貝葉斯核心
選擇具有最高概率的決策是貝葉斯決策理論的核心。
貝葉斯使用
通過已知3個(gè)概率來計(jì)算位置的概率
特征數(shù)量與樣本關(guān)系
通常如果有t個(gè)特征仅讽，每個(gè)特征需要N個(gè)樣本白华，那么就需要個(gè)總樣本數(shù)媳板。
如果特征之間獨(dú)立，那么樣本數(shù)從降到N x t
樸素貝葉斯的假設(shè)
- 1捌朴、 特征之間相互獨(dú)立
- 2、 每個(gè)特征同等重要
代碼
import numpy as np
def loadDataSet():
# 切分的詞條
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']]
# 類別標(biāo)簽向量张抄，1代表侮辱性詞匯砂蔽，0代表不是
classVec = [0, 1, 0, 1, 0, 1]
# 返回實(shí)驗(yàn)樣本切分的詞條、類別標(biāo)簽向量
return postingList, classVec
def createVocabList(dataSet):
# 創(chuàng)建一個(gè)空的不重復(fù)列表
# set是一個(gè)無序且不重復(fù)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):
# 創(chuàng)建一個(gè)其中所含元素都為0的向量
returnVec = [0] * len(vocabList)
# 遍歷每個(gè)詞條
for word in inputSet:
if word in vocabList:
# 如果詞條存在于詞匯表中署惯，則置1
# index返回word出現(xiàn)在vocabList中的索引
# 若這里改為+=則就是基于詞袋的模型左驾，遇到一個(gè)單詞會(huì)增加單詞向量中德對應(yīng)值
returnVec[vocabList.index(word)] = 1
else:
print("the word: %s is not in my Vocabulary" % word)
# 返回文檔向量
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):
# 計(jì)算訓(xùn)練文檔數(shù)目
numTrainDocs = len(trainMatrix)
# 計(jì)算每篇文檔的詞條數(shù)目
numWords = len(trainMatrix[0])
# 文檔屬于侮辱類的概率
pAbusive = sum(trainCategory)/float(numTrainDocs)
# 創(chuàng)建numpy.zeros數(shù)組，詞條出現(xiàn)數(shù)初始化為0
# p0Num = np.zeros(numWords)
# p1Num = np.zeros(numWords)
# 創(chuàng)建numpy.ones數(shù)組极谊，詞條出現(xiàn)數(shù)初始化為1,拉普拉斯平滑
p0Num = np.ones(numWords)
p1Num = np.ones(numWords)
# 分母初始化為0
# p0Denom = 0.0
# p1Denom = 0.0
# 分母初始化為2诡右，拉普拉斯平滑
p0Denom = 2.0
p1Denom = 2.0
for i in range(numTrainDocs):
# 統(tǒng)計(jì)屬于侮辱類的條件概率所需的數(shù)據(jù)，即P(w0|1),P(w1|1),P(w2|1)...
if trainCategory[i] == 1:
# 統(tǒng)計(jì)所有侮辱類文檔中每個(gè)單詞出現(xiàn)的個(gè)數(shù)
p1Num += trainMatrix[i]
# 統(tǒng)計(jì)一共出現(xiàn)的侮辱單詞的個(gè)數(shù)
p1Denom += sum(trainMatrix[i])
# 統(tǒng)計(jì)屬于非侮辱類的條件概率所需的數(shù)據(jù)轻猖，即P(w0|0),P(w1|0),P(w2|0)...
else:
# 統(tǒng)計(jì)所有非侮辱類文檔中每個(gè)單詞出現(xiàn)的個(gè)數(shù)
p0Num += trainMatrix[i]
# 統(tǒng)計(jì)一共出現(xiàn)的非侮辱單詞的個(gè)數(shù)
p0Denom += sum(trainMatrix[i])
# 每個(gè)侮辱類單詞分別出現(xiàn)的概率
# p1Vect = p1Num / p1Denom
# 取對數(shù)帆吻，防止下溢出
p1Vect = np.log(p1Num / p1Denom)
# 每個(gè)非侮辱類單詞分別出現(xiàn)的概率
# p0Vect = p0Num / p0Denom
# 取對數(shù)，防止下溢出
p0Vect = np.log(p0Num / p0Denom)
# 返回屬于侮辱類的條件概率數(shù)組咙边、屬于非侮辱類的條件概率數(shù)組猜煮、文檔屬于侮辱類的概率
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):
# 對應(yīng)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)
# 對應(yīng)元素相乘，logA*B = logA + logB所以這里是累加
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():
# 創(chuàng)建實(shí)驗(yàn)樣本
listOPosts, listclasses = loadDataSet()
# 創(chuàng)建詞匯表,將輸入文本中的不重復(fù)的單詞進(jìn)行提取組成單詞向量
myVocabList = createVocabList(listOPosts)
trainMat = []
for postinDoc in listOPosts:
# 將實(shí)驗(yàn)樣本向量化若postinDoc中的單詞在myVocabList出現(xiàn)則將returnVec該位置的索引置1
# 將6組數(shù)據(jù)list存儲(chǔ)在trainMat中
trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
# 訓(xùn)練樸素貝葉斯分類器
p0V, p1V, pAb = trainNB0(np.array(trainMat), np.array(listclasses))
# 測試樣本1
testEntry = ['love', 'my', 'dalmation']
# 測試樣本向量化返回這三個(gè)單詞出現(xiàn)位置的索引
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于侮辱類')
else:
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于非侮辱類')
# 測試樣本2
testEntry = ['stupid', 'garbage']
# 將實(shí)驗(yàn)樣本向量化
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于侮辱類')
else:
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于非侮辱類')
testEntry = [ 'my','love','dalmation','stupid', 'garbage']
# 將實(shí)驗(yàn)樣本向量化
thisDoc = np.array(setOfWords2Vec(myVocabList, testEntry))
if classifyNB(thisDoc, p0V, p1V, pAb):
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于侮辱類')
else:
# 執(zhí)行分類并打印結(jié)果
print(testEntry, '屬于非侮辱類')
testingNB()
-7.694848072384611 -9.826714493730215
['love', 'my', 'dalmation'] 屬于非侮辱類
-7.20934025660291 -4.702750514326955
['stupid', 'garbage'] 屬于侮辱類
-14.211041148427574 -13.836317827497224
['my', 'love', 'dalmation', 'stupid', 'garbage'] 屬于侮辱類
# 創(chuàng)建實(shí)驗(yàn)樣本
listOPosts, listclasses = loadDataSet()
# 創(chuàng)建詞匯表,將輸入文本中的不重復(fù)的單詞進(jìn)行提取組成單詞向量
myVocabList = createVocabList(listOPosts)
trainMat = []
for postinDoc in listOPosts:
# 將實(shí)驗(yàn)樣本向量化若postinDoc中的單詞在myVocabList出現(xiàn)則將returnVec該位置的索引置1
# 將6組數(shù)據(jù)list存儲(chǔ)在trainMat中
trainMat.append(setOfWords2Vec(myVocabList, postinDoc))
# 訓(xùn)練樸素貝葉斯分類器
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'] 屬于非侮辱類
-7.20934025660291 -4.702750514326955
['stupid', 'garbage'] 屬于侮辱類
-9.774289614064447 -7.747272952050379
['love', 'stupid', 'garbage'] 屬于侮辱類
相關(guān)資料
英語的統(tǒng)計(jì)數(shù)字驚人败许。在世界上所有的語言（目前已達(dá)2700種）中王带，可以說是最豐富的詞匯。簡明的牛津英語詞典列出了大約500,000個(gè)單詞檐束；另有50萬個(gè)技術(shù)和科學(xué)術(shù)語尚未列入目錄辫秧。
根據(jù)傳統(tǒng)的估計(jì)，德語詞匯量約為185,000被丧，而法語的詞匯量則少于100,000盟戏。
