机器学习：决策树算法（简单尝试）

这里只写一下用C++简单实现的ID3算法决策树

ID3算法是基于信息熵和信息获取量

每次建立新节点时，选取一个信息获取量最大（以信息熵为衡量）的属性进行分割

决策树还有很多其他算法，不过都只是衡量标准不同

实质都是按照贪心自上而下地建树

如果深度过深，还要采取剪枝的手段

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <cmath>
using namespace std;
typedef unsigned int ui;
typedef vector< vector<int>> dv;
const int maxm = 100, maxn = 1000;
const double eps = 1e-7;
struct Node
{
    bool flag[maxm];
    int st, yes, no;
}node[maxn];   //结点，flag表示已采用的属性，st为此次划分的标准 

double cal_entropy(double p) //计算信息熵
{
    if(abs(p) <= eps || abs(p-1) <= eps) return 0;
    return -(p*log(p)/log(2)+(1-p)*log(1-p)/log(2));
}

double split(dv v, int k) //算出如果以第k个属性分割得到的信息获取量
{
    int v1, v2, n1, n2;
    v1 = v2 = n1 = n2 = 0;
    for(ui i = 0; i < v.size(); i++)
    {
        if(v[i][k])
        {
            n1++;
            if(v[i][v[i].size()-1]) v1++;
        }
        else
        {
            n2++;
            if(v[i][v[i].size()-1]) v2++;
        }
    }
    int n = n1+n2;
    double ans = (double)n1/n*cal_entropy((double)v1/n1) + (double)n2/n*cal_entropy((double)v2/n2);
    return cal_entropy((double)(v1+v2)/n) - ans;
}



void build(int x, dv vnode) //按照贪心算法建树
{
    double ans = -1;
    int k = -1;
    for(ui i = 0; i < vnode.size(); i++)
        if(vnode[i][vnode[i].size()-1]) node[x].yes++;
    node[x].no = vnode.size() - node[x].yes;
    for(ui i = 0; i < vnode[0].size()-1; i++)
        if(!node[x].flag[i] && (split(vnode, i) - ans > eps))
        {
            ans = split(vnode, i);
            k = i;
        }
    node[x].st = k;
    printf("%d %d %d %d
", x, node[x].yes, node[x].no, node[x].st);  //先序遍历输出树的结构
    if(k == -1) return;
    dv v1, v2;
    for(ui i = 0; i < vnode.size(); i++)
        if(vnode[i][k]) v1.push_back(vnode[i]);
        else v2.push_back(vnode[i]);
    for(ui i = 0; i < v1[0].size(); i++)
    {
        node[x*2].flag[i] = node[x].flag[i];
        node[x*2+1].flag[i] = node[x].flag[i];
    }
    node[x*2].flag[k] = node[x*2+1].flag[k] = 1;
    build(x*2, v1); build(x*2+1, v2);
}

int n, m, x;
dv v;

int dfs(int x, vector<int> vv)  //用于测试集
{
    if(node[x].st == -1) return node[x].yes > node[x].no;
    if(vv[node[x].st]) return dfs(2*x, vv);
    else return dfs(2*x+1, vv);
}

vector <int> vv;
int main()
{
    freopen("a.txt", "r", stdin);
    cin>>n>>m;
    v.resize(n);
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m; j++)
        {
            cin>>x;
            v[i].push_back(x);
        }
    build(1, v);
    for(int i = 0; i < m; i++) cin>>x, vv.push_back(x);
    cout<<dfs(1, vv)<<endl;
}