Spark MLlib 之 Naive Bayes
1、前言:
Naive Bayes(朴素贝叶斯)是一个简单的多类分类算法,该算法的前提是假设各特征之间是相互独立的。Naive Bayes 训练主要是为每一个特征,在给定的标签的条件下,计算每个特征在该标签的条件下的条件概率。最后用这个训练后的条件概率去预测。
由于我使用的Spark的版本是1.3.0。它所包含的Naive Bayes是 Multinomial NB。截至到我写该篇文章,最新的Spark1.6.0包含multinomial naive Bayes and Bernoulli naive Bayes。不管他们支持什么样的贝叶斯,我们知道贝叶斯算法一般应用于文档分类。
2、贝叶斯的应用
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。通俗来说,就好比这么个道理,你在街 上看到一个黑人,我问你你猜这哥们哪里来的,你十有八九猜非洲。为什么呢?因为黑人中非洲人的比率最高,当然人家也可能是美洲人或亚洲人,但在没有其它可 用信息下,我们会选择条件概率最大的类别,这就是朴素贝叶斯的思想基础。
3、贝叶斯的原理
朴素贝叶斯分类的正式定义如下:
(1)、设aaarticlea/png;base64,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" alt="" />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aaarticlea/png;base64,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" alt="" />。
(3)、计算aaarticlea/png;base64,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" alt="" />。
(4)、如果aaarticlea/png;base64,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" alt="" />,则aaarticlea/png;base64,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" alt="" />。
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
aaarticlea/png;base64,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" alt="" />
(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:
aaarticlea/png;base64,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" alt="" />
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:
aaarticlea/png;base64,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" alt="" />
根据上述分析,朴素贝叶斯分类的流程可以由下图表示(暂时不考虑验证):
aaarticlea/png;base64,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" 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可以看到,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、贝叶斯的模型
贝叶斯分类器是一个有监督的机器学习方法,一般应用文档分类,常见的有两种模型:多项式模型和伯努利模型,这两种模型的主要区别是计算条件概率的粒度不一样。多项式模型是以文档中单词为粒度,伯努利模型是以文档为粒度。
(1)多项式模型(词频型)
多项式模型是以“单词”为统计单位,即统计某个单词在文档中出现的次数,当某个特征词在某个文档中出现多次,多项式模型会计算多次。这个模型符合NLP的做法。其基本原理如下:
在多项式模型中, 设某文档d=(t1,t2,…,tk),tk是该文档中出现过的单词,允许重复,则
先验概率P(c)= 类c下单词总数/整个训练样本的单词总数
类条件概率P(tk|c)=(类c下单词tk在各个文档中出现过的次数之和+1)/(类c下单词总数+|V|)
V是训练样本的单词表(即抽取单词,单词出现多次,只算一个),|V|则表示训练样本包含多少种单词。
P(tk|c)可以看作是单词tk在证明d属于类c上提供了多大的证据,而P(c)则可以认为是类别c在整体上占多大比例(有多大可能性)。
(2)伯努利模型(文档型)
伯努利模型是以“文档”为统计单位,即统计某个特征词出现在多少个文档当中,若某个特征词在某个文档中出现了多次,那么伯努利模型只是计算一次。
P(c)= 类c下文件总数/整个训练样本的文件总数
P(tk|c)=(类c下包含单词tk的文件数+1)/(类c下文件总数+2)
备注:P(tk|c) 中的(类c下文件总数+2) 不是网上流传的(类c下单词总数+2)。
(3)高斯模型
当一些特征是连续性的值时,就可以采用高斯模型,一般是假设特征的分布是高斯分布。
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4、Example
val conf = new SparkConf().setAppName("Simple Application").setMaster("local")
val sc = new SparkContext(conf)
//这个输入数据要注意格式
val data = sc.textFile("data/mllib/sample_naive_bayes_data.txt")
val parsedData = data.map { line =>
val parts = line.split(',')
LabeledPoint(parts(0).toDouble, Vectors.dense(parts(1).split(' ').map(_.toDouble)))
}
// Split data into training (60%) and test (40%).
val splits = parsedData.randomSplit(Array(0.6, 0.4), seed = 11L)
val training = splits(0)
val test = splits(1)
//This is the Multinomial NB
val model = NaiveBayes.train(training, lambda=1.0)//(training, lambda = 1.0, modelType = "multinomial") val predictionAndLabel = test.map(p => (model.predict(p.features), p.label))
val accuracy = 1.0 * predictionAndLabel.filter(x => x._1 == x._2).count() / test.count() // Save and load model
model.save(sc, "myModelPath")
val sameModel = NaiveBayesModel.load(sc, "myModelPath") sc.stop()
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