Rosenblatt感知器收敛算法C++实现
算法概述
自己用C++实现了下,测试的例子和模式用的都是双月分类模型,关于双月分类相关看之前的那个笔记:
https://blog.csdn.net/u013761036/article/details/90548819
直接上实现代码:
#pragma once
#include "stdafx.h"
#include <string>
#include <iostream>
using namespace std;
int gnM = 0; //训练集空间维度
int gnN = 0; //突触权值个数
double gdU = 0.01; //学习率参数
void RosenBlattInit(double *dX, int nM, double *dW, int nN ,double dB ,double dU) {
//dX 本次训练数据集
//nM 训练集空间维度
//dW 权值矩阵
//nN 突触权值个数 RosenBlatt只有一个神经元,所以nM==nM
//dB 偏置,正常这个是应该 走退火动态调整的,以后再说,现在固定得了。
//dU 学习率参数
if (nM > 0) {
dX[0] = 1;//把偏置永远当成一个固定的突触
}
for (int i = 0; i <= nN; i++) {
if (i == 0) {
dW[i] = dB;//固定偏置
}
else {
dW[i] = 0.0;
}
}
gnM = nM ,gnN = nN ,gdU = dU;
}
double Sgn(double dNumber) {
return dNumber > 0 ? +1.0 : -1.0;
}
//感知器收敛算法-学习
void RosenBlattStudy(const double *dX, const double dD, double *dW) {
//dX 本次训练数据集
//dD 本次训练数据集的期望值
//dW 动态参数,突触权值
double dY = 0;
for (int i = 0; i <= gnM && i <= gnN; i++) {
dY = dY + dX[i] * dW[i];
}
dY = Sgn(dY);
if (dD == dY) {
return;//不需要进行学习调整突触权值
}
for (int i = 1; i <= gnM && i <= gnN; i++) {
dW[i] = dW[i] + gdU * (dD - dY) * dX[i];
}
}
//感知器收敛算法-泛化
double RosenBlattGeneralization(const double *dX , const double *dW) {
//dX 本次需要泛化的数据集
//dW 已经学习好的突触权值
//返回的是当前需要泛化的数据集的泛化结果(属于那个域的)
double dY = 0;
for (int i = 0; i <= gnM && i <= gnN; i++) {
dY = dY + dX[i] * dW[i];
}
return Sgn(dY);
}
//双月分类模型,随机获取一组值
/* 自己稍微改了下
域1:上半个圆,假设圆心位坐标原点(0,0)
(x - 0) * (x - 0) + (y - 0) * (y - 0) = 10 * 10
x >= -10 && x <= 10
y >= 0 && y <= 10
域2:下半个圆,圆心坐标(10 ,-1)
(x - 10) * (x - 10) + (y + 1) * (y + 1) = 10 * 10;
x >= 0 && x <= 20
y >= -11 && y <= -1
*/
const double gRegionA = 1.0; //双月上
const double gRegionB = -1.0;//双月下
void Bimonthly(double *dX ,double *dY ,double *dResult) {
//dX 坐标x
//dY 坐标y
//dResult 属于哪个分类
*dResult = rand () % 2 == 0 ? gRegionA : gRegionB;
if (*dResult == gRegionA) {
*dX = rand() % 20 - 10;//在区间内随机一个X
*dY = sqrt(10 * 10 - (*dX) * (*dX));//求出Y
}
else {
*dX = rand() % 20;
*dY = sqrt(10 * 10 - (*dX - 10) * (*dX - 10)) - 1;
*dY = *dY * -1;
}
}
int main()
{
//system("color 0b");
double dX[2 + 1], dD, dW[2 + 1]; //输入空间维度为3 平面坐标系+一个偏置
double dU = 0.1;
double dB = 0;
RosenBlattInit(dX, 2, dW, 2, dB, dU);//初始化 感知器
double dBimonthlyX, dBimonthlyY, dBimonthlyResult;
int nLearningTimes = 1024 * 10;//进行10K次学习
for (int nLearning = 0; nLearning <= nLearningTimes; nLearning++) {
Bimonthly(&dBimonthlyX, &dBimonthlyY, &dBimonthlyResult);//随机生成双月数据
dX[1] = dBimonthlyX;
dX[2] = dBimonthlyY;
dD = dBimonthlyResult;
RosenBlattStudy(dX, dD, dW);
//cout <<"Study:" << nLearning << " :X= " << dBimonthlyX << "Y= " << dBimonthlyY << " D=" << dBimonthlyResult<< "----W1= " << dW[1] << " W2= " << dW[2] << endl;
}
//进行感知器泛化能力测试 测试数据量1K
int nGeneralizationTimes = 1 * 1024;
int nGeneralizationYes = 0, nGeneralizationNo = 0;
double dBlattGeneralizationSuccessRate = 0;
for (int nLearning = 1; nLearning <= nGeneralizationTimes; nLearning++) {
Bimonthly(&dBimonthlyX, &dBimonthlyY, &dBimonthlyResult);//随机生成双月数据
dX[1] = dBimonthlyX;
dX[2] = dBimonthlyY;
//cout << "Generalization: " << dBimonthlyX << "," << dBimonthlyY;
if (dBimonthlyResult == RosenBlattGeneralization(dX, dW)) {
nGeneralizationYes++;
//cout << " Yes" << endl;
}
else {
nGeneralizationNo++;
//cout << " No" << endl;
}
}
dBlattGeneralizationSuccessRate = nGeneralizationYes * 1.0 / (nGeneralizationNo + nGeneralizationYes) * 100;
cout << "Study : " << nLearningTimes << " Generalization : " << nGeneralizationTimes << " SuccessRate:" << dBlattGeneralizationSuccessRate << "%" << endl;
getchar();
return 0;
}
结果:
学习了10K次,泛化测试1K次,成功率96%