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 Species1 5.1 3.5 1.4 0.2 setosa2 4.9 3.0 1.4 0.2 setosa3 4.7 3.2 1.3 0.2 setosa4 4.6 3.1 1.5 0.2 setosa5 5.0 3.6 1.4 0.2 setosa6 5.4 3.9 1.7 0.4 setosa7 4.6 3.4 1.4 0.3 setosa8 5.0 3.4 1.5 0.2 setosa9 4.4 2.9 1.4 0.2 setosa10 4.9 3.1 1.5 0.1 setosa11 5.4 3.7 1.5 0.2 setosa12 4.8 3.4 1.6 0.2 setosa13 4.8 3.0 1.4 0.1 setosa14 4.3 3.0 1.1 0.1 setosa15 5.8 4.0 1.2 0.2 setosa16 5.7 4.4 1.5 0.4 setosa17 5.4 3.9 1.3 0.4 setosa18 5.1 3.5 1.4 0.3 setosa19 5.7 3.8 1.7 0.3 setosa20 5.1 3.8 1.5 0.3 setosa21 5.4 3.4 1.7 0.2 setosa22 5.1 3.7 1.5 0.4 setosa23 4.6 3.6 1.0 0.2 setosa24 5.1 3.3 1.7 0.5 setosa25 4.8 3.4 1.9 0.2 setosa26 5.0 3.0 1.6 0.2 setosa27 5.0 3.4 1.6 0.4 setosa28 5.2 3.5 1.5 0.2 setosa29 5.2 3.4 1.4 0.2 setosa30 4.7 3.2 1.6 0.2 setosa31 4.8 3.1 1.6 0.2 setosa32 5.4 3.4 1.5 0.4 setosa33 5.2 4.1 1.5 0.1 setosa34 5.5 4.2 1.4 0.2 setosa35 4.9 3.1 1.5 0.2 setosa36 5.0 3.2 1.2 0.2 setosa37 5.5 3.5 1.3 0.2 setosa38 4.9 3.6 1.4 0.1 setosa39 4.4 3.0 1.3 0.2 setosa40 5.1 3.4 1.5 0.2 setosa41 5.0 3.5 1.3 0.3 setosa42 4.5 2.3 1.3 0.3 setosa43 4.4 3.2 1.3 0.2 setosa44 5.0 3.5 1.6 0.6 setosa45 5.1 3.8 1.9 0.4 setosa46 4.8 3.0 1.4 0.3 setosa47 5.1 3.8 1.6 0.2 setosa48 4.6 3.2 1.4 0.2 setosa49 5.3 3.7 1.5 0.2 setosa50 5.0 3.3 1.4 0.2 setosa51 7.0 3.2 4.7 1.4 versicolor52 6.4 3.2 4.5 1.5 versicolor53 6.9 3.1 4.9 1.5 versicolor54 5.5 2.3 4.0 1.3 versicolor55 6.5 2.8 4.6 1.5 versicolor56 5.7 2.8 4.5 1.3 versicolor57 6.3 3.3 4.7 1.6 versicolor58 4.9 2.4 3.3 1.0 versicolor59 6.6 2.9 4.6 1.3 versicolor60 5.2 2.7 3.9 1.4 versicolor61 5.0 2.0 3.5 1.0 versicolor62 5.9 3.0 4.2 1.5 versicolor63 6.0 2.2 4.0 1.0 versicolor64 6.1 2.9 4.7 1.4 versicolor65 5.6 2.9 3.6 1.3 versicolor66 6.7 3.1 4.4 1.4 versicolor67 5.6 3.0 4.5 1.5 versicolor68 5.8 2.7 4.1 1.0 versicolor69 6.2 2.2 4.5 1.5 versicolor70 5.6 2.5 3.9 1.1 versicolor71 5.9 3.2 4.8 1.8 versicolor72 6.1 2.8 4.0 1.3 versicolor73 6.3 2.5 4.9 1.5 versicolor74 6.1 2.8 4.7 1.2 versicolor75 6.4 2.9 4.3 1.3 versicolor76 6.6 3.0 4.4 1.4 versicolor77 6.8 2.8 4.8 1.4 versicolor78 6.7 3.0 5.0 1.7 versicolor79 6.0 2.9 4.5 1.5 versicolor80 5.7 2.6 3.5 1.0 versicolor81 5.5 2.4 3.8 1.1 versicolor82 5.5 2.4 3.7 1.0 versicolor83 5.8 2.7 3.9 1.2 versicolor84 6.0 2.7 5.1 1.6 versicolor85 5.4 3.0 4.5 1.5 versicolor86 6.0 3.4 4.5 1.6 versicolor87 6.7 3.1 4.7 1.5 versicolor88 6.3 2.3 4.4 1.3 versicolor89 5.6 3.0 4.1 1.3 versicolor90 5.5 2.5 4.0 1.3 versicolor91 5.5 2.6 4.4 1.2 versicolor92 6.1 3.0 4.6 1.4 versicolor93 5.8 2.6 4.0 1.2 versicolor94 5.0 2.3 3.3 1.0 versicolor95 5.6 2.7 4.2 1.3 versicolor96 5.7 3.0 4.2 1.2 versicolor97 5.7 2.9 4.2 1.3 versicolor98 6.2 2.9 4.3 1.3 versicolor99 5.1 2.5 3.0 1.1 versicolor100 5.7 2.8 4.1 1.3 versicolor101 6.3 3.3 6.0 2.5 virginica102 5.8 2.7 5.1 1.9 virginica103 7.1 3.0 5.9 2.1 virginica104 6.3 2.9 5.6 1.8 virginica105 6.5 3.0 5.8 2.2 virginica106 7.6 3.0 6.6 2.1 virginica107 4.9 2.5 4.5 1.7 virginica108 7.3 2.9 6.3 1.8 virginica109 6.7 2.5 5.8 1.8 virginica110 7.2 3.6 6.1 2.5 virginica111 6.5 3.2 5.1 2.0 virginica112 6.4 2.7 5.3 1.9 virginica113 6.8 3.0 5.5 2.1 virginica114 5.7 2.5 5.0 2.0 virginica115 5.8 2.8 5.1 2.4 virginica116 6.4 3.2 5.3 2.3 virginica117 6.5 3.0 5.5 1.8 virginica118 7.7 3.8 6.7 2.2 virginica119 7.7 2.6 6.9 2.3 virginica120 6.0 2.2 5.0 1.5 virginica121 6.9 3.2 5.7 2.3 virginica122 5.6 2.8 4.9 2.0 virginica123 7.7 2.8 6.7 2.0 virginica124 6.3 2.7 4.9 1.8 virginica125 6.7 3.3 5.7 2.1 virginica126 7.2 3.2 6.0 1.8 virginica127 6.2 2.8 4.8 1.8 virginica128 6.1 3.0 4.9 1.8 virginica129 6.4 2.8 5.6 2.1 virginica130 7.2 3.0 5.8 1.6 virginica131 7.4 2.8 6.1 1.9 virginica132 7.9 3.8 6.4 2.0 virginica133 6.4 2.8 5.6 2.2 virginica134 6.3 2.8 5.1 1.5 virginica135 6.1 2.6 5.6 1.4 virginica136 7.7 3.0 6.1 2.3 virginica137 6.3 3.4 5.6 2.4 virginica138 6.4 3.1 5.5 1.8 virginica139 6.0 3.0 4.8 1.8 virginica140 6.9 3.1 5.4 2.1 virginica141 6.7 3.1 5.6 2.4 virginica142 6.9 3.1 5.1 2.3 virginica143 5.8 2.7 5.1 1.9 virginica144 6.8 3.2 5.9 2.3 virginica145 6.7 3.3 5.7 2.5 virginica146 6.7 3.0 5.2 2.3 virginica147 6.3 2.5 5.0 1.9 virginica148 6.5 3.0 5.2 2.0 virginica149 6.2 3.4 5.4 2.3 virginica150 5.9 3.0 5.1 1.8 virginica
Sepal意思是“花萼 ”，Petal意思是“ 花瓣”。很明显，前四列是花萼和花瓣的特征，第五列代表相应的分类。我们可以用这个数据集进行贝叶斯训练。 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]) > classifierNaive Bayes Classifier for Discrete PredictorsCall: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.Lengthiris[, 5] [,1] [,2] setosa 5.006 0.3524897 versicolor 5.936 0.5161711 virginica 6.588 0.6358796 Sepal.Widthiris[, 5] [,1] [,2] setosa 3.428 0.3790644 versicolor 2.770 0.3137983 virginica 2.974 0.3224966 Petal.Lengthiris[, 5] [,1] [,2] setosa 1.462 0.1736640 versicolor 4.260 0.4699110 virginica 5.552 0.5518947 Petal.Widthiris[, 5] [,1] [,2] setosa 0.246 0.1053856 versicolor 1.326 0.1977527 virginica 2.026 0.2746501> classifier$aprioriiris[, 5] setosa versicolor virginica 50 50 50 > classifier$tables$Sepal.Length Sepal.Lengthiris[, 5] [,1] [,2] setosa 5.006 0.3524897 versicolor 5.936 0.5161711 virginica 6.588 0.6358796$Sepal.Width Sepal.Widthiris[, 5] [,1] [,2] setosa 3.428 0.3790644 versicolor 2.770 0.3137983 virginica 2.974 0.3224966$Petal.Length Petal.Lengthiris[, 5] [,1] [,2] setosa 1.462 0.1736640 versicolor 4.260 0.4699110 virginica 5.552 0.5518947$Petal.Width Petal.Widthiris[, 5] [,1] [,2] setosa 0.246 0.1053856 versicolor 1.326 0.1977527 virginica 2.026 0.2746501
classifier中：
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.Widthiris[, 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] setosaLevels: setosa versicolor virginica
iris[1,-5]表示第一行的前4列。
看一下该分类器的效果：
> table(predict(classifier, iris[,-5]), iris[,5], dnn=list('predicted','actual')) actualpredicted setosa versicolor virginica setosa 50 0 0 versicolor 0 47 3 virginica 0 3 47 分类效果还是不错的。
自己构造一个新的数据并预测：> new_data = data.frame(Sepal.Length=7, Sepal.Width=3, Petal.Length=6, Petal.Width=2)> predict(classifier, new_data)[1] virginicaLevels: setosa versicolor virginica
如果少一个特征（只有三个特征）：
> new_data = data.frame(Sepal.Length=7, Sepal.Width=3, Petal.Length=6)> predict(classifier, new_data)[1] virginicaLevels: setosa versicolor virginica
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 = data.frame(model, place, repairs)> dataset model place repairs1 H B Y2 H B N3 H N Y4 H N N5 T B Y6 T B N7 T N Y8 T N N
贝叶斯之：
> classifier<-naiveBayes(dataset[,1:2], dataset[,3]) > classifierNaive Bayes Classifier for Discrete PredictorsCall:naiveBayes.default(x = dataset[, 1:2], y = dataset[, 3])A-priori probabilities:dataset[, 3] N Y 0.5 0.5 Conditional probabilities: modeldataset[, 3] H T N 0.5 0.5 Y 0.5 0.5 placedataset[, 3] B N N 0.5 0.5 Y 0.5 0.5
好了，预测一下：
> new_data = data.frame(model="H", place="B")> predict(classifier, new_data)[1] NLevels: N Y
perfect！
补充一下，如果某个数据缺少某些特征：
可以用NA代替该特征：
> model = c("H", "H", "H", "H", "T", "T", "T", "T")> place = c("B", "B", "N", "N", "B", "B", NA, NA)> repairs = c("Y", "N", "Y", "N", "Y", "N", "Y", "N")> dataset = data.frame(model, place, repairs)> dataset model place repairs1 H B Y2 H B N3 H N Y4 H N N5 T B Y6 T B N7 T Y8 T N> classifier<-naiveBayes(dataset[,1:2], dataset[,3]) > classifierNaive Bayes Classifier for Discrete PredictorsCall:naiveBayes.default(x = dataset[, 1:2], y = dataset[, 3])A-priori probabilities:dataset[, 3] N Y 0.5 0.5 Conditional probabilities: modeldataset[, 3] H T N 0.5 0.5 Y 0.5 0.5 placedataset[, 3] B N N 0.6666667 0.3333333 Y 0.6666667 0.3333333
参考：
http://www-users.cs.york.ac.uk/~jc/teaching/arin/R_practical/
http://pythonhosted.org//NaiveBayes/