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数值型数据的 NB 算法

code • 2022-5-16 • java • 阅读 45

数值型数据的 NB 算法,第1张

学习来源：日撸 Java 三百行（51-60天，kNN 与 NB）

第 59 天: 数值型数据的 NB 算法

前面学习了符号型数据的 NB 算法，今天学习的是数值型数据的 NB 算法。
数据集：

@RELATION iris

@ATTRIBUTE sepallength	REAL
@ATTRIBUTE sepalwidth 	REAL
@ATTRIBUTE petallength 	REAL
@ATTRIBUTE petalwidth	REAL
@ATTRIBUTE class 	{Iris-setosa,Iris-versicolor,Iris-virginica}

@DATA
5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.0,1.4,0.2,Iris-setosa
4.7,3.2,1.3,0.2,Iris-setosa
4.6,3.1,1.5,0.2,Iris-setosa
5.0,3.6,1.4,0.2,Iris-setosa
5.4,3.9,1.7,0.4,Iris-setosa
4.6,3.4,1.4,0.3,Iris-setosa
5.0,3.4,1.5,0.2,Iris-setosa
4.4,2.9,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.4,3.7,1.5,0.2,Iris-setosa
4.8,3.4,1.6,0.2,Iris-setosa
4.8,3.0,1.4,0.1,Iris-setosa
4.3,3.0,1.1,0.1,Iris-setosa
5.8,4.0,1.2,0.2,Iris-setosa
5.7,4.4,1.5,0.4,Iris-setosa
5.4,3.9,1.3,0.4,Iris-setosa
5.1,3.5,1.4,0.3,Iris-setosa
5.7,3.8,1.7,0.3,Iris-setosa
5.1,3.8,1.5,0.3,Iris-setosa
5.4,3.4,1.7,0.2,Iris-setosa
5.1,3.7,1.5,0.4,Iris-setosa
4.6,3.6,1.0,0.2,Iris-setosa
5.1,3.3,1.7,0.5,Iris-setosa
4.8,3.4,1.9,0.2,Iris-setosa
5.0,3.0,1.6,0.2,Iris-setosa
5.0,3.4,1.6,0.4,Iris-setosa
5.2,3.5,1.5,0.2,Iris-setosa
5.2,3.4,1.4,0.2,Iris-setosa
4.7,3.2,1.6,0.2,Iris-setosa
4.8,3.1,1.6,0.2,Iris-setosa
5.4,3.4,1.5,0.4,Iris-setosa
5.2,4.1,1.5,0.1,Iris-setosa
5.5,4.2,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
5.0,3.2,1.2,0.2,Iris-setosa
5.5,3.5,1.3,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
4.4,3.0,1.3,0.2,Iris-setosa
5.1,3.4,1.5,0.2,Iris-setosa
5.0,3.5,1.3,0.3,Iris-setosa
4.5,2.3,1.3,0.3,Iris-setosa
4.4,3.2,1.3,0.2,Iris-setosa
5.0,3.5,1.6,0.6,Iris-setosa
5.1,3.8,1.9,0.4,Iris-setosa
4.8,3.0,1.4,0.3,Iris-setosa
5.1,3.8,1.6,0.2,Iris-setosa
4.6,3.2,1.4,0.2,Iris-setosa
5.3,3.7,1.5,0.2,Iris-setosa
5.0,3.3,1.4,0.2,Iris-setosa
7.0,3.2,4.7,1.4,Iris-versicolor
6.4,3.2,4.5,1.5,Iris-versicolor
6.9,3.1,4.9,1.5,Iris-versicolor
5.5,2.3,4.0,1.3,Iris-versicolor
6.5,2.8,4.6,1.5,Iris-versicolor
5.7,2.8,4.5,1.3,Iris-versicolor
6.3,3.3,4.7,1.6,Iris-versicolor
4.9,2.4,3.3,1.0,Iris-versicolor
6.6,2.9,4.6,1.3,Iris-versicolor
5.2,2.7,3.9,1.4,Iris-versicolor
5.0,2.0,3.5,1.0,Iris-versicolor
5.9,3.0,4.2,1.5,Iris-versicolor
6.0,2.2,4.0,1.0,Iris-versicolor
6.1,2.9,4.7,1.4,Iris-versicolor
5.6,2.9,3.6,1.3,Iris-versicolor
6.7,3.1,4.4,1.4,Iris-versicolor
5.6,3.0,4.5,1.5,Iris-versicolor
5.8,2.7,4.1,1.0,Iris-versicolor
6.2,2.2,4.5,1.5,Iris-versicolor
5.6,2.5,3.9,1.1,Iris-versicolor
5.9,3.2,4.8,1.8,Iris-versicolor
6.1,2.8,4.0,1.3,Iris-versicolor
6.3,2.5,4.9,1.5,Iris-versicolor
6.1,2.8,4.7,1.2,Iris-versicolor
6.4,2.9,4.3,1.3,Iris-versicolor
6.6,3.0,4.4,1.4,Iris-versicolor
6.8,2.8,4.8,1.4,Iris-versicolor
6.7,3.0,5.0,1.7,Iris-versicolor
6.0,2.9,4.5,1.5,Iris-versicolor
5.7,2.6,3.5,1.0,Iris-versicolor
5.5,2.4,3.8,1.1,Iris-versicolor
5.5,2.4,3.7,1.0,Iris-versicolor
5.8,2.7,3.9,1.2,Iris-versicolor
6.0,2.7,5.1,1.6,Iris-versicolor
5.4,3.0,4.5,1.5,Iris-versicolor
6.0,3.4,4.5,1.6,Iris-versicolor
6.7,3.1,4.7,1.5,Iris-versicolor
6.3,2.3,4.4,1.3,Iris-versicolor
5.6,3.0,4.1,1.3,Iris-versicolor
5.5,2.5,4.0,1.3,Iris-versicolor
5.5,2.6,4.4,1.2,Iris-versicolor
6.1,3.0,4.6,1.4,Iris-versicolor
5.8,2.6,4.0,1.2,Iris-versicolor
5.0,2.3,3.3,1.0,Iris-versicolor
5.6,2.7,4.2,1.3,Iris-versicolor
5.7,3.0,4.2,1.2,Iris-versicolor
5.7,2.9,4.2,1.3,Iris-versicolor
6.2,2.9,4.3,1.3,Iris-versicolor
5.1,2.5,3.0,1.1,Iris-versicolor
5.7,2.8,4.1,1.3,Iris-versicolor
6.3,3.3,6.0,2.5,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
7.1,3.0,5.9,2.1,Iris-virginica
6.3,2.9,5.6,1.8,Iris-virginica
6.5,3.0,5.8,2.2,Iris-virginica
7.6,3.0,6.6,2.1,Iris-virginica
4.9,2.5,4.5,1.7,Iris-virginica
7.3,2.9,6.3,1.8,Iris-virginica
6.7,2.5,5.8,1.8,Iris-virginica
7.2,3.6,6.1,2.5,Iris-virginica
6.5,3.2,5.1,2.0,Iris-virginica
6.4,2.7,5.3,1.9,Iris-virginica
6.8,3.0,5.5,2.1,Iris-virginica
5.7,2.5,5.0,2.0,Iris-virginica
5.8,2.8,5.1,2.4,Iris-virginica
6.4,3.2,5.3,2.3,Iris-virginica
6.5,3.0,5.5,1.8,Iris-virginica
7.7,3.8,6.7,2.2,Iris-virginica
7.7,2.6,6.9,2.3,Iris-virginica
6.0,2.2,5.0,1.5,Iris-virginica
6.9,3.2,5.7,2.3,Iris-virginica
5.6,2.8,4.9,2.0,Iris-virginica
7.7,2.8,6.7,2.0,Iris-virginica
6.3,2.7,4.9,1.8,Iris-virginica
6.7,3.3,5.7,2.1,Iris-virginica
7.2,3.2,6.0,1.8,Iris-virginica
6.2,2.8,4.8,1.8,Iris-virginica
6.1,3.0,4.9,1.8,Iris-virginica
6.4,2.8,5.6,2.1,Iris-virginica
7.2,3.0,5.8,1.6,Iris-virginica
7.4,2.8,6.1,1.9,Iris-virginica
7.9,3.8,6.4,2.0,Iris-virginica
6.4,2.8,5.6,2.2,Iris-virginica
6.3,2.8,5.1,1.5,Iris-virginica
6.1,2.6,5.6,1.4,Iris-virginica
7.7,3.0,6.1,2.3,Iris-virginica
6.3,3.4,5.6,2.4,Iris-virginica
6.4,3.1,5.5,1.8,Iris-virginica
6.0,3.0,4.8,1.8,Iris-virginica
6.9,3.1,5.4,2.1,Iris-virginica
6.7,3.1,5.6,2.4,Iris-virginica
6.9,3.1,5.1,2.3,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
6.8,3.2,5.9,2.3,Iris-virginica
6.7,3.3,5.7,2.5,Iris-virginica
6.7,3.0,5.2,2.3,Iris-virginica
6.3,2.5,5.0,1.9,Iris-virginica
6.5,3.0,5.2,2.0,Iris-virginica
6.2,3.4,5.4,2.3,Iris-virginica
5.9,3.0,5.1,1.8,Iris-virginica

算法思想：
对于数值型数据来说，我们没有办法使用 P ( h u m i d i t y = 87 ) P ( h u m i d i t y = 87 ) P(humidity=87) , 因为湿度刚刚好为 87 (而不是 87.001) 的概率为 0。
因此我们需要将概率密度当成概率值直接使用 Bayes 公式，即直接用函数p(x)来代替概率 P ( x j ∣ D i ) P(x_j|D_i) P(xj​∣Di​)。这里我们假设所有属性的属性值都服从高斯分布，则p(x)如下所示：

这里的 σ 表示方差，μ表示均值。

我们将上次学习的符号型数据NB算法中的预测方案进行改造，用函数p(x)来代替概率 P ( x j ∣ D i ) P(x_j|D_i) P(xj​∣Di​)：

改造后的预测方案为：

这里的k表示样本的种类数，k取值为3；i代表具体的种类，可取值1、2、3； P L ( D i ) P^L(D_i) PL(Di​)表示进行 Laplacian 平滑后的先验概率；m表示属性总数，m值为4； σ i j σ_{ij} σij​ 和 μ i j μ_{ij} μij​ 表示与类别、属性相关的方差与均值。

代码:

package machine_learning;

import java.io.FileReader;
import java.util.Arrays;
import weka.core.*;

/**
 * @Description: The Naive Bayes algorithm.
 * @author: Xin-Yu Li
 * @time: May 11(th),2022
 */
public class NaiveBayes {
	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

	Instances dataset;
	int numClasses;
	int numInstances;
	int numConditions;
	
	int[] predicts;
	double[] classDistribution;
	double[] classDistributionLaplacian;
	double[][][] conditionalCounts;
	double[][][] conditionalProbabilitiesLaplacian;

	GaussianParamters[][] gaussianParameters;

	int dataType;
	public static final int NOMINAL = 0;
	public static final int NUMERICAL = 1;

	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

	public void setDataType(int paraDataType) {
		dataType = paraDataType;
	}// Of setDataType

	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

	public void calculateConditionalProbabilities() {
		conditionalCounts = new double[numClasses][numConditions][];
		conditionalProbabilitiesLaplacian = new double[numClasses][numConditions][];

		for (int i = 0; i < numClasses; i++) {
			for (int j = 0; j < numConditions; j++) {
				int tempNumValues = (int) dataset.attribute(j).numValues();
				conditionalCounts[i][j] = new double[tempNumValues];
				conditionalProbabilitiesLaplacian[i][j] = new double[tempNumValues];
			} // Of for j
		} // Of for i

		int[] tempClassCounts = new int[numClasses];
		for (int i = 0; i < numInstances; i++) {
			int tempClass = (int) dataset.instance(i).classValue();
			tempClassCounts[tempClass]++;
			for (int j = 0; j < numConditions; j++) {
				int tempValue = (int) dataset.instance(i).value(j);
				conditionalCounts[tempClass][j][tempValue]++;
			} // Of for j
		} // Of for i

		for (int i = 0; i < numClasses; i++) {
			for (int j = 0; j < numConditions; j++) {
				int tempNumValues = (int) dataset.attribute(j).numValues();
				for (int k = 0; k < tempNumValues; k++) {
					conditionalProbabilitiesLaplacian[i][j][k] = (conditionalCounts[i][j][k] + 1)/ (tempClassCounts[i] + tempNumValues);
				} // Of for k
			} // Of for j
		} // Of for i

		System.out.println("Conditional probabilities: " + Arrays.deepToString(conditionalCounts));
	}// Of calculateConditionalProbabilities

	public void calculateGausssianParameters() {
		gaussianParameters = new GaussianParamters[numClasses][numConditions];

		double[] tempValuesArray = new double[numInstances];
		int tempNumValues = 0;
		double tempSum = 0;

		for (int i = 0; i < numClasses; i++) {
			for (int j = 0; j < numConditions; j++) {
				tempSum = 0;

				// Obtain values for this class.
				tempNumValues = 0;
				for (int k = 0; k < numInstances; k++) {
					if ((int) dataset.instance(k).classValue() != i) {
						continue;
					} // Of if

					tempValuesArray[tempNumValues] = dataset.instance(k).value(j);
					tempSum += tempValuesArray[tempNumValues];
					tempNumValues++;
				} // Of for k

				// Obtain parameters.
				double tempMu = tempSum / tempNumValues;

				double tempSigma = 0;
				for (int k = 0; k < tempNumValues; k++) {
					tempSigma += (tempValuesArray[k] - tempMu) * (tempValuesArray[k] - tempMu);
				} // Of for k
				tempSigma /= tempNumValues;
				tempSigma = Math.sqrt(tempSigma);

				gaussianParameters[i][j] = new GaussianParamters(tempMu, tempSigma);
			} // Of for j
		} // Of for i

		System.out.println(Arrays.deepToString(gaussianParameters));
	}// Of calculateGausssianParameters

	
	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

	public int classify(Instance paraInstance) {
		if (dataType == NOMINAL) {
			return classifyNominal(paraInstance);
		} 
		else if (dataType == NUMERICAL) {
				return classifyNumerical(paraInstance);
			} // Of if

			return -1;
	}// Of classify

	public int classifyNominal(Instance paraInstance) {
		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);

				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
	
	public int classifyNumerical(Instance paraInstance) {
		// Find the biggest one
		double tempBiggest = -10000;
		int resultBestIndex = 0;

		for (int i = 0; i < numClasses; i++) {
			double tempPseudoProbability = Math.log(classDistributionLaplacian[i]);
			for (int j = 0; j < numConditions; j++) {
				double tempAttributeValue = paraInstance.value(j);
				double tempSigma = gaussianParameters[i][j].sigma;
				double tempMu = gaussianParameters[i][j].mu;

				tempPseudoProbability += -Math.log(tempSigma)
						- (tempAttributeValue - tempMu) * (tempAttributeValue - tempMu) / (2 * tempSigma * tempSigma);
			} // Of for j

			if (tempBiggest < tempPseudoProbability) {
				tempBiggest = tempPseudoProbability;
				resultBestIndex = i;
			} // Of if
		} // Of for i

		return resultBestIndex;
	}// Of classifyNumerical

	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

	public static void testNominal() {
		System.out.println("Hello, Naive Bayes. I only want to test the nominal data.");
		String tempFilename = "C:\Users\LXY\Desktop\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
	
	public static void testNumerical() {
		System.out.println("Hello, Naive Bayes. I only want to test the numerical data with Gaussian assumption.");
		String tempFilename = "C:\Users\LXY\Desktop\iris.arff";

		NaiveBayes tempLearner = new NaiveBayes(tempFilename);
		tempLearner.setDataType(NUMERICAL);
		tempLearner.calculateClassDistribution();
		tempLearner.calculateGausssianParameters();
		tempLearner.classify();

		System.out.println("The accuracy is: " + tempLearner.computeAccuracy());
	}// Of testNumerical



	public static void main(String[] args) {
		testNumerical();
	}// Of main
	
	
}// Of class NaiveBayes

运行截图：

欢迎分享，转载请注明来源：内存溢出

原文地址: http://outofmemory.cn/langs/920038.html

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