朴素贝叶斯算法原理及实现

朴素贝叶斯算法简单高效，在处理分类问题上，是应该首先考虑的方法之一。

1、准备知识

 贝叶斯分类是一类分类算法的总称，这类算法均以贝叶斯定理为基础，故统称为贝叶斯分类。

这个定理解决了现实生活里经常遇到的问题：已知某条件概率，如何得到两个事件交换后的概率，也就是在已知P(A|B)的情况下如何求得P(B|A)。这里先解释什么是条件概率：

 表示事件B已经发生的前提下，事件A发生的概率，叫做事件B发生下事件A的条件概率。其基本求解公式为：。

下面不加证明地直接给出贝叶斯定理：

      

2、朴素贝叶斯分类

2.1、朴素贝叶斯分类原理

 

 朴素贝叶斯分类是一种十分简单的分类算法，叫它朴素贝叶斯分类是因为这种方法的思想真的很朴素，朴素贝叶斯的思想基础是这样的：对于给出的待分类项，求解在此项出现的条件下各个类别出现的概率，哪个最大，就认为此待分类项属于哪个类别。

朴素贝叶斯分类的正式定义如下：

1、设为一个待分类项，而每个a为x的一个特征属性。

2、有类别集合。

3、计算。

4、如果，则。

那么现在的关键就是如何计算第3步中的各个条件概率。我们可以这么做：

1、找到一个已知分类的待分类项集合，这个集合叫做训练样本集。

2、统计得到在各类别下各个特征属性的条件概率估计。即

。

3、如果各个特征属性是条件独立的，则根据贝叶斯定理有如下推导：

      

因为分母对于所有类别为常数，因为我们只要将分子最大化皆可。又因为各特征属性是条件独立的，所以有：

      

2.2、朴素贝叶斯分类流程图 

整个朴素贝叶斯分类分为三个阶段：

第一阶段——准备工作阶段，这个阶段的任务是为朴素贝叶斯分类做必要的准备，主要工作是根据具体情况确定特征属性，并对每个特征属性进行适当划分，然后由人工对一部分待分类项进行分类，形成训练样本集合。这一阶段的输入是所有待分类数据，输出是特征属性和训练样本。这一阶段是整个朴素贝叶斯分类中唯一需要人工完成的阶段，其质量对整个过程将有重要影响，分类器的质量很大程度上由特征属性、特征属性划分及训练样本质量决定。

第二阶段——分类器训练阶段，这个阶段的任务就是生成分类器，主要工作是计算每个类别在训练样本中的出现频率及每个特征属性划分对每个类别的条件概率估计，并将结果记录。其输入是特征属性和训练样本，输出是分类器。这一阶段是机械性阶段，根据前面讨论的公式可以由程序自动计算完成。

第三阶段——应用阶段。这个阶段的任务是使用分类器对待分类项进行分类，其输入是分类器和待分类项，输出是待分类项与类别的映射关系。这一阶段也是机械性阶段，由程序完成。

3、预测糖尿病的发生

本文使用的测试问题是“皮马印第安人糖尿病问题”。

这个问题包括768个对于皮马印第安患者的医疗观测细节，记录所描述的瞬时测量取自诸如患者的年纪，怀孕和血液检查的次数。所有患者都是21岁以上（含21岁）的女性，所有属性都是数值型，而且属性的单位各不相同。

每一个记录归属于一个类，这个类指明以测量时间为止，患者是否是在5年之内感染的糖尿病。如果是，则为1，否则为0。

训练数据：

6,148,72,35,0,33.6,0.627,50,1
1,85,66,29,0,26.6,0.351,31,0
8,183,64,0,0,23.3,0.672,32,1
1,89,66,23,94,28.1,0.167,21,0
0,137,40,35,168,43.1,2.288,33,1
5,116,74,0,0,25.6,0.201,30,0
3,78,50,32,88,31.0,0.248,26,1
10,115,0,0,0,35.3,0.134,29,0
2,197,70,45,543,30.5,0.158,53,1
8,125,96,0,0,0.0,0.232,54,1
4,110,92,0,0,37.6,0.191,30,0
10,168,74,0,0,38.0,0.537,34,1
10,139,80,0,0,27.1,1.441,57,0
1,189,60,23,846,30.1,0.398,59,1
5,166,72,19,175,25.8,0.587,51,1
7,100,0,0,0,30.0,0.484,32,1
0,118,84,47,230,45.8,0.551,31,1
7,107,74,0,0,29.6,0.254,31,1
1,103,30,38,83,43.3,0.183,33,0
1,115,70,30,96,34.6,0.529,32,1
3,126,88,41,235,39.3,0.704,27,0
8,99,84,0,0,35.4,0.388,50,0
7,196,90,0,0,39.8,0.451,41,1
9,119,80,35,0,29.0,0.263,29,1
11,143,94,33,146,36.6,0.254,51,1
10,125,70,26,115,31.1,0.205,41,1
7,147,76,0,0,39.4,0.257,43,1
1,97,66,15,140,23.2,0.487,22,0
13,145,82,19,110,22.2,0.245,57,0
5,117,92,0,0,34.1,0.337,38,0
5,109,75,26,0,36.0,0.546,60,0
3,158,76,36,245,31.6,0.851,28,1
3,88,58,11,54,24.8,0.267,22,0
6,92,92,0,0,19.9,0.188,28,0
10,122,78,31,0,27.6,0.512,45,0
4,103,60,33,192,24.0,0.966,33,0
11,138,76,0,0,33.2,0.420,35,0
9,102,76,37,0,32.9,0.665,46,1
2,90,68,42,0,38.2,0.503,27,1
4,111,72,47,207,37.1,1.390,56,1
3,180,64,25,70,34.0,0.271,26,0
7,133,84,0,0,40.2,0.696,37,0
7,106,92,18,0,22.7,0.235,48,0
9,171,110,24,240,45.4,0.721,54,1
7,159,64,0,0,27.4,0.294,40,0
0,180,66,39,0,42.0,1.893,25,1
1,146,56,0,0,29.7,0.564,29,0
2,71,70,27,0,28.0,0.586,22,0
7,103,66,32,0,39.1,0.344,31,1
7,105,0,0,0,0.0,0.305,24,0
1,103,80,11,82,19.4,0.491,22,0
1,101,50,15,36,24.2,0.526,26,0
5,88,66,21,23,24.4,0.342,30,0
8,176,90,34,300,33.7,0.467,58,1
7,150,66,42,342,34.7,0.718,42,0
1,73,50,10,0,23.0,0.248,21,0
7,187,68,39,304,37.7,0.254,41,1
0,100,88,60,110,46.8,0.962,31,0
0,146,82,0,0,40.5,1.781,44,0
0,105,64,41,142,41.5,0.173,22,0
2,84,0,0,0,0.0,0.304,21,0
8,133,72,0,0,32.9,0.270,39,1
5,44,62,0,0,25.0,0.587,36,0
2,141,58,34,128,25.4,0.699,24,0
7,114,66,0,0,32.8,0.258,42,1
5,99,74,27,0,29.0,0.203,32,0
0,109,88,30,0,32.5,0.855,38,1
2,109,92,0,0,42.7,0.845,54,0
1,95,66,13,38,19.6,0.334,25,0
4,146,85,27,100,28.9,0.189,27,0
2,100,66,20,90,32.9,0.867,28,1
5,139,64,35,140,28.6,0.411,26,0
13,126,90,0,0,43.4,0.583,42,1
4,129,86,20,270,35.1,0.231,23,0
1,79,75,30,0,32.0,0.396,22,0
1,0,48,20,0,24.7,0.140,22,0
7,62,78,0,0,32.6,0.391,41,0
5,95,72,33,0,37.7,0.370,27,0
0,131,0,0,0,43.2,0.270,26,1
2,112,66,22,0,25.0,0.307,24,0
3,113,44,13,0,22.4,0.140,22,0
2,74,0,0,0,0.0,0.102,22,0
7,83,78,26,71,29.3,0.767,36,0
0,101,65,28,0,24.6,0.237,22,0
5,137,108,0,0,48.8,0.227,37,1
2,110,74,29,125,32.4,0.698,27,0
13,106,72,54,0,36.6,0.178,45,0
2,100,68,25,71,38.5,0.324,26,0
15,136,70,32,110,37.1,0.153,43,1
1,107,68,19,0,26.5,0.165,24,0
1,80,55,0,0,19.1,0.258,21,0
4,123,80,15,176,32.0,0.443,34,0
7,81,78,40,48,46.7,0.261,42,0
4,134,72,0,0,23.8,0.277,60,1
2,142,82,18,64,24.7,0.761,21,0
6,144,72,27,228,33.9,0.255,40,0
2,92,62,28,0,31.6,0.130,24,0
1,71,48,18,76,20.4,0.323,22,0
6,93,50,30,64,28.7,0.356,23,0
1,122,90,51,220,49.7,0.325,31,1
1,163,72,0,0,39.0,1.222,33,1
1,151,60,0,0,26.1,0.179,22,0
0,125,96,0,0,22.5,0.262,21,0
1,81,72,18,40,26.6,0.283,24,0
2,85,65,0,0,39.6,0.930,27,0
1,126,56,29,152,28.7,0.801,21,0
1,96,122,0,0,22.4,0.207,27,0
4,144,58,28,140,29.5,0.287,37,0
3,83,58,31,18,34.3,0.336,25,0
0,95,85,25,36,37.4,0.247,24,1
3,171,72,33,135,33.3,0.199,24,1
8,155,62,26,495,34.0,0.543,46,1
1,89,76,34,37,31.2,0.192,23,0
4,76,62,0,0,34.0,0.391,25,0
7,160,54,32,175,30.5,0.588,39,1
4,146,92,0,0,31.2,0.539,61,1
5,124,74,0,0,34.0,0.220,38,1
5,78,48,0,0,33.7,0.654,25,0
4,97,60,23,0,28.2,0.443,22,0
4,99,76,15,51,23.2,0.223,21,0
0,162,76,56,100,53.2,0.759,25,1
6,111,64,39,0,34.2,0.260,24,0
2,107,74,30,100,33.6,0.404,23,0
5,132,80,0,0,26.8,0.186,69,0
0,113,76,0,0,33.3,0.278,23,1
1,88,30,42,99,55.0,0.496,26,1
3,120,70,30,135,42.9,0.452,30,0
1,118,58,36,94,33.3,0.261,23,0
1,117,88,24,145,34.5,0.403,40,1
0,105,84,0,0,27.9,0.741,62,1
4,173,70,14,168,29.7,0.361,33,1
9,122,56,0,0,33.3,1.114,33,1
3,170,64,37,225,34.5,0.356,30,1
8,84,74,31,0,38.3,0.457,39,0
2,96,68,13,49,21.1,0.647,26,0
2,125,60,20,140,33.8,0.088,31,0
0,100,70,26,50,30.8,0.597,21,0
0,93,60,25,92,28.7,0.532,22,0
0,129,80,0,0,31.2,0.703,29,0
5,105,72,29,325,36.9,0.159,28,0
3,128,78,0,0,21.1,0.268,55,0
5,106,82,30,0,39.5,0.286,38,0
2,108,52,26,63,32.5,0.318,22,0
10,108,66,0,0,32.4,0.272,42,1
4,154,62,31,284,32.8,0.237,23,0
0,102,75,23,0,0.0,0.572,21,0
9,57,80,37,0,32.8,0.096,41,0
2,106,64,35,119,30.5,1.400,34,0
5,147,78,0,0,33.7,0.218,65,0
2,90,70,17,0,27.3,0.085,22,0
1,136,74,50,204,37.4,0.399,24,0
4,114,65,0,0,21.9,0.432,37,0
9,156,86,28,155,34.3,1.189,42,1
1,153,82,42,485,40.6,0.687,23,0
8,188,78,0,0,47.9,0.137,43,1
7,152,88,44,0,50.0,0.337,36,1
2,99,52,15,94,24.6,0.637,21,0
1,109,56,21,135,25.2,0.833,23,0
2,88,74,19,53,29.0,0.229,22,0
17,163,72,41,114,40.9,0.817,47,1
4,151,90,38,0,29.7,0.294,36,0
7,102,74,40,105,37.2,0.204,45,0
0,114,80,34,285,44.2,0.167,27,0
2,100,64,23,0,29.7,0.368,21,0
0,131,88,0,0,31.6,0.743,32,1
6,104,74,18,156,29.9,0.722,41,1
3,148,66,25,0,32.5,0.256,22,0
4,120,68,0,0,29.6,0.709,34,0
4,110,66,0,0,31.9,0.471,29,0
3,111,90,12,78,28.4,0.495,29,0
6,102,82,0,0,30.8,0.180,36,1
6,134,70,23,130,35.4,0.542,29,1
2,87,0,23,0,28.9,0.773,25,0
1,79,60,42,48,43.5,0.678,23,0
2,75,64,24,55,29.7,0.370,33,0
8,179,72,42,130,32.7,0.719,36,1
6,85,78,0,0,31.2,0.382,42,0
0,129,110,46,130,67.1,0.319,26,1
5,143,78,0,0,45.0,0.190,47,0
5,130,82,0,0,39.1,0.956,37,1
6,87,80,0,0,23.2,0.084,32,0
0,119,64,18,92,34.9,0.725,23,0
1,0,74,20,23,27.7,0.299,21,0
5,73,60,0,0,26.8,0.268,27,0
4,141,74,0,0,27.6,0.244,40,0
7,194,68,28,0,35.9,0.745,41,1
8,181,68,36,495,30.1,0.615,60,1
1,128,98,41,58,32.0,1.321,33,1
8,109,76,39,114,27.9,0.640,31,1
5,139,80,35,160,31.6,0.361,25,1
3,111,62,0,0,22.6,0.142,21,0
9,123,70,44,94,33.1,0.374,40,0
7,159,66,0,0,30.4,0.383,36,1
11,135,0,0,0,52.3,0.578,40,1
8,85,55,20,0,24.4,0.136,42,0
5,158,84,41,210,39.4,0.395,29,1
1,105,58,0,0,24.3,0.187,21,0
3,107,62,13,48,22.9,0.678,23,1
4,109,64,44,99,34.8,0.905,26,1
4,148,60,27,318,30.9,0.150,29,1
0,113,80,16,0,31.0,0.874,21,0
1,138,82,0,0,40.1,0.236,28,0
0,108,68,20,0,27.3,0.787,32,0
2,99,70,16,44,20.4,0.235,27,0
6,103,72,32,190,37.7,0.324,55,0
5,111,72,28,0,23.9,0.407,27,0
8,196,76,29,280,37.5,0.605,57,1
5,162,104,0,0,37.7,0.151,52,1
1,96,64,27,87,33.2,0.289,21,0
7,184,84,33,0,35.5,0.355,41,1
2,81,60,22,0,27.7,0.290,25,0
0,147,85,54,0,42.8,0.375,24,0
7,179,95,31,0,34.2,0.164,60,0
0,140,65,26,130,42.6,0.431,24,1
9,112,82,32,175,34.2,0.260,36,1
12,151,70,40,271,41.8,0.742,38,1
5,109,62,41,129,35.8,0.514,25,1
6,125,68,30,120,30.0,0.464,32,0
5,85,74,22,0,29.0,1.224,32,1
5,112,66,0,0,37.8,0.261,41,1
0,177,60,29,478,34.6,1.072,21,1
2,158,90,0,0,31.6,0.805,66,1
7,119,0,0,0,25.2,0.209,37,0
7,142,60,33,190,28.8,0.687,61,0
1,100,66,15,56,23.6,0.666,26,0
1,87,78,27,32,34.6,0.101,22,0
0,101,76,0,0,35.7,0.198,26,0
3,162,52,38,0,37.2,0.652,24,1
4,197,70,39,744,36.7,2.329,31,0
0,117,80,31,53,45.2,0.089,24,0
4,142,86,0,0,44.0,0.645,22,1
6,134,80,37,370,46.2,0.238,46,1
1,79,80,25,37,25.4,0.583,22,0
4,122,68,0,0,35.0,0.394,29,0
3,74,68,28,45,29.7,0.293,23,0
4,171,72,0,0,43.6,0.479,26,1
7,181,84,21,192,35.9,0.586,51,1
0,179,90,27,0,44.1,0.686,23,1
9,164,84,21,0,30.8,0.831,32,1
0,104,76,0,0,18.4,0.582,27,0
1,91,64,24,0,29.2,0.192,21,0
4,91,70,32,88,33.1,0.446,22,0
3,139,54,0,0,25.6,0.402,22,1
6,119,50,22,176,27.1,1.318,33,1
2,146,76,35,194,38.2,0.329,29,0
9,184,85,15,0,30.0,1.213,49,1
10,122,68,0,0,31.2,0.258,41,0
0,165,90,33,680,52.3,0.427,23,0
9,124,70,33,402,35.4,0.282,34,0
1,111,86,19,0,30.1,0.143,23,0
9,106,52,0,0,31.2,0.380,42,0
2,129,84,0,0,28.0,0.284,27,0
2,90,80,14,55,24.4,0.249,24,0
0,86,68,32,0,35.8,0.238,25,0
12,92,62,7,258,27.6,0.926,44,1
1,113,64,35,0,33.6,0.543,21,1
3,111,56,39,0,30.1,0.557,30,0
2,114,68,22,0,28.7,0.092,25,0
1,193,50,16,375,25.9,0.655,24,0
11,155,76,28,150,33.3,1.353,51,1
3,191,68,15,130,30.9,0.299,34,0
3,141,0,0,0,30.0,0.761,27,1
4,95,70,32,0,32.1,0.612,24,0
3,142,80,15,0,32.4,0.200,63,0
4,123,62,0,0,32.0,0.226,35,1
5,96,74,18,67,33.6,0.997,43,0
0,138,0,0,0,36.3,0.933,25,1
2,128,64,42,0,40.0,1.101,24,0
0,102,52,0,0,25.1,0.078,21,0
2,146,0,0,0,27.5,0.240,28,1
10,101,86,37,0,45.6,1.136,38,1
2,108,62,32,56,25.2,0.128,21,0
3,122,78,0,0,23.0,0.254,40,0
1,71,78,50,45,33.2,0.422,21,0
13,106,70,0,0,34.2,0.251,52,0
2,100,70,52,57,40.5,0.677,25,0
7,106,60,24,0,26.5,0.296,29,1
0,104,64,23,116,27.8,0.454,23,0
5,114,74,0,0,24.9,0.744,57,0
2,108,62,10,278,25.3,0.881,22,0
0,146,70,0,0,37.9,0.334,28,1
10,129,76,28,122,35.9,0.280,39,0
7,133,88,15,155,32.4,0.262,37,0
7,161,86,0,0,30.4,0.165,47,1
2,108,80,0,0,27.0,0.259,52,1
7,136,74,26,135,26.0,0.647,51,0
5,155,84,44,545,38.7,0.619,34,0
1,119,86,39,220,45.6,0.808,29,1
4,96,56,17,49,20.8,0.340,26,0
5,108,72,43,75,36.1,0.263,33,0
0,78,88,29,40,36.9,0.434,21,0
0,107,62,30,74,36.6,0.757,25,1
2,128,78,37,182,43.3,1.224,31,1
1,128,48,45,194,40.5,0.613,24,1
0,161,50,0,0,21.9,0.254,65,0
6,151,62,31,120,35.5,0.692,28,0
2,146,70,38,360,28.0,0.337,29,1
0,126,84,29,215,30.7,0.520,24,0
14,100,78,25,184,36.6,0.412,46,1
8,112,72,0,0,23.6,0.840,58,0
0,167,0,0,0,32.3,0.839,30,1
2,144,58,33,135,31.6,0.422,25,1
5,77,82,41,42,35.8,0.156,35,0
5,115,98,0,0,52.9,0.209,28,1
3,150,76,0,0,21.0,0.207,37,0
2,120,76,37,105,39.7,0.215,29,0
10,161,68,23,132,25.5,0.326,47,1
0,137,68,14,148,24.8,0.143,21,0
0,128,68,19,180,30.5,1.391,25,1
2,124,68,28,205,32.9,0.875,30,1
6,80,66,30,0,26.2,0.313,41,0
0,106,70,37,148,39.4,0.605,22,0
2,155,74,17,96,26.6,0.433,27,1
3,113,50,10,85,29.5,0.626,25,0
7,109,80,31,0,35.9,1.127,43,1
2,112,68,22,94,34.1,0.315,26,0
3,99,80,11,64,19.3,0.284,30,0
3,182,74,0,0,30.5,0.345,29,1
3,115,66,39,140,38.1,0.150,28,0
6,194,78,0,0,23.5,0.129,59,1
4,129,60,12,231,27.5,0.527,31,0
3,112,74,30,0,31.6,0.197,25,1
0,124,70,20,0,27.4,0.254,36,1
13,152,90,33,29,26.8,0.731,43,1
2,112,75,32,0,35.7,0.148,21,0
1,157,72,21,168,25.6,0.123,24,0
1,122,64,32,156,35.1,0.692,30,1
10,179,70,0,0,35.1,0.200,37,0
2,102,86,36,120,45.5,0.127,23,1
6,105,70,32,68,30.8,0.122,37,0
8,118,72,19,0,23.1,1.476,46,0
2,87,58,16,52,32.7,0.166,25,0
1,180,0,0,0,43.3,0.282,41,1
12,106,80,0,0,23.6,0.137,44,0
1,95,60,18,58,23.9,0.260,22,0
0,165,76,43,255,47.9,0.259,26,0
0,117,0,0,0,33.8,0.932,44,0
5,115,76,0,0,31.2,0.343,44,1
9,152,78,34,171,34.2,0.893,33,1
7,178,84,0,0,39.9,0.331,41,1
1,130,70,13,105,25.9,0.472,22,0
1,95,74,21,73,25.9,0.673,36,0
1,0,68,35,0,32.0,0.389,22,0
5,122,86,0,0,34.7,0.290,33,0
8,95,72,0,0,36.8,0.485,57,0
8,126,88,36,108,38.5,0.349,49,0
1,139,46,19,83,28.7,0.654,22,0
3,116,0,0,0,23.5,0.187,23,0
3,99,62,19,74,21.8,0.279,26,0
5,0,80,32,0,41.0,0.346,37,1
4,92,80,0,0,42.2,0.237,29,0
4,137,84,0,0,31.2,0.252,30,0
3,61,82,28,0,34.4,0.243,46,0
1,90,62,12,43,27.2,0.580,24,0
3,90,78,0,0,42.7,0.559,21,0
9,165,88,0,0,30.4,0.302,49,1
1,125,50,40,167,33.3,0.962,28,1
13,129,0,30,0,39.9,0.569,44,1
12,88,74,40,54,35.3,0.378,48,0
1,196,76,36,249,36.5,0.875,29,1
5,189,64,33,325,31.2,0.583,29,1
5,158,70,0,0,29.8,0.207,63,0
5,103,108,37,0,39.2,0.305,65,0
4,146,78,0,0,38.5,0.520,67,1
4,147,74,25,293,34.9,0.385,30,0
5,99,54,28,83,34.0,0.499,30,0
6,124,72,0,0,27.6,0.368,29,1
0,101,64,17,0,21.0,0.252,21,0
3,81,86,16,66,27.5,0.306,22,0
1,133,102,28,140,32.8,0.234,45,1
3,173,82,48,465,38.4,2.137,25,1
0,118,64,23,89,0.0,1.731,21,0
0,84,64,22,66,35.8,0.545,21,0
2,105,58,40,94,34.9,0.225,25,0
2,122,52,43,158,36.2,0.816,28,0
12,140,82,43,325,39.2,0.528,58,1
0,98,82,15,84,25.2,0.299,22,0
1,87,60,37,75,37.2,0.509,22,0
4,156,75,0,0,48.3,0.238,32,1
0,93,100,39,72,43.4,1.021,35,0
1,107,72,30,82,30.8,0.821,24,0
0,105,68,22,0,20.0,0.236,22,0
1,109,60,8,182,25.4,0.947,21,0
1,90,62,18,59,25.1,1.268,25,0
1,125,70,24,110,24.3,0.221,25,0
1,119,54,13,50,22.3,0.205,24,0
5,116,74,29,0,32.3,0.660,35,1
8,105,100,36,0,43.3,0.239,45,1
5,144,82,26,285,32.0,0.452,58,1
3,100,68,23,81,31.6,0.949,28,0
1,100,66,29,196,32.0,0.444,42,0
5,166,76,0,0,45.7,0.340,27,1
1,131,64,14,415,23.7,0.389,21,0
4,116,72,12,87,22.1,0.463,37,0
4,158,78,0,0,32.9,0.803,31,1
2,127,58,24,275,27.7,1.600,25,0
3,96,56,34,115,24.7,0.944,39,0
0,131,66,40,0,34.3,0.196,22,1
3,82,70,0,0,21.1,0.389,25,0
3,193,70,31,0,34.9,0.241,25,1
4,95,64,0,0,32.0,0.161,31,1
6,137,61,0,0,24.2,0.151,55,0
5,136,84,41,88,35.0,0.286,35,1
9,72,78,25,0,31.6,0.280,38,0
5,168,64,0,0,32.9,0.135,41,1
2,123,48,32,165,42.1,0.520,26,0
4,115,72,0,0,28.9,0.376,46,1
0,101,62,0,0,21.9,0.336,25,0
8,197,74,0,0,25.9,1.191,39,1
1,172,68,49,579,42.4,0.702,28,1
6,102,90,39,0,35.7,0.674,28,0
1,112,72,30,176,34.4,0.528,25,0
1,143,84,23,310,42.4,1.076,22,0
1,143,74,22,61,26.2,0.256,21,0
0,138,60,35,167,34.6,0.534,21,1
3,173,84,33,474,35.7,0.258,22,1
1,97,68,21,0,27.2,1.095,22,0
4,144,82,32,0,38.5,0.554,37,1
1,83,68,0,0,18.2,0.624,27,0
3,129,64,29,115,26.4,0.219,28,1
1,119,88,41,170,45.3,0.507,26,0
2,94,68,18,76,26.0,0.561,21,0
0,102,64,46,78,40.6,0.496,21,0
2,115,64,22,0,30.8,0.421,21,0
8,151,78,32,210,42.9,0.516,36,1
4,184,78,39,277,37.0,0.264,31,1
0,94,0,0,0,0.0,0.256,25,0
1,181,64,30,180,34.1,0.328,38,1
0,135,94,46,145,40.6,0.284,26,0
1,95,82,25,180,35.0,0.233,43,1
2,99,0,0,0,22.2,0.108,23,0
3,89,74,16,85,30.4,0.551,38,0
1,80,74,11,60,30.0,0.527,22,0
2,139,75,0,0,25.6,0.167,29,0
1,90,68,8,0,24.5,1.138,36,0
0,141,0,0,0,42.4,0.205,29,1
12,140,85,33,0,37.4,0.244,41,0
5,147,75,0,0,29.9,0.434,28,0
1,97,70,15,0,18.2,0.147,21,0
6,107,88,0,0,36.8,0.727,31,0
0,189,104,25,0,34.3,0.435,41,1
2,83,66,23,50,32.2,0.497,22,0
4,117,64,27,120,33.2,0.230,24,0
8,108,70,0,0,30.5,0.955,33,1
4,117,62,12,0,29.7,0.380,30,1
0,180,78,63,14,59.4,2.420,25,1
1,100,72,12,70,25.3,0.658,28,0
0,95,80,45,92,36.5,0.330,26,0
0,104,64,37,64,33.6,0.510,22,1
0,120,74,18,63,30.5,0.285,26,0
1,82,64,13,95,21.2,0.415,23,0
2,134,70,0,0,28.9,0.542,23,1
0,91,68,32,210,39.9,0.381,25,0
2,119,0,0,0,19.6,0.832,72,0
2,100,54,28,105,37.8,0.498,24,0
14,175,62,30,0,33.6,0.212,38,1
1,135,54,0,0,26.7,0.687,62,0
5,86,68,28,71,30.2,0.364,24,0
10,148,84,48,237,37.6,1.001,51,1
9,134,74,33,60,25.9,0.460,81,0
9,120,72,22,56,20.8,0.733,48,0
1,71,62,0,0,21.8,0.416,26,0
8,74,70,40,49,35.3,0.705,39,0
5,88,78,30,0,27.6,0.258,37,0
10,115,98,0,0,24.0,1.022,34,0
0,124,56,13,105,21.8,0.452,21,0
0,74,52,10,36,27.8,0.269,22,0
0,97,64,36,100,36.8,0.600,25,0
8,120,0,0,0,30.0,0.183,38,1
6,154,78,41,140,46.1,0.571,27,0
1,144,82,40,0,41.3,0.607,28,0
0,137,70,38,0,33.2,0.170,22,0
0,119,66,27,0,38.8,0.259,22,0
7,136,90,0,0,29.9,0.210,50,0
4,114,64,0,0,28.9,0.126,24,0
0,137,84,27,0,27.3,0.231,59,0
2,105,80,45,191,33.7,0.711,29,1
7,114,76,17,110,23.8,0.466,31,0
8,126,74,38,75,25.9,0.162,39,0
4,132,86,31,0,28.0,0.419,63,0
3,158,70,30,328,35.5,0.344,35,1
0,123,88,37,0,35.2,0.197,29,0
4,85,58,22,49,27.8,0.306,28,0
0,84,82,31,125,38.2,0.233,23,0
0,145,0,0,0,44.2,0.630,31,1
0,135,68,42,250,42.3,0.365,24,1
1,139,62,41,480,40.7,0.536,21,0
0,173,78,32,265,46.5,1.159,58,0
4,99,72,17,0,25.6,0.294,28,0
8,194,80,0,0,26.1,0.551,67,0
2,83,65,28,66,36.8,0.629,24,0
2,89,90,30,0,33.5,0.292,42,0
4,99,68,38,0,32.8,0.145,33,0
4,125,70,18,122,28.9,1.144,45,1
3,80,0,0,0,0.0,0.174,22,0
6,166,74,0,0,26.6,0.304,66,0
5,110,68,0,0,26.0,0.292,30,0
2,81,72,15,76,30.1,0.547,25,0
7,195,70,33,145,25.1,0.163,55,1
6,154,74,32,193,29.3,0.839,39,0
2,117,90,19,71,25.2,0.313,21,0
3,84,72,32,0,37.2,0.267,28,0
6,0,68,41,0,39.0,0.727,41,1
7,94,64,25,79,33.3,0.738,41,0
3,96,78,39,0,37.3,0.238,40,0
10,75,82,0,0,33.3,0.263,38,0
0,180,90,26,90,36.5,0.314,35,1
1,130,60,23,170,28.6,0.692,21,0
2,84,50,23,76,30.4,0.968,21,0
8,120,78,0,0,25.0,0.409,64,0
12,84,72,31,0,29.7,0.297,46,1
0,139,62,17,210,22.1,0.207,21,0
9,91,68,0,0,24.2,0.200,58,0
2,91,62,0,0,27.3,0.525,22,0
3,99,54,19,86,25.6,0.154,24,0
3,163,70,18,105,31.6,0.268,28,1
9,145,88,34,165,30.3,0.771,53,1
7,125,86,0,0,37.6,0.304,51,0
13,76,60,0,0,32.8,0.180,41,0
6,129,90,7,326,19.6,0.582,60,0
2,68,70,32,66,25.0,0.187,25,0
3,124,80,33,130,33.2,0.305,26,0
6,114,0,0,0,0.0,0.189,26,0
9,130,70,0,0,34.2,0.652,45,1
3,125,58,0,0,31.6,0.151,24,0
3,87,60,18,0,21.8,0.444,21,0
1,97,64,19,82,18.2,0.299,21,0
3,116,74,15,105,26.3,0.107,24,0
0,117,66,31,188,30.8,0.493,22,0
0,111,65,0,0,24.6,0.660,31,0
2,122,60,18,106,29.8,0.717,22,0
0,107,76,0,0,45.3,0.686,24,0
1,86,66,52,65,41.3,0.917,29,0
6,91,0,0,0,29.8,0.501,31,0
1,77,56,30,56,33.3,1.251,24,0
4,132,0,0,0,32.9,0.302,23,1
0,105,90,0,0,29.6,0.197,46,0
0,57,60,0,0,21.7,0.735,67,0
0,127,80,37,210,36.3,0.804,23,0
3,129,92,49,155,36.4,0.968,32,1
8,100,74,40,215,39.4,0.661,43,1
3,128,72,25,190,32.4,0.549,27,1
10,90,85,32,0,34.9,0.825,56,1
4,84,90,23,56,39.5,0.159,25,0
1,88,78,29,76,32.0,0.365,29,0
8,186,90,35,225,34.5,0.423,37,1
5,187,76,27,207,43.6,1.034,53,1
4,131,68,21,166,33.1,0.160,28,0
1,164,82,43,67,32.8,0.341,50,0
4,189,110,31,0,28.5,0.680,37,0
1,116,70,28,0,27.4,0.204,21,0
3,84,68,30,106,31.9,0.591,25,0
6,114,88,0,0,27.8,0.247,66,0
1,88,62,24,44,29.9,0.422,23,0
1,84,64,23,115,36.9,0.471,28,0
7,124,70,33,215,25.5,0.161,37,0
1,97,70,40,0,38.1,0.218,30,0
8,110,76,0,0,27.8,0.237,58,0
11,103,68,40,0,46.2,0.126,42,0
11,85,74,0,0,30.1,0.300,35,0
6,125,76,0,0,33.8,0.121,54,1
0,198,66,32,274,41.3,0.502,28,1
1,87,68,34,77,37.6,0.401,24,0
6,99,60,19,54,26.9,0.497,32,0
0,91,80,0,0,32.4,0.601,27,0
2,95,54,14,88,26.1,0.748,22,0
1,99,72,30,18,38.6,0.412,21,0
6,92,62,32,126,32.0,0.085,46,0
4,154,72,29,126,31.3,0.338,37,0
0,121,66,30,165,34.3,0.203,33,1
3,78,70,0,0,32.5,0.270,39,0
2,130,96,0,0,22.6,0.268,21,0
3,111,58,31,44,29.5,0.430,22,0
2,98,60,17,120,34.7,0.198,22,0
1,143,86,30,330,30.1,0.892,23,0
1,119,44,47,63,35.5,0.280,25,0
6,108,44,20,130,24.0,0.813,35,0
2,118,80,0,0,42.9,0.693,21,1
10,133,68,0,0,27.0,0.245,36,0
2,197,70,99,0,34.7,0.575,62,1
0,151,90,46,0,42.1,0.371,21,1
6,109,60,27,0,25.0,0.206,27,0
12,121,78,17,0,26.5,0.259,62,0
8,100,76,0,0,38.7,0.190,42,0
8,124,76,24,600,28.7,0.687,52,1
1,93,56,11,0,22.5,0.417,22,0
8,143,66,0,0,34.9,0.129,41,1
6,103,66,0,0,24.3,0.249,29,0
3,176,86,27,156,33.3,1.154,52,1
0,73,0,0,0,21.1,0.342,25,0
11,111,84,40,0,46.8,0.925,45,1
2,112,78,50,140,39.4,0.175,24,0
3,132,80,0,0,34.4,0.402,44,1
2,82,52,22,115,28.5,1.699,25,0
6,123,72,45,230,33.6,0.733,34,0
0,188,82,14,185,32.0,0.682,22,1
0,67,76,0,0,45.3,0.194,46,0
1,89,24,19,25,27.8,0.559,21,0
1,173,74,0,0,36.8,0.088,38,1
1,109,38,18,120,23.1,0.407,26,0
1,108,88,19,0,27.1,0.400,24,0
6,96,0,0,0,23.7,0.190,28,0
1,124,74,36,0,27.8,0.100,30,0
7,150,78,29,126,35.2,0.692,54,1
4,183,0,0,0,28.4,0.212,36,1
1,124,60,32,0,35.8,0.514,21,0
1,181,78,42,293,40.0,1.258,22,1
1,92,62,25,41,19.5,0.482,25,0
0,152,82,39,272,41.5,0.270,27,0
1,111,62,13,182,24.0,0.138,23,0
3,106,54,21,158,30.9,0.292,24,0
3,174,58,22,194,32.9,0.593,36,1
7,168,88,42,321,38.2,0.787,40,1
6,105,80,28,0,32.5,0.878,26,0
11,138,74,26,144,36.1,0.557,50,1
3,106,72,0,0,25.8,0.207,27,0
6,117,96,0,0,28.7,0.157,30,0
2,68,62,13,15,20.1,0.257,23,0
9,112,82,24,0,28.2,1.282,50,1
0,119,0,0,0,32.4,0.141,24,1
2,112,86,42,160,38.4,0.246,28,0
2,92,76,20,0,24.2,1.698,28,0
6,183,94,0,0,40.8,1.461,45,0
0,94,70,27,115,43.5,0.347,21,0
2,108,64,0,0,30.8,0.158,21,0
4,90,88,47,54,37.7,0.362,29,0
0,125,68,0,0,24.7,0.206,21,0
0,132,78,0,0,32.4,0.393,21,0
5,128,80,0,0,34.6,0.144,45,0
4,94,65,22,0,24.7,0.148,21,0
7,114,64,0,0,27.4,0.732,34,1
0,102,78,40,90,34.5,0.238,24,0
2,111,60,0,0,26.2,0.343,23,0
1,128,82,17,183,27.5,0.115,22,0
10,92,62,0,0,25.9,0.167,31,0
13,104,72,0,0,31.2,0.465,38,1
5,104,74,0,0,28.8,0.153,48,0
2,94,76,18,66,31.6,0.649,23,0
7,97,76,32,91,40.9,0.871,32,1
1,100,74,12,46,19.5,0.149,28,0
0,102,86,17,105,29.3,0.695,27,0
4,128,70,0,0,34.3,0.303,24,0
6,147,80,0,0,29.5,0.178,50,1
4,90,0,0,0,28.0,0.610,31,0
3,103,72,30,152,27.6,0.730,27,0
2,157,74,35,440,39.4,0.134,30,0
1,167,74,17,144,23.4,0.447,33,1
0,179,50,36,159,37.8,0.455,22,1
11,136,84,35,130,28.3,0.260,42,1
0,107,60,25,0,26.4,0.133,23,0
1,91,54,25,100,25.2,0.234,23,0
1,117,60,23,106,33.8,0.466,27,0
5,123,74,40,77,34.1,0.269,28,0
2,120,54,0,0,26.8,0.455,27,0
1,106,70,28,135,34.2,0.142,22,0
2,155,52,27,540,38.7,0.240,25,1
2,101,58,35,90,21.8,0.155,22,0
1,120,80,48,200,38.9,1.162,41,0
11,127,106,0,0,39.0,0.190,51,0
3,80,82,31,70,34.2,1.292,27,1
10,162,84,0,0,27.7,0.182,54,0
1,199,76,43,0,42.9,1.394,22,1
8,167,106,46,231,37.6,0.165,43,1
9,145,80,46,130,37.9,0.637,40,1
6,115,60,39,0,33.7,0.245,40,1
1,112,80,45,132,34.8,0.217,24,0
4,145,82,18,0,32.5,0.235,70,1
10,111,70,27,0,27.5,0.141,40,1
6,98,58,33,190,34.0,0.430,43,0
9,154,78,30,100,30.9,0.164,45,0
6,165,68,26,168,33.6,0.631,49,0
1,99,58,10,0,25.4,0.551,21,0
10,68,106,23,49,35.5,0.285,47,0
3,123,100,35,240,57.3,0.880,22,0
8,91,82,0,0,35.6,0.587,68,0
6,195,70,0,0,30.9,0.328,31,1
9,156,86,0,0,24.8,0.230,53,1
0,93,60,0,0,35.3,0.263,25,0
3,121,52,0,0,36.0,0.127,25,1
2,101,58,17,265,24.2,0.614,23,0
2,56,56,28,45,24.2,0.332,22,0
0,162,76,36,0,49.6,0.364,26,1
0,95,64,39,105,44.6,0.366,22,0
4,125,80,0,0,32.3,0.536,27,1
5,136,82,0,0,0.0,0.640,69,0
2,129,74,26,205,33.2,0.591,25,0
3,130,64,0,0,23.1,0.314,22,0
1,107,50,19,0,28.3,0.181,29,0
1,140,74,26,180,24.1,0.828,23,0
1,144,82,46,180,46.1,0.335,46,1
8,107,80,0,0,24.6,0.856,34,0
13,158,114,0,0,42.3,0.257,44,1
2,121,70,32,95,39.1,0.886,23,0
7,129,68,49,125,38.5,0.439,43,1
2,90,60,0,0,23.5,0.191,25,0
7,142,90,24,480,30.4,0.128,43,1
3,169,74,19,125,29.9,0.268,31,1
0,99,0,0,0,25.0,0.253,22,0
4,127,88,11,155,34.5,0.598,28,0
4,118,70,0,0,44.5,0.904,26,0
2,122,76,27,200,35.9,0.483,26,0
6,125,78,31,0,27.6,0.565,49,1
1,168,88,29,0,35.0,0.905,52,1
2,129,0,0,0,38.5,0.304,41,0
4,110,76,20,100,28.4,0.118,27,0
6,80,80,36,0,39.8,0.177,28,0
10,115,0,0,0,0.0,0.261,30,1
2,127,46,21,335,34.4,0.176,22,0
9,164,78,0,0,32.8,0.148,45,1
2,93,64,32,160,38.0,0.674,23,1
3,158,64,13,387,31.2,0.295,24,0
5,126,78,27,22,29.6,0.439,40,0
10,129,62,36,0,41.2,0.441,38,1
0,134,58,20,291,26.4,0.352,21,0
3,102,74,0,0,29.5,0.121,32,0
7,187,50,33,392,33.9,0.826,34,1
3,173,78,39,185,33.8,0.970,31,1
10,94,72,18,0,23.1,0.595,56,0
1,108,60,46,178,35.5,0.415,24,0
5,97,76,27,0,35.6,0.378,52,1
4,83,86,19,0,29.3,0.317,34,0
1,114,66,36,200,38.1,0.289,21,0
1,149,68,29,127,29.3,0.349,42,1
5,117,86,30,105,39.1,0.251,42,0
1,111,94,0,0,32.8,0.265,45,0
4,112,78,40,0,39.4,0.236,38,0
1,116,78,29,180,36.1,0.496,25,0
0,141,84,26,0,32.4,0.433,22,0
2,175,88,0,0,22.9,0.326,22,0
2,92,52,0,0,30.1,0.141,22,0
3,130,78,23,79,28.4,0.323,34,1
8,120,86,0,0,28.4,0.259,22,1
2,174,88,37,120,44.5,0.646,24,1
2,106,56,27,165,29.0,0.426,22,0
2,105,75,0,0,23.3,0.560,53,0
4,95,60,32,0,35.4,0.284,28,0
0,126,86,27,120,27.4,0.515,21,0
8,65,72,23,0,32.0,0.600,42,0
2,99,60,17,160,36.6,0.453,21,0
1,102,74,0,0,39.5,0.293,42,1
11,120,80,37,150,42.3,0.785,48,1
3,102,44,20,94,30.8,0.400,26,0
1,109,58,18,116,28.5,0.219,22,0
9,140,94,0,0,32.7,0.734,45,1
13,153,88,37,140,40.6,1.174,39,0
12,100,84,33,105,30.0,0.488,46,0
1,147,94,41,0,49.3,0.358,27,1
1,81,74,41,57,46.3,1.096,32,0
3,187,70,22,200,36.4,0.408,36,1
6,162,62,0,0,24.3,0.178,50,1
4,136,70,0,0,31.2,1.182,22,1
1,121,78,39,74,39.0,0.261,28,0
3,108,62,24,0,26.0,0.223,25,0
0,181,88,44,510,43.3,0.222,26,1
8,154,78,32,0,32.4,0.443,45,1
1,128,88,39,110,36.5,1.057,37,1
7,137,90,41,0,32.0,0.391,39,0
0,123,72,0,0,36.3,0.258,52,1
1,106,76,0,0,37.5,0.197,26,0
6,190,92,0,0,35.5,0.278,66,1
2,88,58,26,16,28.4,0.766,22,0
9,170,74,31,0,44.0,0.403,43,1
9,89,62,0,0,22.5,0.142,33,0
10,101,76,48,180,32.9,0.171,63,0
2,122,70,27,0,36.8,0.340,27,0
5,121,72,23,112,26.2,0.245,30,0
1,126,60,0,0,30.1,0.349,47,1
1,93,70,31,0,30.4,0.315,23,0

python实现

#!/usr/bin/python
import sys
import copy
import math
import getopt

def usage():
    print '''Help Information:
    -h, --help: show help information;
    -r, --train: train file;
    -t, --test: test file;
    '''

def getparamenter():
    try:
      opts, args = getopt.getopt(sys.argv[1:], "hr:t:k:", ["help", "train=","test=","kst="])
    except getopt.GetoptError, err:
      print str(err)
      usage()
      sys.exit(1)

    sys.stderr.write("\ntrain.py : a python script for perception training.\n")
    sys.stderr.write("Copyright 2016 sxron, search, Sogou. \n")
    sys.stderr.write("Email: shixiang08abc@gmail.com \n\n")

    train = ''
    test = ''
    for i, f in opts:
      if i in ("-h", "--help"):
        usage()
        sys.exit(1)
      elif i in ("-r", "--train"):
        train = f
      elif i in ("-t", "--test"):
        test = f
      else:
        assert False, "unknown option"
  
    print "start trian parameter \ttrain:%s\ttest:%s" % (train,test)

    return train,test

def loaddata(train):
    datavec = []
    fin = open(train,'r')
    while 1:
        line = fin.readline()
        if not line:
            break
        line = line.strip()
        datavec.append(line)
    fin.close

    return datavec

def separatebyclass(trainvec):
    separated = {}
    for line in trainvec:
        ts = line.strip().split(':')
        if len(ts)!=2:
            continue
        try:
            classify = int(ts[0])
            feas = ts[1].strip().split(' ')
            fea_vec = []
            for i in range(0,len(feas),1):
                score = float(feas[i])
                fea_vec.append(score)
        except:
            continue

        value = []
        if separated.has_key(classify):
            value = separated[classify]
        value.append(fea_vec)
        separated[classify] = value
                
    return separated

def mean(vec):
    sum = 0.0
    for i in range(0,len(vec),1):
        sum = sum + float(vec[i])
    return sum/len(vec)

def stdev(vec):
    avg = mean(vec)
    var = 0.0
    for i in range(0,len(vec),1):
      score = float(vec[i])
      var = var + math.pow(vec[i]-avg,2)
    var = var/(len(vec)-1)
    return math.sqrt(var)

def summarize(value):
    sumValue = []
    for i in range(0,len(value[0]),1):
        vec = []
        resVec = []
        for k in range(0,len(value),1):
            score = float(value[k][i])
            vec.append(score)
        avg = mean(vec)
        var = stdev(vec)
        resVec.append(avg)
        resVec.append(var)
        sumValue.append(resVec)
    return sumValue

def summarizeByClass(classdic):
    sumdic = {}
    for key,value in classdic.items():
        sumdic[key] = summarize(value)
    return sumdic

def calculateProbability(x,avg,var):
    exponent = math.exp(-(math.pow(x-avg,2)/(2*math.pow(var,2))))
    return (1 / (math.sqrt(2*math.pi) * var)) * exponent

def calculateClassProbabilities(testVec,sumDic):
    probabilities = {}
    for classValue,classSummaries in sumDic.items():
        probabily = 1.0
        for i in range(0,len(classSummaries),1):
            avg = float(classSummaries[i][0])
            var = float(classSummaries[i][1])
            x = float(testVec[i])
            probabily = probabily * calculateProbability(x,avg,var)
        probabilities[classValue] = probabily
    return probabilities

def getClass(probabilities):
    prob = sorted(probabilities.iteritems(),key=lambda d:d[1],reverse = True)
    return prob[0][0]

def getPredictions(testvec,sumDic):
    testNum = 0
    rightNum = 0
    for i in range(0,len(testvec),1):
        ts = testvec[i].strip().split(':')
        if len(ts)!=2:
            continue
        try:
            targetClass = int(ts[0])
            feas = ts[1].strip().split(' ')
            feaVec = []
            for i in range(0,len(feas),1):
                score = float(feas[i])
                feaVec.append(score)
        except:
            continue

        testNum += 1
        probabilities = calculateClassProbabilities(feaVec,sumDic)
        if targetClass==getClass(probabilities):
            rightNum += 1
    print 'testNum:%d\trightNum:%d\tratio:%f' % (testNum,rightNum,float(rightNum)/testNum)

def main():
    #set parameter
    train,test = getparamenter()
    trainvec = loaddata(train)
    testvec  =loaddata(test)
    
    #Separate by class
    classdic = separatebyclass(trainvec)

    #feature means and variance for class
    sumDic = summarizeByClass(classdic)

    #prediction
    getPredictions(testvec,sumDic)

if __name__=="__main__":
    main()