@relation weather.symbolic
@attribute outlook {sunny, overcast, rainy}
@attribute temperature {hot, mild, cool}
@attribute humidity {high, normal}
@attribute windy {TRUE, FALSE}
@attribute play {yes, no}
@data
sunny,hot,high,FALSE,no
sunny,hot,high,TRUE,no
overcast,hot,high,FALSE,yes
rainy,mild,high,FALSE,yes
rainy,cool,normal,FALSE,yes
rainy,cool,normal,TRUE,no
overcast,cool,normal,TRUE,yes
sunny,mild,high,FALSE,no
sunny,cool,normal,FALSE,yes
rainy,mild,normal,FALSE,yes
sunny,mild,normal,TRUE,yes
overcast,mild,high,TRUE,yes
overcast,hot,normal,FALSE,yes
rainy,mild,high,TRUE,no
(1)
其中，P(AB)表示事件A和B同时发生的概率；P(A)表示事件A发生的概率；P(B|A)表示在事件A发生的情况下，事件B发生的概率。
独立性假设令x = x1∧x2∧...∧xn 表示一个条件组合，例如：outoutlook=sunny∧temperature=hot∧humidity=high∧windy=FALSE（对应数据集的第一行）。再令表示play=yes/no的事件。假设对于x中每个条件都是独立的，所以：
(2)
各类别的的概率根据式(1)得：
(3)
由于对于每一个都会除以，所以都舍去这一项。对于各类别，哪个概率高测试数据就属于哪个类别，综合式(2)，(3)得：
(4)
并且由于和都属于小数，乘积之后会导致值特别小，所以采用log的方法解决：
(5)
Laplacian平滑由于在求可能会是0，例如在数据集中可以发现在不出去玩时，天气不可能是多云，或出去玩时，温度不可能高。如果在预测的那一天这两个条件都满足，出不出去玩的概率都是0。所以为了解决这种问题就引入Laplacian平滑：
(6)
其中，表示属于类别的个数，表示属性的属性值个数。也需要对平滑：
(7)
其中，表示属性的个数。最终优化目标为：
(8)
代码：
package 日撸Java300行_51_60;
import java.io.FileReader;
import java.util.Arrays;
import weka.core.*;
public class NaiveBayes {
/**
*************************
* An inner class to store parameters.
*************************
*/
private class GaussianParamters {
double mu;
double sigma;
public GaussianParamters(double paraMu, double paraSigma) {
mu = paraMu;
sigma = paraSigma;
}// Of the constructor
public String toString() {
return "(" + mu + ", " + sigma + ")";
}// Of toString
}// Of GaussianParamters
/**
* The data.
*/
Instances dataset;
/**
* The number of classes. For binary classification it is 2.
*/
int numClasses;
/**
* The number of instances.
*/
int numInstances;
/**
* The number of conditional attributes.
*/
int numConditions;
/**
* The prediction, including queried and predicted labels.
*/
int[] predicts;
/**
* Class distribution.
*/
double[] classDistribution;
/**
* Class distribution with Laplacian smooth.
*/
double[] classDistributionLaplacian;
/**
* To calculate the conditional probabilities for all classes over all
* attributes on all values.
*/
double[][][] conditionalCounts;
/**
* The conditional probabilities with Laplacian smooth.
*/
double[][][] conditionalProbabilitiesLaplacian;
/**
* The Guassian parameters.
*/
GaussianParamters[][] gaussianParameters;
/**
* Data type.
*/
int dataType;
/**
* Nominal.
*/
public static final int NOMINAL = 0;
/**
* Numerical.
*/
public static final int NUMERICAL = 1;
/**
********************
* The constructor.
*
* @param paraFilename
* The given file.
********************
*/
public NaiveBayes(String paraFilename) {
dataset = null;
try {
FileReader fileReader = new FileReader(paraFilename);
dataset = new Instances(fileReader);
fileReader.close();
} catch (Exception ee) {
System.out.println("Cannot read the file: " + paraFilename + "\r\n" + ee);
System.exit(0);
} // Of try
dataset.setClassIndex(dataset.numAttributes() - 1);
numConditions = dataset.numAttributes() - 1;
numInstances = dataset.numInstances();
numClasses = dataset.attribute(numConditions).numValues();
}// Of the constructor
/**
********************
* Set the data type.
********************
*/
public void setDataType(int paraDataType) {
dataType = paraDataType;
}// Of setDataType
/**
********************
* Calculate the class distribution with Laplacian smooth.
********************
*/
public void calculateClassDistribution() {
classDistribution = new double[numClasses];
classDistributionLaplacian = new double[numClasses];
double[] tempCounts = new double[numClasses];
for (int i = 0; i < numInstances; i++) {
int tempClassValue = (int) dataset.instance(i).classValue();
tempCounts[tempClassValue]++;
} // Of for i
for (int i = 0; i < numClasses; i++) {
classDistribution[i] = tempCounts[i] / numInstances;
classDistributionLaplacian[i] = (tempCounts[i] + 1) / (numInstances + numClasses);
} // Of for i
System.out.println("Class distribution: " + Arrays.toString(classDistribution));
System.out.println(
"Class distribution Laplacian: " + Arrays.toString(classDistributionLaplacian));
}// Of calculateClassDistribution
/**
********************
* Classify all instances, the results are stored in predicts[].
********************
*/
public void classify() {
predicts = new int[numInstances];
for (int i = 0; i < numInstances; i++) {
predicts[i] = classify(dataset.instance(i));
} // Of for i
}// Of classify
/**
********************
* Classify an instances.
********************
*/
public int classify(Instance paraInstance) {
if (dataType == NOMINAL) {
return classifyNominal(paraInstance);
} else if (dataType == NUMERICAL) {
return classifyNumerical(paraInstance);
} // Of if
return -1;
}// Of classify
/**
********************
* Classify an instances with nominal data.
********************
*/
public int classifyNominal(Instance paraInstance) {
// Find the biggest one
double tempBiggest = -10000;
int resultBestIndex = 0;
for (int i = 0; i < numClasses; i++) {
double tempClassProbabilityLaplacian = Math.log(classDistributionLaplacian[i]);
double tempPseudoProbability = tempClassProbabilityLaplacian;
for (int j = 0; j < numConditions; j++) {
int tempAttributeValue = (int) paraInstance.value(j);
// Laplacian smooth.
tempPseudoProbability += Math.log(conditionalCounts[i][j][tempAttributeValue])
- tempClassProbabilityLaplacian;
} // Of for j
if (tempBiggest < tempPseudoProbability) {
tempBiggest = tempPseudoProbability;
resultBestIndex = i;
} // Of if
} // Of for i
return resultBestIndex;
}// Of classifyNominal
/**
********************
* Compute accuracy.
********************
*/
public double computeAccuracy() {
double tempCorrect = 0;
for (int i = 0; i < numInstances; i++) {
if (predicts[i] == (int) dataset.instance(i).classValue()) {
tempCorrect++;
} // Of if
} // Of for i
double resultAccuracy = tempCorrect / numInstances;
return resultAccuracy;
}// Of computeAccuracy
/**
*************************
* Test nominal data.
*************************
*/
public static void testNominal() {
System.out.println("Hello, Naive Bayes. I only want to test the nominal data.");
String tempFilename = "D:/data/weather.arff";
NaiveBayes tempLearner = new NaiveBayes(tempFilename);
tempLearner.setDataType(NOMINAL);
tempLearner.calculateClassDistribution();
tempLearner.calculateConditionalProbabilities();
tempLearner.classify();
System.out.println("The accuracy is: " + tempLearner.computeAccuracy());
}// Of testNominal
/**
*************************
* Test this class.
*
* @param args
* Not used now.
*************************
*/
public static void main(String[] args) {
testNominal();
}// Of main
}// Of class NaiveBayes
截图：
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