Linearization of the kernel functions in SVM

Baiyi_destroyer

于 2018-05-02 20:15:28 发布

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本文介绍了一种将SVM中的复杂二次多项式核函数转换为线性函数的方法，并提供了一个具体的编程实现示例。该方法通过引入新的变量实现了函数形式的简化，有助于提高支持向量机算法在处理特定类型数据时的效率。

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Description

SVM（Support Vector Machine）is an important classification tool, which has a wide range of applications in cluster analysis, community division and so on. SVM The kernel functions used in SVM have many forms. Here we only discuss the function of the form f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j. By introducing new variables p, q, r, u, v, w, the linearization of the function f(x,y,z) is realized by setting the correspondence x^2 <-> p, y^2 <-> q, z^2 <-> r, xy <-> u, yz <-> v, zx<-> w and the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j can be written as g(p,q,r,u,v,w,x,y,z) = ap + bq + cr + du + ev + fw + gx + hy + iz + j, which is a linear function with 9 variables.
Now your task is to write a program to change f into g.

Input

The input of the first line is an integer T, which is the number of test data (T<120). Then T data follows. For each data, there are 10 integer numbers on one line, which are the coefficients and constant a, b, c, d, e, f, g, h, i, j of the function f(x,y,z) = ax^2 + by^2 + cy^2 + dxy + eyz + fzx + gx + hy + iz + j.

Output

For each input function, print its correspondent linear function with 9 variables in conventional way on one line.

Sample Input

2
0 46 3 4 -5 -22 -8 -32 24 27
2 31 -5 0 0 12 0 0 -49 12

Sample Output

46q+3r+4u-5v-22w-8x-32y+24z+27
2p+31q-5r+12w-49z+12

代码如下：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#define mem(a,b) memset(a,b,sizeof(a))
#define For(a,b) for(ll a=0;a<b;a++)
using namespace std;
const int maxn = 1e3+500;
const int INF = 0x3f3f3f3f;
const int inf = 0x3f;
typedef long long ll;
const ll mod = 1e9+7;
char c[] = {"pqruvwxyz"};
int a[maxn];
int main() {
int t;
cin>>t;
while(t--)
{
int k=0,s=0;
for(int i=0;i<10;i++)
cin>>a[i];
for(int i=0;i<9;i++)
{
if(a[i]==0)
s++;
else
{
if(a[i]>0)
{
if(k>0)
cout<<"+";
if(a[i]!=1)
cout<<a[i];
k=1;
}
else
{
if(a[i]!=-1)
cout<<a[i];
else
cout<<"-";
k=1;
}
cout<<c[i];
}
}
if(s==9&&a[9]==0)
cout<<"0";
else if(s==9)
cout<<a[9];
else if(a[9]>0)
cout<<"+"<<a[9];
else if(a[9]<0)
cout<<a[9];
cout<<endl;
}
return 0;
}