识别练习.cpp

通过已知的先验概率

#include <stdio.h>
#include <iostream.h>
#include <iomanip.h>
#include <math.h>
#include"stdlib.h"
//定义PI的大小
#define pi 3.1415926
double AverageRandom(double min,double max);      
double Normal(double x,double mean,double variance);
void NormalRandom(double mean, double variance,double min,double max,int number,double* sample);
void Estimate(double* mean,double* variance,double* sample,int number);
void Distinguish(double x,double mean_1,double variance_1,double mean_2,double variance_2);

void main()
{
	double sample_1[200];//训练样本1 
	double sample_2[200];//训练样本2  
	double mean_1;//样本1的均值
    double variance_1;//样本1的方差
	double mean_2;//样本2的均值
	double variance_2;//样本2的方差
	cout<<"样本数据：\n";
	NormalRandom(72,25,62,82,200,sample_1);//用于产生200个均值为72，方差为25的样本放于sample_1中
	NormalRandom(184,36,172,196,200,sample_2);//用于产生200个均值为184，方差为36的样本放于sample_2中	
	Estimate(& mean_1,& variance_1,& sample_1[0],200);//用于估计样本1的均值与方差
    Estimate(& mean_2,& variance_2,& sample_2[0],200);//用于估计样本2的均值与方差
    cout<<"两类的均值和方差的估计值分别为：\n";
	cout<<setw(10)<<mean_1<<setw(10)<<variance_1<<endl;//输出样本1的均值与方差
    cout<<setw(10)<<mean_2<<setw(10)<<variance_2<<endl;//输出样本2的均值与方差
    double x=1;
	while(x!=NULL)
	{
		
		    cout<<"请输入待识别数x:\n";
            cin>>x;
            cout<<"x="<<x<<endl;
	       	Distinguish(x,mean_1,variance_1,mean_2,variance_2);//调用分类器函数判别属于哪一类
	}
}

double AverageRandom(double min,double max)      
{
    long minInteger = (int)(min*10000);
    long maxInteger = (int)(max*10000);
    long randInteger = rand()*rand();
    long diffInteger = maxInteger - minInteger;
    long resultInteger = randInteger % diffInteger + minInteger;
    return resultInteger/10000.0;
}

double Normal(double x,double mean,double variance)     
{
    return 1.0/sqrt(2*pi*variance) * exp(-1*(x-mean)*(x-mean)/(2*variance));
}
//用于产生测试序列放在SAMPLE数组中
void NormalRandom(double mean, double variance,double min,double max,int number,double* sample)
{
	for (int i=0;i<number;i++)
	{
		double x;
        double dScope;
        double y;
        do
		{
             x = AverageRandom(min,max); 
             y = Normal(x, mean, variance);
             dScope = AverageRandom(0, Normal(mean,mean,variance));
		}while( dScope > y);
        sample[i]=x;
		cout<<x<<endl;
     }
}
//用于估计样本的均值和方差
void Estimate(double* mean,double* variance,double* sample,int number)
{
	*mean=0;
    *variance=0;
	for (int i=0;i<number;i++)
	{
		*mean=*mean+1.0/number*sample[i];
    }
	for (int j=0;j<number;j++)
	{
		*variance=*variance+1.0/number*(sample[j]-*mean)*(sample[j]-*mean);

	}
}
//分类器函数
void Distinguish(double x,double mean_1,double variance_1,double mean_2,double variance_2)
{
	double P_w1,P_w2,P_x_w1,P_x_w2,P_w1_x;
	P_w1=0.4;//先验概率
	P_w2=0.6;//先验概率
	
		P_x_w1=Normal(x,mean_1,variance_1);
	    P_x_w2=Normal(x,mean_2,variance_2);
        P_w1_x=P_x_w1*P_w1/(P_x_w1*P_w1+P_x_w2*P_w2);
	    if (P_w1_x>=0.5)
		{
		    cout<<"x属于第一类\n";
		}
	    else
		{
		    cout<<"x属于第二类\n";
		}
  }