的距离；
2）按照距离的递增关系进行排序；
3）选取距离最小的K个点；
4）确定前K个点所在类别的出现频率；
5）返回前K个点中出现频率最高的类别作为测试数据的预测分类。
# knn算法步骤 # 1）计算测试数据与各个训练数据之间的距离，一般选取数据的10分之1作为测试集，其余为训练集； # 2）按照距离的递增关系进行排序； # 3）选取距离最小的K个点，这里可以为前k个数分配权重； # 4）确定前K个点所在类别的出现频率； # 5）返回前K个点中出现频率最高的类别作为测试数据的预测分类。 #读取数据 def Read(): listinfo = [] with open('test.csv', 'rb') as myFile: for line in myFile: info = line.decode('utf-8') info = info.rstrip(' ') listinfo.append(info.split(',')) #print(info.split(',')) return listinfo #计算距离并排序 def Distance(listinfo,list): diclist = [] id = 1 for i in range(0,len(listinfo)): # print(listinfo[i]) dic = {} distance = 0 for j in range(2,len(listinfo[i])): #print(listinfo[i][j],list[j]) distance += (float(listinfo[i][j]) -float(list[j]))**2 distance = distance**0.5 dic['距离'] = distance dic['类别'] = listinfo[i][1] diclist.append(dic) id+=1 #升序排序 diclist.sort(key=f1) # print(diclist) return diclist #以某个特征 def f1(x): return x['距离'] #选取k个数，并计算k个数的类别概率 def Count(listinfo,k,kinddic): #获取距离最小/最近的几个训练集 list = listinfo[0:k] print(list) for l in list: if l['类别'] == "M": kinddic[l['类别']] +=1 else:kinddic[l['类别']] +=1 print(kinddic) return kinddic #选取类别概率最大类别作为测试集的预测类别 def outcome(kinddic): global testid #获取字典中最大的元素 max_prices = max(zip(kinddic.values(), kinddic.keys())) # print(max_prices) print(testid,"号的预测测试结果:",max_prices[1]) listinfo = Read() listinfo = listinfo[1:] #训练集 newlistinfo = listinfo[0:90] #测试集 testinfo = listinfo[90:] testid = 9 diclist = Distance(newlistinfo,testinfo[testid]) kinddic ={'M':0,'B':0} kinddic = Count(diclist,10,kinddic) outcome(kinddic)
id,diagnosis_result,radius,texture,perimeter,area,smoothness,compactness,symmetry,fractal_dimension
1,M,23,12,151,954,0.143,0.278,0.242,0.079
2,B,9,13,133,1326,0.143,0.079,0.181,0.057
3,M,21,27,130,1203,0.125,0.16,0.207,0.06
4,M,14,16,78,386,0.07,0.284,0.26,0.097
5,M,9,19,135,1297,0.141,0.133,0.181,0.059
6,B,25,25,83,477,0.128,0.17,0.209,0.076
7,M,16,26,120,1040,0.095,0.109,0.179,0.057
8,M,15,18,90,578,0.119,0.165,0.22,0.075
9,M,19,24,88,520,0.127,0.193,0.235,0.074
10,M,25,11,84,476,0.119,0.24,0.203,0.082
11,M,24,21,103,798,0.082,0.067,0.153,0.057
12,M,17,15,104,781,0.097,0.129,0.184,0.061
13,B,14,15,132,1123,0.097,0.246,0.24,0.078
14,M,12,22,104,783,0.084,0.1,0.185,0.053
15,M,12,13,94,578,0.113,0.229,0.207,0.077
16,M,22,19,97,659,0.114,0.16,0.23,0.071
17,M,10,16,95,685,0.099,0.072,0.159,0.059
18,M,15,14,108,799,0.117,0.202,0.216,0.074
19,M,20,14,130,1260,0.098,0.103,0.158,0.054
20,B,17,11,87,566,0.098,0.081,0.189,0.058
21,B,16,14,86,520,0.108,0.127,0.197,0.068
22,B,17,24,60,274,0.102,0.065,0.182,0.069
23,M,20,27,103,704,0.107,0.214,0.252,0.07
24,M,19,12,137,1404,0.094,0.102,0.177,0.053
25,M,9,13,110,905,0.112,0.146,0.2,0.063
26,M,19,27,116,913,0.119,0.228,0.304,0.074
27,M,10,24,97,645,0.105,0.187,0.225,0.069
28,M,16,24,122,1094,0.094,0.107,0.17,0.057
29,M,15,15,102,732,0.108,0.17,0.193,0.065
30,M,11,16,115,955,0.098,0.116,0.174,0.061
31,M,11,22,125,1088,0.106,0.189,0.218,0.062
32,M,23,26,78,441,0.111,0.152,0.23,0.078
33,M,20,18,113,899,0.12,0.15,0.225,0.064
34,M,11,21,128,1162,0.094,0.172,0.185,0.063
35,M,16,23,107,807,0.104,0.156,0.2,0.065
36,M,10,13,110,870,0.096,0.134,0.19,0.057
37,M,18,12,94,633,0.098,0.11,0.189,0.061
38,B,21,11,83,524,0.09,0.038,0.147,0.059
39,M,11,15,96,699,0.094,0.051,0.157,0.055
40,M,10,14,88,559,0.102,0.126,0.172,0.064
41,M,24,16,86,563,0.082,0.06,0.178,0.056
42,M,19,27,72,371,0.123,0.122,0.19,0.069
43,M,11,11,128,1104,0.091,0.219,0.231,0.063
44,M,15,21,87,545,0.104,0.144,0.197,0.068
45,M,10,15,85,532,0.097,0.105,0.175,0.062
46,M,18,11,124,1076,0.11,0.169,0.191,0.06
47,B,22,12,52,202,0.086,0.059,0.177,0.065
48,M,20,14,86,535,0.116,0.123,0.213,0.068
49,B,20,21,78,449,0.103,0.091,0.168,0.06
50,B,25,11,87,561,0.088,0.077,0.181,0.057
51,B,19,25,75,428,0.086,0.05,0.15,0.059
52,B,19,22,87,572,0.077,0.061,0.135,0.06
53,B,25,15,76,438,0.083,0.048,0.187,0.061
54,M,14,26,120,1033,0.115,0.149,0.209,0.063
55,M,18,25,97,713,0.091,0.071,0.162,0.057
56,B,18,13,73,409,0.095,0.055,0.192,0.059
57,M,10,19,126,1152,0.105,0.127,0.192,0.06
58,M,17,20,96,657,0.114,0.137,0.203,0.068
59,B,22,15,83,527,0.081,0.038,0.182,0.055
60,B,23,26,54,225,0.098,0.053,0.168,0.072
61,B,15,18,65,312,0.113,0.081,0.274,0.07
62,B,25,15,55,222,0.124,0.09,0.183,0.068
63,M,12,22,96,646,0.105,0.201,0.195,0.073
64,B,24,17,59,261,0.077,0.088,0.234,0.07
65,M,16,19,83,499,0.112,0.126,0.191,0.066
66,M,11,21,97,668,0.117,0.148,0.195,0.067
67,B,12,13,60,269,0.104,0.078,0.172,0.069
68,B,18,12,72,394,0.081,0.047,0.152,0.057
69,B,16,17,59,251,0.107,0.141,0.211,0.08
70,B,17,21,81,503,0.098,0.052,0.159,0.057
71,M,21,18,124,1130,0.09,0.103,0.158,0.055
72,B,9,26,59,244,0.098,0.153,0.19,0.09
73,M,21,12,114,929,0.107,0.183,0.193,0.065
74,M,22,25,90,584,0.101,0.128,0.166,0.066
75,B,18,13,79,471,0.092,0.068,0.172,0.059
76,M,21,18,104,818,0.092,0.084,0.18,0.054
77,B,10,17,88,559,0.129,0.105,0.24,0.066
78,M,11,21,120,1006,0.107,0.215,0.215,0.067
79,M,16,18,144,1245,0.129,0.345,0.291,0.081
80,B,22,16,83,506,0.099,0.095,0.172,0.06
81,B,10,18,74,402,0.11,0.094,0.184,0.07
82,B,17,21,86,520,0.108,0.154,0.194,0.069
83,M,10,15,172,1878,0.106,0.267,0.183,0.068
84,M,20,14,129,1132,0.122,0.179,0.163,0.072
85,B,25,21,77,443,0.097,0.072,0.208,0.06
86,M,14,13,121,1075,0.099,0.105,0.213,0.06
87,M,19,26,94,648,0.094,0.099,0.208,0.056
88,M,19,11,122,1076,0.09,0.121,0.195,0.056
89,B,11,11,80,466,0.088,0.094,0.193,0.064
90,B,12,23,96,652,0.113,0.134,0.212,0.063
91,B,23,27,95,663,0.09,0.086,0.169,0.059
92,M,10,12,100,728,0.092,0.104,0.172,0.061
93,B,14,14,85,552,0.074,0.051,0.139,0.053
94,B,10,17,87,555,0.102,0.082,0.164,0.057
95,M,22,26,100,706,0.104,0.155,0.186,0.063
96,M,23,16,132,1264,0.091,0.131,0.21,0.056
97,B,22,14,78,451,0.105,0.071,0.19,0.066
98,B,19,27,62,295,0.102,0.053,0.135,0.069
99,B,21,24,74,413,0.09,0.075,0.162,0.066
100,M,16,27,94,643,0.098,0.114,0.188,0.064
