private static CARTTree GetSubTree(CARTTree tree)
{
var root = tree._root;
var stack = new Stack <CARTNode>();
AccessNonLeaf(root, stack);
double minAlpha = double.MaxValue; // 最小alpha
CARTNode minNode = null; // 最小alpha对应的内部节点
while (stack.Count > 0)
{
var t = stack.Pop(); // 某一内部节点
// 以 t 为根节点的子树的所有叶节点
var leaves_t = CARTUtil.GetLeaves(t);
// 以 t 为单节点，平方误差为
var var_t = CARTUtil.GetVar(t);
// 以 t 为根节点的子树，平方误差为
double var_subtree = 0;
for (int i = 0; i < leaves_t.Count; i++)
{
var leaf = leaves_t[i];
var_subtree += CARTUtil.GetVar(leaf);
}
var alpha_t = (var_t - var_subtree) / (leaves_t.Count - 1);
if (minAlpha > alpha_t)
{
minAlpha = alpha_t;
minNode = t;
}
}
// 获得最小的alpha，则对此节点剪枝，
// 需要注意的是，由于最终要生成一个子树序列，所以，我们不对原来的树剪枝，而是复制一个树并剪枝
return(PrunedClone(tree, minNode));
}
/// <summary>
/// 根据样本数据创建CART决策树
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
public static CARTTree Create(CARTData data)
{
var tree = new CARTTree()
{
_root = new CARTNode()
};
var attrIdxs = Enumerable.Range(0, data.J - 1).ToList(); // 输入属性索引列表
Create(tree._root, attrIdxs, data.trainSet);
return(Prune(tree, data));
}
/// <summary>
/// 是否是三节点组成的树， 即一个根节点加两个子节点
/// </summary>
/// <param name="tree"></param>
/// <returns></returns>
private static bool Is_ThreeNode_Tree(CARTTree tree)
{
var left = tree._root.left;
var right = tree._root.right;
if (left.left != null || right.left != null)
{
return(false);
}
return(true);
}
private static CARTTree PrunedClone(CARTTree tree, CARTNode node)
{
var queue = new Queue <CARTNode>(); // 原始树队列
queue.Enqueue(tree._root);
var root_1 = new CARTNode(); // 新树根节点
var queue_1 = new Queue <CARTNode>(); // 同步队列
queue_1.Enqueue(root_1);
while (queue.Count > 0)
{
var n = queue.Dequeue();
var n_1 = queue_1.Dequeue();
if (n == node) // 遇到需要被剪枝的内部节点，则需要剪枝为叶节点
{
// 设置叶节点的必要字段
n_1.output = n.region.Sum(p => p.vals.LastOrDefault()) / n.region.Count;
n_1.region = n.region;
}
else
{
n_1.Update(n); // 更新节点的固有属性（字段）
if (n.left != null)
{
// 非叶节点
n_1.left = new CARTNode()
{
parent = n_1
};
n_1.right = new CARTNode()
{
parent = n_1
};
queue.Enqueue(n.left);
queue.Enqueue(n.right);
queue_1.Enqueue(n_1.left);
queue_1.Enqueue(n_1.right);
}
// else，是叶节点，无需其他操作
}
}
return(new CARTTree()
{
_root = root_1
});
}
/// <summary>
/// 剪枝
/// </summary>
/// <param name="tree">完全生长的决策树</param>
/// <param name="data">提供验证数据集</param>
/// <returns></returns>
private static CARTTree Prune(CARTTree tree, CARTData data)
{
// 获取最优子树序列
var list = new List <CARTTree>()
{
tree
}; // 最优子树序列
var curTree = tree;
while (!Is_ThreeNode_Tree(curTree))
{
curTree = GetSubTree(curTree);
list.Add(curTree);
}
// 使用验证集获得最终的最优子树
// 验证集，最小平方误差
double min_err = double.MaxValue;
CARTTree best_tree = null; // 最小平方误差对应的最优子树
for (int i = 0; i < list.Count; i++)
{
var sub_tree = list[i];
double squareErrSum = 0;
for (int k = 0; k < data.verifySet.Count; k++)
{
squareErrSum += Judge(data.verifySet[k], sub_tree);
}
if (min_err > squareErrSum)
{
min_err = squareErrSum;
best_tree = sub_tree;
}
}
return(best_tree);
}
/// <summary> /// 决策：根据输入计算模型输出值 /// </summary> /// <param name="point">样本点</param> /// <param name="tree">决策树</param> /// <returns></returns> public static double Judge(CARTPoint point, CARTTree tree) => Judge(point, tree._root);
