C++实现SVM

Julia999 · 发表于 2019-7-31 22:47:59

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在机器学习中，SVM相对来说是比较难的了，所以我对SVM也是琢磨了很久，所以利用C++来实现SVM，来加深自己对SVM的理解。

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include<string>
#include<fstream>
#include<sstream>
using std::sort;
using std::fabs;
using namespace std;
const int MAX_DIMENSION = 3;
const int MAX_SAMPLES = 306;
double x[MAX_SAMPLES][MAX_DIMENSION];
double y[MAX_SAMPLES];
double alpha[MAX_SAMPLES];
double w[MAX_DIMENSION];
double b;
double c;
double eps = 1e-6;
int num_samples = 306;
int num_dimension = 3;
struct _E {
double val;
int index;
}E[MAX_SAMPLES];
bool cmp(const _E & a, const _E & b)
{
return a.val < b.val;
}
double max(double a, double b)
{
return a > b ? a : b;
}
double min(double a, double b)
{
return a > b ? b : a;
}
double kernal(double x1[], double x2[], double dimension)
{
double ans = 0;
for (int i = 0; i < dimension; i++)
{
ans += x1[i] * x2[i];
}
return ans;
}
double target_function()
{
double ans = 0;
for (int i = 0; i < num_samples; i++)
{
for (int j = 0; j < num_samples; j++)
{
ans += alpha[i] * alpha[j] * y[i] * y[j] * kernal(x[i], x[j], num_dimension);
}
}
for (int i = 0; i < num_samples; i++)
{
ans -= alpha[i];
}
return ans;
}
double g(double _x[], int dimension)
{
double ans = b;
for (int i = 0; i < num_samples; i++)
{
ans += alpha[i] * y[i] * kernal(x[i], _x, dimension);
}
return ans;
}
bool satisfy_constrains(int i, int dimension)
{
if (alpha[i] == 0)
{
if (y[i] * g(x[i], dimension) >= 1)
return true;
else
return false;
}
else if (alpha[i] > 0 && alpha[i] < c)
{
if (y[i] * g(x[i], dimension) == 1)
return true;
else
return false;
}
else
{
if (y[i] * g(x[i], dimension) <= 1)
return true;
else
return false;
}
}
double calE(int i, int dimension)
{
return g(x[i], dimension) - y[i];
}
void calW()
{
for (int i = 0; i < num_dimension; i++)
{
w[i] = 0;
for (int j = 0; j < num_samples; j++)
{
w[i] += alpha[j] * y[j] * x[j][i];
}
}
return;
}
void calB()
{
double ans = y[0];
for (int i = 0; i < num_samples; i++)
{
ans -= y[i] * alpha[i] * kernal(x[i], x[0], num_dimension);
}
b = ans;
return;
}
void recalB(int alpha1index, int alpha2index, int dimension, double alpha1old, double alpha2old)
{
double alpha1new = alpha[alpha1index];
double alpha2new = alpha[alpha2index];
alpha[alpha1index] = alpha1old;
alpha[alpha2index] = alpha2old;
double e1 = calE(alpha1index, num_dimension);
double e2 = calE(alpha2index, num_dimension);
alpha[alpha1index] = alpha1new;
alpha[alpha2index] = alpha2new;
double b1new = -e1 - y[alpha1index] * kernal(x[alpha1index], x[alpha1index], dimension)*(alpha1new - alpha1old);
b1new -= y[alpha2index] * kernal(x[alpha2index], x[alpha1index], dimension)*(alpha2new - alpha2old) + b;
double b2new = -e2 - y[alpha1index] * kernal(x[alpha1index], x[alpha2index], dimension)*(alpha1new - alpha1old);
b1new -= y[alpha2index] * kernal(x[alpha2index], x[alpha2index], dimension)*(alpha2new - alpha2old) + b;
b = (b1new + b2new) / 2;
}
bool optimizehelp(int alpha1index, int alpha2index)
{
double alpha1new = alpha[alpha1index];
double alpha2new = alpha[alpha2index];
double alpha1old = alpha[alpha1index];
double alpha2old = alpha[alpha2index];
double H, L;
if (fabs(y[alpha1index] - y[alpha2index]) > eps)
{
L = max(0, alpha2old - alpha1old);
H = min(c, c + alpha2old - alpha1old);
}
else
{
L = max(0, alpha2old + alpha1old - c);
H = min(c, alpha2old + alpha1old);
}
//cal new
double lena = kernal(x[alpha1index], x[alpha1index], num_dimension) + kernal(x[alpha2index], x[alpha2index], num_dimension) - 2 * kernal(x[alpha1index], x[alpha2index], num_dimension);
alpha2new = alpha2old + y[alpha2index] * (calE(alpha1index, num_dimension) - calE(alpha2index, num_dimension)) / lena;
if (alpha2new > H)
{
alpha2new = H;
}
else if (alpha2new < L)
{
alpha2new = L;
}
alpha1new = alpha1old + y[alpha1index] * y[alpha2index] * (alpha2old - alpha2new);
double energyold = target_function();
alpha[alpha1index] = alpha1new;
alpha[alpha2index] = alpha2new;
double gap = 0.001;
recalB(alpha1index, alpha2index, num_dimension, alpha1old, alpha2old);
return true;
}
bool optimize()
{
int alpha1index = -1;
int alpha2index = -1;
double alpha2new = 0;
double alpha1new = 0;
//cal E[]
for (int i = 0; i < num_samples; i++)
{
E[i].val = calE(i, num_dimension);
E[i].index = i;
}
//traverse the alpha1index with 0 < && < c
for (int i = 0; i < num_samples; i++)
{
alpha1new = alpha[i];
if (alpha1new > 0 && alpha1new < c)
{
if (satisfy_constrains(i, num_dimension))
continue;
sort(E, E + num_samples, cmp);
//simply find the maximum or minimun;
if (alpha1new > 0)
{
if (E[0].index == i)
{
;
}
else
{
alpha1index = i;
alpha2index = E[0].index;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
else
{
if (E[num_samples - 1].index == i)
{
;
}
else
{
alpha1index = i;
alpha2index = E[num_samples - 1].index;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
//find the alpha2 > 0 && < c
for (int j = 0; j < num_samples; j++)
{
alpha2new = alpha[j];
if (alpha2new > 0 && alpha2new < c)
{
alpha1index = i;
alpha2index = j;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
//find other alpha2
for (int j = 0; j < num_samples; j++)
{
alpha2new = alpha[j];
if (!(alpha2new > 0 && alpha2new < c))
{
alpha1index = i;
alpha2index = j;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
}
}
//find all alpha1
for (int i = 0; i < num_samples; i++)
{
alpha1new = alpha[i];
if (!(alpha1new > 0 && alpha1new < c))
{
if (satisfy_constrains(i, num_dimension))
continue;
sort(E, E + num_samples, cmp);
//simply find the maximum or minimun;
if (alpha1new > 0)
{
if (E[0].index == i)
{
;
}
else
{
alpha1index = i;
alpha2index = E[0].index;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
else
{
if (E[num_samples - 1].index == i)
{
;
}
else
{
alpha1index = i;
alpha2index = E[num_samples - 1].index;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
//find the alpha2 > 0 && < c
for (int j = 0; j < num_samples; j++)
{
alpha2new = alpha[j];
if (alpha2new > 0 && alpha2new < c)
{
alpha1index = i;
alpha2index = j;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
//find other alpha2
for (int j = 0; j < num_samples; j++)
{
alpha2new = alpha[j];
if (!(alpha2new > 0 && alpha2new < c))
{
alpha1index = i;
alpha2index = j;
if (optimizehelp(alpha1index, alpha2index))
{
return true;
}
}
}
}
}
//for(int i = 0 ; i < num_samples; i++)
//{
// alpha1new = alpha[i];
// for(int j = 0 ; j < num_samples; j++)
// {
// if(1)
// {
// alpha1index = i;
// alpha2index = j;
// if(optimizehelp(alpha1index , alpha2index))
// {
// return true;
// }
// }
// }
//}
return false;
}
bool check()
{
double sum = 0;
for (int i = 0; i < num_samples; i++)
{
sum += alpha[i] * y[i];
if (!(0 <= alpha[i] && alpha[i] <= c))
{
printf("alpha[%d]: %lf wrong\n", i, alpha[i]);
return false;
}
if (!satisfy_constrains(i, num_dimension))
{
printf("alpha[%d] not satisfy constrains\n", i);
return false;
}
}
if (fabs(sum) > eps)
{
printf("Sum = %lf\n", sum);
return false;
}
return true;
}
int toNum(string str)//Enclave无法接受string类型数据
{
int ans = 0;
for (int i = 0; i < str.length(); i++)
{
ans = ans * 10 + (str[i] - '0');
}
return ans;
}
void loaddata(string path)
{
ifstream Filein;
try { Filein.open(path); }
catch (exception e)
{
cout << "File open failed!";
}
string line;
int data_num = 0;
while (getline(Filein, line)) {
int before = 0;
int cnt = 0;
data_num++;
//cout << data_num << endl;
for (unsigned int i = 0; i < line.length(); i++) {
if (line[i] == ',' || line[i] == '\n') {
string sub = line.substr(before, i - before);
before = i + 1;
x[data_num - 1][cnt] = toNum(sub);
cnt++;
}
}
//Data[data_num - 1][cnt] = toNum(line.substr(before, line.length()));
y[data_num - 1] = toNum(line.substr(before, line.length()));
}
cout << "data loading done.\nthe amount of data is: " << data_num << endl;
}
int main()
{
/*scanf_s("%d%d", &num_samples, &num_dimension);
for (int i = 0; i < num_samples; i++)
{
for (int j = 0; j < num_dimension; j++)
{
scanf_s("%lf", &x[i][j]);
}
scanf_s("%lf", &y[i]);
}*/
loaddata("C:\\Users\\YY\\Desktop\\haberman1.txt");//获取数据集，并存于Data数组
c = 1;
//初值附为0；
for (int i = 0; i < num_samples; i++)
{
alpha[i] = 0;
}
int count = 0;
while (optimize()) {
calB();
count++;
}
printf("%d ", count);
calW();
calB();
printf("y = ");
for (int i = 0; i < num_dimension; i++)
{
printf("%lf * x[%d] + ", w[i], i);
}
//计算精度
int countt = 0;
for (int i = 0; i < num_samples; i++)
{
double Y = 0;
for (int j = 0; j < num_dimension; j++)
{
Y += x[i][j] * w[j];
}
if (Y + b == y[i])
{
countt++;
}
}
printf("%lf\n", b);
double pro = double(countt) / double(num_samples);
printf("%f\n ", pro);
if (!check())
printf("Not satisfy KKT.\n");
else
printf("Satisfy KKT\n");
system("pause");
return 0;
}

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