神经网络与机器学习 笔记—Rosenblatt感知器收敛算法C++实现

神经网络与机器学习 笔记—Rosenblatt感知器收敛算法C++实现

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：

直接上实现代码：

#pragma once#include "stdafx.h"#include #include 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%

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