贝叶斯核心
选择具有最高概率的决策是贝叶斯决策理论的核心。
贝叶斯使用
通过已知3个概率来计算位置的概率
特征数量与样本关系
通常如果有t个特征，每个特征需要N个样本，那么就需要个总样本数。
如果特征之间独立，那么样本数从降到N x t
朴素贝叶斯的假设
- 1、 特征之间相互独立
- 2、 每个特征同等重要
代码
import numpy as np
def loadDataSet():
# 切分的词条
postingList = [['my', 'dog', 'has', 'flea', 'problems', 'help', 'please'],
['maybe', 'not', 'take', 'him', 'to', 'dog', 'park', 'stupid'],
['my', 'dalmation', 'is', 'so', 'cute', 'I', 'love', 'him'],
['stop', 'posting', 'stupid', 'worthless', 'garbage'],
['mr', 'licks', 'ate', 'my', 'steak', 'how', 'to', 'stop', 'him'],
['quit', 'buying', 'worthless', 'dog', 'food', 'stupid']]
# 类别标签向量，1代表侮辱性词汇，0代表不是
classVec = [0, 1, 0, 1, 0, 1]
# 返回实验样本切分的词条、类别标签向量
return postingList, classVec
def createVocabList(dataSet):
# 创建一个空的不重复列表
# set是一个无序且不重复的元素集合
vocabSet = set([])
for document in dataSet:
# 取并集
vocabSet = vocabSet | set(document)
return list(vocabSet)
def setOfWords2Vec(vocabList, inputSet):
# 创建一个其中所含元素都为0的向量
returnVec = [0] * len(vocabList)
# 遍历每个词条
for word in inputSet:
if word in vocabList:
# 如果词条存在于词汇表中，则置1
# index返回word出现在vocabList中的索引
# 若这里改为+=则就是基于词袋的模型，遇到一个单词会增加单词向量中德对应值
returnVec[vocabList.index(word)] = 1
else:
print("the word: %s is not in my Vocabulary" % word)
# 返回文档向量
return returnVec
listOposts,listClasses = loadDataSet()
listOposts
[['my', 'dog', 'has', 'flea', 'problems', 'help', 'please'],
['maybe', 'not', 'take', 'him', 'to', 'dog', 'park', 'stupid'],
['my', 'dalmation', 'is', 'so', 'cute', 'I', 'love', 'him'],
['stop', 'posting', 'stupid', 'worthless', 'garbage'],
['mr', 'licks', 'ate', 'my', 'steak', 'how', 'to', 'stop', 'him'],
['quit', 'buying', 'worthless', 'dog', 'food', 'stupid']]
myVocabList = createVocabList(listOposts)
myVocabList
setOfWords2Vec(myVocabList,listOposts[0])
def trainNB0(trainMatrix, trainCategory):
# 计算训练文档数目
numTrainDocs = len(trainMatrix)
# 计算每篇文档的词条数目
numWords = len(trainMatrix[0])
# 文档属于侮辱类的概率
pAbusive = sum(trainCategory)/float(numTrainDocs)
# 创建numpy.zeros数组，词条出现数初始化为0
# p0Num = np.zeros(numWords)
# p1Num = np.zeros(numWords)
# 创建numpy.ones数组，词条出现数初始化为1,拉普拉斯平滑
p0Num = np.ones(numWords)
p1Num = np.ones(numWords)
# 分母初始化为0
# p0Denom = 0.0
# p1Denom = 0.0
# 分母初始化为2，拉普拉斯平滑
p0Denom = 2.0
p1Denom = 2.0
for i in range(numTrainDocs):
# 统计属于侮辱类的条件概率所需的数据，即P(w0|1),P(w1|1),P(w2|1)...
if trainCategory[i] == 1:
# 统计所有侮辱类文档中每个单词出现的个数
p1Num += trainMatrix[i]
# 统计一共出现的侮辱单词的个数
p1Denom += sum(trainMatrix[i])
# 统计属于非侮辱类的条件概率所需的数据，即P(w0|0),P(w1|0),P(w2|0)...
else:
# 统计所有非侮辱类文档中每个单词出现的个数
p0Num += trainMatrix[i]
# 统计一共出现的非侮辱单词的个数
p0Denom += sum(trainMatrix[i])
# 每个侮辱类单词分别出现的概率
# p1Vect = p1Num / p1Denom
# 取对数，防止下溢出
p1Vect = np.log(p1Num / p1Denom)
# 每个非侮辱类单词分别出现的概率
# p0Vect = p0Num / p0Denom
# 取对数，防止下溢出
p0Vect = np.log(p0Num / p0Denom)
# 返回属于侮辱类的条件概率数组、属于非侮辱类的条件概率数组、文档属于侮辱类的概率
return p0Vect, p1Vect, pAbusive
trainMat = []
for postinDoc in listOposts:
trainMat.append(setOfWords2Vec(myVocabList,postinDoc))
p0V,p1V,pAb = trainNB0(trainMat,listClasses)
pAb
0.5
p0V
array([-2.56494936, -2.56494936, -1.87180218, -3.25809654, -3.25809654,
-2.15948425, -2.56494936, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -3.25809654, -2.56494936, -2.56494936, -2.56494936,
-3.25809654, -3.25809654, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -3.25809654, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -2.56494936, -3.25809654, -3.25809654, -2.56494936,
-2.56494936, -2.56494936])
len(p0V)
32
len(myVocabList)
32
p1V
array([-3.04452244, -3.04452244, -3.04452244, -2.35137526, -2.35137526,
-2.35137526, -3.04452244, -3.04452244, -3.04452244, -2.35137526,
-3.04452244, -2.35137526, -2.35137526, -3.04452244, -3.04452244,
-2.35137526, -1.65822808, -3.04452244, -3.04452244, -2.35137526,
-2.35137526, -2.35137526, -3.04452244, -3.04452244, -2.35137526,
-3.04452244, -3.04452244, -1.94591015, -2.35137526, -3.04452244,
-1.94591015, -3.04452244])
def classifyNB(vec2Classify, p0Vec, p1Vec, pClass1):
# 对应元素相乘
# p1 = reduce(lambda x,y:x*y, vec2Classify * p1Vec) * pClass1
# p0 = reduce(lambda x,y:x*y, vec2Classify * p0Vec) * (1.0 - pClass1)
# 对应元素相乘，logA*B = logA + logB所以这里是累加
p1 = sum(vec2Classify * p1Vec) + np.log(pClass1)
p0 = sum(vec2Classify * p0Vec) + np.log(1.0 - pClass1)
print(p0,p1)
# print('p0:', p0)
# print('p1:', p1)
if p1 > p0:
return 1
else:
return 0
def testingNB():
# 创建实验样本
listOPosts, listclasses = loadDataSet()
# 创建词汇表,将输入文本中的不重复的单词进行提取组成单词向量
myVocabList = createVocabList(listOPosts)
trainMat = []
for postinDoc in listOPosts:
# 将实验样本向量化若postinDoc中的单词在myVocabList出现则将returnVec该位置的索引置1
# 将6组数据list存储在trainMat中
trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
# 训练朴素贝叶斯分类器
p0V, p1V, pAb = trainNB0(np.array(trainMat), np.array(listclasses))
# 测试样本1
testEntry = ['love', 'my', 'dalmation']
# 测试样本向量化返回这三个单词出现位置的索引
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 执行分类并打印结果
print(testEntry, '属于侮辱类')
else:
# 执行分类并打印结果
print(testEntry, '属于非侮辱类')
# 测试样本2
testEntry = ['stupid', 'garbage']
# 将实验样本向量化
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 执行分类并打印结果
print(testEntry, '属于侮辱类')
else:
# 执行分类并打印结果
print(testEntry, '属于非侮辱类')
testEntry = [ 'my','love','dalmation','stupid', 'garbage']
# 将实验样本向量化
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 执行分类并打印结果
print(testEntry, '属于侮辱类')
else:
# 执行分类并打印结果
print(testEntry, '属于非侮辱类')
testingNB()
-7.694848072384611 -9.826714493730215
['love', 'my', 'dalmation'] 属于非侮辱类
-7.20934025660291 -4.702750514326955
['stupid', 'garbage'] 属于侮辱类
-14.211041148427574 -13.836317827497224
['my', 'love', 'dalmation', 'stupid', 'garbage'] 属于侮辱类
# 创建实验样本
listOPosts, listclasses = loadDataSet()
# 创建词汇表,将输入文本中的不重复的单词进行提取组成单词向量
myVocabList = createVocabList(listOPosts)
trainMat = []
for postinDoc in listOPosts:
# 将实验样本向量化若postinDoc中的单词在myVocabList出现则将returnVec该位置的索引置1
# 将6组数据list存储在trainMat中
trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
# 训练朴素贝叶斯分类器
p0V, p1V, pAb = trainNB0(np.array(trainMat), np.array(listclasses))
testEntry = ['love', 'my', 'dalmation']
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
thisDoc
array([0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0])
p0V
array([-2.56494936, -2.56494936, -1.87180218, -3.25809654, -3.25809654,
-2.15948425, -2.56494936, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -3.25809654, -2.56494936, -2.56494936, -2.56494936,
-3.25809654, -3.25809654, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -3.25809654, -2.56494936, -2.56494936, -3.25809654,
-2.56494936, -2.56494936, -3.25809654, -3.25809654, -2.56494936,
-2.56494936, -2.56494936])
vec2Classify = thisDoc
p0Vec =p0V
p1Vec =p1V
pClass1 =pAb
vec2Classify * p1Vec
array([-0. , -0. , -3.04452244, -0. , -0. ,
-0. , -0. , -0. , -0. , -0. ,
-3.04452244, -0. , -0. , -0. , -0. ,
-0. , -0. , -0. , -0. , -0. ,
-0. , -0. , -0. , -0. , -0. ,
-0. , -0. , -0. , -0. , -3.04452244,
-0. , -0. ])
testingNB()
-7.694848072384611 -9.826714493730215
['love', 'my', 'dalmation'] 属于非侮辱类
-7.20934025660291 -4.702750514326955
['stupid', 'garbage'] 属于侮辱类
-9.774289614064447 -7.747272952050379
['love', 'stupid', 'garbage'] 属于侮辱类
相关资料
英语的统计数字惊人。在世界上所有的语言（目前已达2700种）中，可以说是最丰富的词汇。简明的牛津英语词典列出了大约500,000个单词；另有50万个技术和科学术语尚未列入目录。
根据传统的估计，德语词汇量约为185,000，而法语的词汇量则少于100,000。
- https://hypertextbook.com/facts/2001/JohnnyLing.shtml