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：

/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 * 10x >= -10 && x <= 10y >= 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 <= 20y >= -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1Kint 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%