weka: naive bayes
m_NumClasses???????????????訓練數據中類的個數
m_NumAttributes??????????? 屬性的個數
m_Instances?????????????????? 訓練數據
m_ClassDistribution????????類的概率分布, 即P(C)。 其類型是Estimator, 估值器
m_Distributions[m_NumAttributes][m_NumClasses]? 每個屬性在每個類中的概率分布。 其類型也是Estimator。
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1) 數值類型要用連續分布的Estimator, 如NormalEstimator
2) 名詞性類型, 如(少年人、中年人、老年人), 需要離散化, 如DiscreteEstimator
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然后增量式的訓練。
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針對每個樣本, 修改m_Distributions[m_NumAttributes][m_NumClasses], 以及 m_ClassDistribution
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識別時, 通過調用函數 distributionForInstance, 該函數返回正規化的一組值, 表示該待測樣本在每個類中的概率
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public void updateClassifier(Instance instance) throws Exception {if (!instance.classIsMissing()) {Enumeration enumAtts = m_Instances.enumerateAttributes();int attIndex = 0;while (enumAtts.hasMoreElements()) {Attribute attribute = (Attribute) enumAtts.nextElement();if (!instance.isMissing(attribute)) {m_Distributions[attIndex][(int)instance.classValue()].addValue(instance.value(attribute), instance.weight());}attIndex++;}m_ClassDistribution.addValue(instance.classValue(),instance.weight());}}
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核心是? Estimator, 如NormalEstimator
//data表示屬性的值, weight表示該屬性值所在樣本的樣本權重 public void addValue(double data, double weight) {if (weight == 0) {return;}data = round(data);m_SumOfWeights += weight;m_SumOfValues += data * weight;m_SumOfValuesSq += data * data * weight;if (m_SumOfWeights > 0) {m_Mean = m_SumOfValues / m_SumOfWeights;double stdDev = Math.sqrt(Math.abs(m_SumOfValuesSq - m_Mean * m_SumOfValues) / m_SumOfWeights);// If the stdDev ~= 0, we really have no idea of scale yet, // so stick with the default. Otherwise...if (stdDev > 1e-10) {m_StandardDev = Math.max(m_Precision / (2 * 3), // allow at most 3sd's within one interval stdDev);}}}/*** Get a probability estimate for a value** @param data the value to estimate the probability of* @return the estimated probability of the supplied value*///計算該屬性的值為data的概率public double getProbability(double data) {data = round(data);double zLower = (data - m_Mean - (m_Precision / 2)) / m_StandardDev;double zUpper = (data - m_Mean + (m_Precision / 2)) / m_StandardDev;double pLower = Statistics.normalProbability(zLower);double pUpper = Statistics.normalProbability(zUpper);return pUpper - pLower;}
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對應到bogofilter的bayes,
類個數為2; 屬性個數就是token的個數
Estimator就是簡單的計數
訓練時,
掃描待訓練郵件的逐個token,增加其在對應類別中的計數===>m_Distributions;
增加對應類別的樣本數====> m_ClassDistribution
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分類時,
1)得到各個類的先驗概率??????????????????????????? P(C)
2)乘以該屬性在該類中出現的概率??????????????? P(D|C), D為待測文檔,D由一組token組成
P(C|D) = P(C) *P(D|C)/P(D); 其中P(D)不必求,都一樣, 只需要求出P(C)*P(D|C)即可
其中, P(D|C) = P(t1|C)*,,,*P(tn|C)........條件獨立。 只需要 P(ti|C) 與 P(tj|C) 獨立即可。 因此是條件獨立
總結
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