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R：朴素贝叶斯
安装package：
> install.packages("e1071")
导入e1071：
> library(e1071)
找一个数据集：
> data(iris)
> iris
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosa
7 4.6 3.4 1.4 0.3 setosa
8 5.0 3.4 1.5 0.2 setosa
9 4.4 2.9 1.4 0.2 setosa
10 4.9 3.1 1.5 0.1 setosa
11 5.4 3.7 1.5 0.2 setosa
12 4.8 3.4 1.6 0.2 setosa
13 4.8 3.0 1.4 0.1 setosa
14 4.3 3.0 1.1 0.1 setosa
15 5.8 4.0 1.2 0.2 setosa
16 5.7 4.4 1.5 0.4 setosa
17 5.4 3.9 1.3 0.4 setosa
18 5.1 3.5 1.4 0.3 setosa
19 5.7 3.8 1.7 0.3 setosa
20 5.1 3.8 1.5 0.3 setosa
21 5.4 3.4 1.7 0.2 setosa
22 5.1 3.7 1.5 0.4 setosa
23 4.6 3.6 1.0 0.2 setosa
24 5.1 3.3 1.7 0.5 setosa
25 4.8 3.4 1.9 0.2 setosa
26 5.0 3.0 1.6 0.2 setosa
27 5.0 3.4 1.6 0.4 setosa
28 5.2 3.5 1.5 0.2 setosa
29 5.2 3.4 1.4 0.2 setosa
30 4.7 3.2 1.6 0.2 setosa
31 4.8 3.1 1.6 0.2 setosa
32 5.4 3.4 1.5 0.4 setosa
33 5.2 4.1 1.5 0.1 setosa
34 5.5 4.2 1.4 0.2 setosa
35 4.9 3.1 1.5 0.2 setosa
36 5.0 3.2 1.2 0.2 setosa
37 5.5 3.5 1.3 0.2 setosa
38 4.9 3.6 1.4 0.1 setosa
39 4.4 3.0 1.3 0.2 setosa
40 5.1 3.4 1.5 0.2 setosa
41 5.0 3.5 1.3 0.3 setosa
42 4.5 2.3 1.3 0.3 setosa
43 4.4 3.2 1.3 0.2 setosa
44 5.0 3.5 1.6 0.6 setosa
45 5.1 3.8 1.9 0.4 setosa
46 4.8 3.0 1.4 0.3 setosa
47 5.1 3.8 1.6 0.2 setosa
48 4.6 3.2 1.4 0.2 setosa
49 5.3 3.7 1.5 0.2 setosa
50 5.0 3.3 1.4 0.2 setosa
51 7.0 3.2 4.7 1.4 versicolor
52 6.4 3.2 4.5 1.5 versicolor
53 6.9 3.1 4.9 1.5 versicolor
54 5.5 2.3 4.0 1.3 versicolor
55 6.5 2.8 4.6 1.5 versicolor
56 5.7 2.8 4.5 1.3 versicolor
57 6.3 3.3 4.7 1.6 versicolor
58 4.9 2.4 3.3 1.0 versicolor
59 6.6 2.9 4.6 1.3 versicolor
60 5.2 2.7 3.9 1.4 versicolor
61 5.0 2.0 3.5 1.0 versicolor
62 5.9 3.0 4.2 1.5 versicolor
63 6.0 2.2 4.0 1.0 versicolor
64 6.1 2.9 4.7 1.4 versicolor
65 5.6 2.9 3.6 1.3 versicolor
66 6.7 3.1 4.4 1.4 versicolor
67 5.6 3.0 4.5 1.5 versicolor
68 5.8 2.7 4.1 1.0 versicolor
69 6.2 2.2 4.5 1.5 versicolor
70 5.6 2.5 3.9 1.1 versicolor
71 5.9 3.2 4.8 1.8 versicolor
72 6.1 2.8 4.0 1.3 versicolor
73 6.3 2.5 4.9 1.5 versicolor
74 6.1 2.8 4.7 1.2 versicolor
75 6.4 2.9 4.3 1.3 versicolor
76 6.6 3.0 4.4 1.4 versicolor
77 6.8 2.8 4.8 1.4 versicolor
78 6.7 3.0 5.0 1.7 versicolor
79 6.0 2.9 4.5 1.5 versicolor
80 5.7 2.6 3.5 1.0 versicolor
81 5.5 2.4 3.8 1.1 versicolor
82 5.5 2.4 3.7 1.0 versicolor
83 5.8 2.7 3.9 1.2 versicolor
84 6.0 2.7 5.1 1.6 versicolor
85 5.4 3.0 4.5 1.5 versicolor
86 6.0 3.4 4.5 1.6 versicolor
87 6.7 3.1 4.7 1.5 versicolor
88 6.3 2.3 4.4 1.3 versicolor
89 5.6 3.0 4.1 1.3 versicolor
90 5.5 2.5 4.0 1.3 versicolor
91 5.5 2.6 4.4 1.2 versicolor
92 6.1 3.0 4.6 1.4 versicolor
93 5.8 2.6 4.0 1.2 versicolor
94 5.0 2.3 3.3 1.0 versicolor
95 5.6 2.7 4.2 1.3 versicolor
96 5.7 3.0 4.2 1.2 versicolor
97 5.7 2.9 4.2 1.3 versicolor
98 6.2 2.9 4.3 1.3 versicolor
99 5.1 2.5 3.0 1.1 versicolor
100 5.7 2.8 4.1 1.3 versicolor
101 6.3 3.3 6.0 2.5 virginica
102 5.8 2.7 5.1 1.9 virginica
103 7.1 3.0 5.9 2.1 virginica
104 6.3 2.9 5.6 1.8 virginica
105 6.5 3.0 5.8 2.2 virginica
106 7.6 3.0 6.6 2.1 virginica
107 4.9 2.5 4.5 1.7 virginica
108 7.3 2.9 6.3 1.8 virginica
109 6.7 2.5 5.8 1.8 virginica
110 7.2 3.6 6.1 2.5 virginica
111 6.5 3.2 5.1 2.0 virginica
112 6.4 2.7 5.3 1.9 virginica
113 6.8 3.0 5.5 2.1 virginica
114 5.7 2.5 5.0 2.0 virginica
115 5.8 2.8 5.1 2.4 virginica
116 6.4 3.2 5.3 2.3 virginica
117 6.5 3.0 5.5 1.8 virginica
118 7.7 3.8 6.7 2.2 virginica
119 7.7 2.6 6.9 2.3 virginica
120 6.0 2.2 5.0 1.5 virginica
121 6.9 3.2 5.7 2.3 virginica
122 5.6 2.8 4.9 2.0 virginica
123 7.7 2.8 6.7 2.0 virginica
124 6.3 2.7 4.9 1.8 virginica
125 6.7 3.3 5.7 2.1 virginica
126 7.2 3.2 6.0 1.8 virginica
127 6.2 2.8 4.8 1.8 virginica
128 6.1 3.0 4.9 1.8 virginica
129 6.4 2.8 5.6 2.1 virginica
130 7.2 3.0 5.8 1.6 virginica
131 7.4 2.8 6.1 1.9 virginica
132 7.9 3.8 6.4 2.0 virginica
133 6.4 2.8 5.6 2.2 virginica
134 6.3 2.8 5.1 1.5 virginica
135 6.1 2.6 5.6 1.4 virginica
136 7.7 3.0 6.1 2.3 virginica
137 6.3 3.4 5.6 2.4 virginica
138 6.4 3.1 5.5 1.8 virginica
139 6.0 3.0 4.8 1.8 virginica
140 6.9 3.1 5.4 2.1 virginica
141 6.7 3.1 5.6 2.4 virginica
142 6.9 3.1 5.1 2.3 virginica
143 5.8 2.7 5.1 1.9 virginica
144 6.8 3.2 5.9 2.3 virginica
145 6.7 3.3 5.7 2.5 virginica
146 6.7 3.0 5.2 2.3 virginica
147 6.3 2.5 5.0 1.9 virginica
148 6.5 3.0 5.2 2.0 virginica
149 6.2 3.4 5.4 2.3 virginica
150 5.9 3.0 5.1 1.8 virginica
先看一下，对这个数据集summary的结果：
> summary(iris) Sepal.Length Sepal.Width Petal.Length Petal.Width Species Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100 setosa :50 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300 versicolor:50 Median :5.800 Median :3.000 Median :4.350 Median :1.300 virginica :50 Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800 Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
训练并查看训练结果：
> classifier<-naiveBayes(iris[,1:4], iris[,5])
> classifier
Naive Bayes Classifier for Discrete Predictors
Call:
naiveBayes.default(x = iris[, 1:4], y = iris[, 5])
A-priori probabilities:
iris[, 5]
setosa versicolor virginica
0.3333333 0.3333333 0.3333333
Conditional probabilities:
Sepal.Length
iris[, 5] [,1] [,2]
setosa 5.006 0.3524897
versicolor 5.936 0.5161711
virginica 6.588 0.6358796
Sepal.Width
iris[, 5] [,1] [,2]
setosa 3.428 0.3790644
versicolor 2.770 0.3137983
virginica 2.974 0.3224966
Petal.Length
iris[, 5] [,1] [,2]
setosa 1.462 0.1736640
versicolor 4.260 0.4699110
virginica 5.552 0.5518947
Petal.Width
iris[, 5] [,1] [,2]
setosa 0.246 0.1053856
versicolor 1.326 0.1977527
virginica 2.026 0.2746501
> classifier$apriori
iris[, 5]
setosa versicolor virginica
50 50 50
> classifier$tables
$Sepal.Length
Sepal.Length
iris[, 5] [,1] [,2]
setosa 5.006 0.3524897
versicolor 5.936 0.5161711
virginica 6.588 0.6358796
$Sepal.Width
Sepal.Width
iris[, 5] [,1] [,2]
setosa 3.428 0.3790644
versicolor 2.770 0.3137983
virginica 2.974 0.3224966
$Petal.Length
Petal.Length
iris[, 5] [,1] [,2]
setosa 1.462 0.1736640
versicolor 4.260 0.4699110
virginica 5.552 0.5518947
$Petal.Width
Petal.Width
iris[, 5] [,1] [,2]
setosa 0.246 0.1053856
versicolor 1.326 0.1977527
virginica 2.026 0.2746501
A-priori probabilities:
iris[, 5]
setosa versicolor virginica
0.3333333 0.3333333 0.3333333 很好理解，就是类别的先验概率。
而：
$Petal.Width Petal.Width iris[, 5] [,1] [,2] setosa 0.246 0.1053856 versicolor 1.326 0.1977527 virginica 2.026 0.2746501是特征Petal.Width的条件概率，在这个贝叶斯实现中，特征是数值型数据（而且还还有小数部分），这里假设概率密度符合高斯分布。比如对于特征Petal.Width，其属于setosa的概率符合mean为0.246，标准方差为0.1053856的高斯分布。
预测：
预测iris数据集中的第一个数据：
> predict(classifier, iris[1, -5]) [1] setosa Levels: setosa versicolor virginica
> new_data = http://www.mamicode.com/data.frame(Sepal.Length=7, Sepal.Width=3, Petal.Length=6, Petal.Width=2)>
下面看一下，这个库如何处理标称型特征：
数据如下：
> model = c("H", "H", "H", "H", "T", "T", "T", "T") > place = c("B", "B", "N", "N", "B", "B", "N", "N") > repairs = c("Y", "N", "Y", "N", "Y", "N", "Y", "N") > dataset model place repairs 1 H B Y 2 H B N 3 H N Y 4 H N N 5 T B Y 6 T B N 7 T N Y 8 T N N
贝叶斯之：
> classifier<-naiveBayes(dataset[,1:2], dataset[,3]) > classifier Naive Bayes Classifier for Discrete Predictors Call: naiveBayes.default(x = dataset[, 1:2], y = dataset[, 3]) A-priori probabilities: dataset[, 3] N Y 0.5 0.5 Conditional probabilities: model dataset[, 3] H T N 0.5 0.5 Y 0.5 0.5 place dataset[, 3] B N N 0.5 0.5 Y 0.5 0.5
好了，预测一下：
> new_data = http://www.mamicode.com/data.frame(model="H", place="B") > predict(classifier, new_data) [1] N Levels: N Y
perfect！
参考：
http://www-users.cs.york.ac.uk/~jc/teaching/arin/R_practical/
http://pythonhosted.org//NaiveBayes/R：朴素贝叶斯
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