机器学习-感知机笔记（题目举例和代码解答）

1.题目

2.解答

#include<iostream>#include<vector>#include<string>#include<fstream>using namespace std;typedef vector<double> featureVct;typedef int label;class Perceptron;void printRes(Perceptron pp);class Perceptron{private:vector<featureVct> FtSet;  //特征向量数据集vector<label> labelSet;   //二分类label数据集 +1或-1double LearnRate;//学习率featureVct w;//感知机模型参数double bias;//偏置项int dimension;//特征向量维度int count;public:Perceptron(int dimension,featureVct w,double bias = 0.0,double learnRate = 1);int GetCount() const;  //获取迭代次数const featureVct& GetW() const ;     //获取模型参数void SetW(const featureVct& w);  //设置模型参数double GetBias() const;//获取偏置项void SetBias(double bias);//设置骗置项bool ReadSource(const string& filePath); //读取数据源void Train();//训练模型，得到感知机模型public:double VectorDotProduct(const featureVct& f1, const featureVct& f2);  //向量点积运算）featureVct VectorScalarMulti(double num, const featureVct f); //向量数乘运算featureVct VectorAdd(const featureVct& f1, const featureVct& f2);  //向量加法运算};const featureVct& Perceptron::GetW() const{return w;}void Perceptron::SetW(const featureVct& w){this->w = w;}double Perceptron::GetBias() const{return bias;}void Perceptron::SetBias(double bias){this->bias = bias;}/*文件格式：每行表示一个样本点，特征值之间用空格隔开，最后一列存储类别信息1或-1*/bool Perceptron::ReadSource(const string& filePath){ifstream file(filePath);if (!file)return false;while (!file.eof()){featureVct dataTmp;double tmp;for (int i = 0; i < dimension; ++i){file >> tmp;dataTmp.push_back(tmp);}FtSet.push_back(dataTmp);label labelData;file >> labelData;labelSet.push_back(labelData);}return true;}void Perceptron::Train(){//感知机训练过程int flag = true;while (flag){for (int i = 0; i < FtSet.size(); i++){flag = false;if (labelSet[i] * (VectorDotProduct(w,FtSet[i]) + bias) <= 0){//此处的打印只是为了更直观的给大家展示学习过程，工程中最后不要直接在类中打印信息printRes(*this);flag = true;w = VectorAdd(w, VectorScalarMulti(labelSet[i]*LearnRate,FtSet[i]));bias += LearnRate * labelSet[i];++count;break;}}//此处的打印只是为了更直观的给大家展示学习过程，工程中最后不要直接在类中打印信息if(!flag)  printRes(*this);}}Perceptron::Perceptron(int dimension, featureVct w, double bias, double learnRate){this->dimension = dimension;this->bias = bias;this->LearnRate = learnRate;this->w = w;count = 0;}double Perceptron::VectorDotProduct(const featureVct& f1, const featureVct& f2){double sum = 0.0;for (int i = 0; i != f1.size(); ++i){sum += f1[i] * f2[i];}return sum;}featureVct Perceptron::VectorScalarMulti(double num, const featureVct f){featureVct tmp;for (int i = 0; i != f.size(); ++i){tmp.push_back(num*f[i]);}return tmp;}featureVct Perceptron::VectorAdd(const featureVct& f1, const featureVct& f2){featureVct tmp(0);for (int i = 0; i != f1.size(); ++i){tmp.push_back(f1[i] + f2[i]);}return tmp;}int Perceptron::GetCount() const{return count;}void printRes(Perceptron pp){cout << "迭代次数:" << pp.GetCount() << endl;cout << "w:";featureVct tmp = pp.GetW();for (int i = 0; i < tmp.size() - 1; ++i){cout << tmp[i] << " ";}cout << tmp[tmp.size() - 1] << endl;cout << "bias：";cout << pp.GetBias() << endl;cout << "---------------------------" << endl;}int main(){featureVct w;w.push_back(0.0); //设置w初始化参数w.push_back(0.0);Perceptron pp(2, w);  //创建特征向量为2维的感知机对象if (!pp.ReadSource("sun.txt")){cout << "读取文件失败";exit(-1);}pp.Train();  //训练得到感知机模型}

数据源：

3 3 14 3 11 1 -1

运行截图：

最后得到 w(1,1) b = -3

大家可能会问，这到底表示什么意思？

其实就是，得到的感知模型表达式为 f(x) = sign(x1+x2-3)      意思也就是我们得到了一条直线x+y-3 = 0 可以作为一个二类划分

注意：感知机器学习算法由于采用不同的初值或选取不同的误分类点，解可以不同

此题的详细解法描述参照《统计学习方法》赵航P45