1 #include <iostream>
  2 #include <vector>
  3 #include <algorithm>
  4
  5 #define random(x) (rand()%(x))
  6
  7 //向量的点积
  8 double dot_product(std::vector<double>& a, std::vector<double>& b){
  9     if(a.size() != b.size()) return 0;
 10     double res = 0;
 11     for(int i = 0 ; i < a.size(); ++ i){
 12         res +=a[i]*b[i];
 13     }
 14     return res;
 15 }
 16
 17 //感知机模型类
 18 class Preception{
 19 public:
 20     Preception(int iters = 100,int learnRate = 1,double initw = 0, double initb = 0){
 21         iterators = iters;
 22         a.push_back(initw);
 23         b = initb;
 24         step = learnRate;
 25     }
 26
 27     ~Preception(){
 28         a.clear();
 29         b = 0;
 30     }
 31
 32     //训练数据
 33     //如果迭代次数完，还没有找到a和b， 则认为数据集不是线性可分的，返回false
 34     //如果找到了a和b，则认为数据集是线性可分的，返回true
 35     bool train(std::vector<std::vector<double> >& train_x,std::vector<int>& train_y){
 36         if(train_x.size() != train_y.size()) return false;
 37         initWeight(train_x.size());
 38         std::vector<std::vector<double> > gram = productGram(train_x);
 39         for(int i = 0 ; i < a.size(); ++ i){
 40             int iter = 0;
 41             while(iter < iterators){
 42                 double sum = b;
 43                 for(int j = 0; j < a.size(); ++ j){
 44                     sum += a[j]*train_y[j]*gram[j][i];
 45                 }
 46                 sum *= train_y[i];
 47                 if(sum <= 0) update(i,train_y[i]);
 48                 else break;
 49                 ++iter;
 50             }
 51             if(iter >= iterators) return false;
 52         }
 53         return true;
 54     }
 55
 56     //批量预测数据
 57     std::vector<int> predict(std::vector<std::vector<double> >& data_x){
 58         std::vector<int> ret;
 59         for(int i = 0 ; i < data_x.size(); ++ i){
 60             ret.push_back(predict(data_x[i]));
 61         }
 62         return ret;
 63     }
 64
 65     //预测x
 66     int predict(std::vector<double>& x){
 67         return dot_product(x,a)+ b > 0 ? 1 : -1;
 68     }
 69
 70     //打印感知机模型
 71     void printPreceptronModel(){
 72         std::cout<<"原始形式感知机模型：f(x)=sign(";
 73         for(int i = 0 ; i < a.size(); ++ i){
 74             if( i ) std::cout<<"+";
 75             if(a[i]!=1) std::cout<<a[i];
 76             std::cout<<"x"<<i+1;
 77         }
 78         if(b > 0) std::cout<<"+";
 79         std::cout<<b<<")"<<std::endl;
 80     }
 81
 82 private:
 83     //初始化向量a的维数
 84     void initWeight(int size){
 85         for(int i = 1; i < size; ++ i){
 86             a.push_back(a[0]);
 87         }
 88     }
 89
 90     //生成Gram矩阵
 91     std::vector<std::vector<double> > productGram(std::vector<std::vector<double> >& train_x){
 92         int n = train_x.size();
 93         std::vector<std::vector<double> > gram(n, std::vector<double>(n,0));
 94         for(int i = 0 ; i < n ; ++ i){
 95             for(int j = 0 ; j  < n; ++ j){
 96                 gram[i][j] = dot_product(train_x[i], train_x[j]);
 97             }
 98         }
 99         return gram;
100     }
101
102     //更新w和b
103     void update(int index, double y){
104         a[index] +=1;
105         b += step*y;
106     }
107
108 private:
109     int iterators;          //迭代次数
110
111     std::vector<double> a;    //注意w是向量
112     double b;
113
114     double step;  //学习速率
115 };
116
117 int main(){
118     std::vector<std::vector<double> >test_x(3);
119     test_x[0].push_back(3);test_x[0].push_back(3);
120     test_x[1].push_back(4);test_x[1].push_back(3);
121     test_x[2].push_back(1);test_x[2].push_back(1);
122     std::vector<int> test_y(3);
123     test_y[0] = 1;
124     test_y[1] = 1;
125     test_y[2] = -1;
126
127     Preception *model = new Preception();
128     model->train(test_x,test_y);
129     model->printPreceptronModel();
130 }