二话不说先上题目：

训练数据格式如下：

输入有4个维度，输出为{-1，+1}。共有400条数据。

题目要求将权向量元素初始化为0，然后使用“Naive Cycle”遍历训练集，求停止迭代时共对权向量更新了几次。

所谓“Naive Cycle”指的是在某数据条目x(i)上发现错误并更新权向量后，下次从x(i+1)继续读数据，而不是回到第一条数据x(0)从头开始。

#include <fstream>
#include <iostream>
#include <vector>using namespace std;#define DEMENSION 5                //数据维度double weights[DEMENSION];         //权重向量
int step= 0;                       //迭代次数
int length = 0;                    //数据条目个数
int index = 0;                     //当前数据条目索引
bool isFinished = false;           //迭代终止状态
char *file = "training_data.txt";struct record {double input[DEMENSION];   //输入int output;                //输出
};
vector<record> trainingSet;        //训练数据int sign(double x)
{if(x<0)      return -1;else if(x>0) return 1;else         return -1;
}//两个向量相加，更新第一个向量
void add(double *v1, double *v2, int demension)
{for(int i=0;i<demension;++i){ v1[i] = v1[i] + v2[i]; }
}//两个向量相乘,返回内积
double multiply(double *v1, double *v2, int demension)
{double innerProd = 0.0;for(int i=0;i<demension;++i){innerProd += v1[i] * v2[i];}return innerProd;
}//向量与实数相乘，结果通过*result返回，不改变参与计算的向量
void multiply(double *result, double *v, double num, int demension)
{for(int i=0;i<demension;++i){ result[i] = v[i] * num; }
}//读取所有训练数据
void getData(ifstream & dataFile)
{while(!dataFile.eof()){record curRecord;curRecord.input[0] = 1;      for(int i=1;i<DEMENSION;++i){ dataFile>>curRecord.input[i]; }dataFile>>curRecord.output;trainingSet.push_back(curRecord);}dataFile.close();length = trainingSet.size();
}void PLA()
{int start = index;double curInput[DEMENSION];//找到下一个错误记录的indexwhile( trainingSet[index].output == sign(multiply(weights,trainingSet[index].input,DEMENSION)) ){ if(index==length-1)   {index = 0;}else           {index++;}if(index==start)  {isFinished = true; break;}    //没发现错误，迭代结束}if(isFinished){cout<<"计算结果：step = "<<step<<", weights = \n";for(int i=0;i<DEMENSION;++i){ cout<<weights[i]<<endl; }    return;}else{step++;//更新: weights = weights + curOutput * curInputmultiply( curInput, trainingSet[index].input, trainingSet[index].output, DEMENSION ); add( weights, curInput, DEMENSION );    if(index==length-1)   {index = 0;}else           {index++;}PLA();  }return;
}void main()
{   ifstream dataFile(file);if(dataFile.is_open()){getData(dataFile);       }else{cerr<<"ERROR ---> 文件打开失败"<<endl;exit(1);}for(int i=0;i<DEMENSION;++i){ weights[i] = 0.0; }PLA();
}

多次运行程序，迭代次数均为45次。

该题要求使用“fixed,pre-determined random cycle”对数据进行遍历，即对400条数据进行随机排序，然后在这轮计算中始终使用这一排序，直到下一轮计算开始再重新排序，重复2000次，求对权向量的平均修正次数。

#include <fstream>
#include <iostream>
#include <vector>
#include <ctime>using namespace std;#define DEMENSION 5                //数据维度int step= 0;                       //迭代次数
int index = 0;                     //当前数据条目索引
bool isFinished = false;           //迭代终止状态
char *file = "training_data.txt";struct record {double input[DEMENSION];   //输入int output;                //输出
};int sign(double x)
{//同Q15
}void add(double *v1, double *v2, int demension)
{//同Q15
}//两个向量相乘,返回内积
double multiply(double *v1, double *v2, int demension)
{//同Q15
}//向量与实数相乘，结果通过*result返回，不改变参与计算的向量
void multiply(double *result, double *v, double num, int demension)
{//同Q15
}//对 traininig set 创建一个随机排序
void setRandomOrder(vector<record> &trainingSet, vector<int> &randIndexes)
{srand((unsigned)time(NULL)); int length = trainingSet.size(); vector<bool> assignedIndexes(length,false);     for(int i=0;i<length;++i){int randIndex = rand()%length;while(assignedIndexes[randIndex]==true){randIndex = rand()%length;  }randIndexes.push_back(randIndex); assignedIndexes[randIndex] = true;      }
}//读取所有训练数据
void getData(ifstream & dataFile, vector<record> &trainingSet)
{while(!dataFile.eof()){record curRecord;curRecord.input[0] = 1;      for(int i=1;i<DEMENSION;++i){ dataFile>>curRecord.input[i]; }dataFile>>curRecord.output;trainingSet.push_back(curRecord);}dataFile.close();
}void PLA(vector<record> &trainingSet, vector<int> &randIndexes, double *weights)
{int length = trainingSet.size();int start = index;   double curInput[DEMENSION];//找到下一个错误记录的indexwhile( trainingSet[randIndexes[index]].output == sign(multiply(weights,trainingSet[randIndexes[index]].input,DEMENSION)) ){   if(index==length-1)   {index = 0;}else               {index++;}if(index==start)  {isFinished = true; break;}    //没发现错误，迭代结束}if(isFinished){return;}else{step++;//更新: weights = weights + curOutput * curInputmultiply( curInput, trainingSet[randIndexes[index]].input, trainingSet[randIndexes[index]].output, DEMENSION );    add( weights, curInput, DEMENSION );    if(index==length-1)   {index = 0;}else               {index++;}PLA(trainingSet, randIndexes, weights); }return;
}void main()
{int totalSteps = 0;for(int i=0;i<2000;++i){double weights[DEMENSION];      //权重向量vector<record> trainingSet;     //训练数据vector<int> randIndexes;        //访问数据的随机索引列表ifstream dataFile(file);step = 0;             index = 0;             isFinished = false;   if(dataFile.is_open()){getData(dataFile,trainingSet); setRandomOrder(trainingSet,randIndexes);}else{cerr<<"ERROR ---> 文件打开失败"<<endl;exit(1);}for(int i=0;i<DEMENSION;++i){ weights[i] = 0.0; }PLA(trainingSet, randIndexes, weights);totalSteps += step;}cout<<"Average Step = "<<totalSteps/2000<<endl;
}

本题要求在更新权向量时乘以一个0.5的系数，代码变动很少。