cart.py

import numpy as np
from utils import feature_split, calculate_gini

### 定义树结点
class TreeNode():
    def __init__(self, feature_i=None, threshold=None,
               leaf_value=None, left_branch=None, right_branch=None):
        # 特征索引
        self.feature_i = feature_i          
        # 特征划分阈值
        self.threshold = threshold 
        # 叶子节点取值
        self.leaf_value = leaf_value   
        # 左子树
        self.left_branch = left_branch     
        # 右子树
        self.right_branch = right_branch

		
### 定义二叉决策树
class BinaryDecisionTree(object):
    ### 决策树初始参数
    def __init__(self, min_samples_split=2, min_gini_impurity=999,
                 max_depth=float("inf"), loss=None):
        # 根结点
        self.root = None  
        # 节点最小分裂样本数
        self.min_samples_split = min_samples_split
        # 节点初始化基尼不纯度
        self.mini_gini_impurity = min_gini_impurity
        # 树最大深度
        self.max_depth = max_depth
        # 基尼不纯度计算函数
        self.gini_impurity_calculation = None
        # 叶子节点值预测函数
        self._leaf_value_calculation = None
        # 损失函数
        self.loss = loss

    ### 决策树拟合函数
    def fit(self, X, y, loss=None):
        # 递归构建决策树
        self.root = self._build_tree(X, y)
        self.loss=None

    ### 决策树构建函数
    def _build_tree(self, X, y, current_depth=0):
        # 初始化最小基尼不纯度
        init_gini_impurity = 999
        # 初始化最佳特征索引和阈值
        best_criteria = None    
        # 初始化数据子集
        best_sets = None        
        
        if len(np.shape(y)) == 1:
            y = np.expand_dims(y, axis=1)

        # 合并输入和标签
        Xy = np.concatenate((X, y), axis=1)
        # 获取样本数和特征数
        n_samples, n_features = X.shape
        # 设定决策树构建条件
        # 训练样本数量大于节点最小分裂样本数且当前树深度小于最大深度
        if n_samples >= self.min_samples_split and current_depth <= self.max_depth:
            # 遍历计算每个特征的基尼不纯度
            for feature_i in range(n_features):
                # 获取第i特征的所有取值
                feature_values = np.expand_dims(X[:, feature_i], axis=1)
                # 获取第i个特征的唯一取值
                unique_values = np.unique(feature_values)

                # 遍历取值并寻找最佳特征分裂阈值
                for threshold in unique_values:
                    # 特征节点二叉分裂
                    Xy1, Xy2 = feature_split(Xy, feature_i, threshold)
                    # 如果分裂后的子集大小都不为0
                    if len(Xy1) > 0 and len(Xy2) > 0:
                        # 获取两个子集的标签值
                        y1 = Xy1[:, n_features:]
                        y2 = Xy2[:, n_features:]

                        # 计算基尼不纯度
                        impurity = self.impurity_calculation(y, y1, y2)

                        # 获取最小基尼不纯度
                        # 最佳特征索引和分裂阈值
                        if impurity < init_gini_impurity:
                            init_gini_impurity = impurity
                            best_criteria = {"feature_i": feature_i, "threshold": threshold}
                            best_sets = {
                                "leftX": Xy1[:, :n_features],   
                                "lefty": Xy1[:, n_features:],   
                                "rightX": Xy2[:, :n_features],  
                                "righty": Xy2[:, n_features:]   
                                }
        
        # 如果计算的最小不纯度小于设定的最小不纯度
        if init_gini_impurity < self.mini_gini_impurity:
            # 分别构建左右子树
            left_branch = self._build_tree(best_sets["leftX"], best_sets["lefty"], current_depth + 1)
            right_branch = self._build_tree(best_sets["rightX"], best_sets["righty"], current_depth + 1)
            return TreeNode(feature_i=best_criteria["feature_i"], threshold=best_criteria["threshold"], left_branch=left_branch, right_branch=right_branch)

        # 计算叶子计算取值
        leaf_value = self._leaf_value_calculation(y)
        return TreeNode(leaf_value=leaf_value)

    ### 定义二叉树值预测函数
    def predict_value(self, x, tree=None):
        if tree is None:
            tree = self.root
        # 如果叶子节点已有值，则直接返回已有值
        if tree.leaf_value is not None:
            return tree.leaf_value
        # 选择特征并获取特征值
        feature_value = x[tree.feature_i]
        # 判断落入左子树还是右子树
        branch = tree.right_branch
        if isinstance(feature_value, int) or isinstance(feature_value, float):
            if feature_value >= tree.threshold:
                branch = tree.left_branch
        elif feature_value == tree.threshold:
            branch = tree.right_branch
        # 测试子集
        return self.predict_value(x, branch)

    ### 数据集预测函数
    def predict(self, X):
        y_pred = [self.predict_value(sample) for sample in X]
        return y_pred

# CART分类树		
class ClassificationTree(BinaryDecisionTree):
    ### 定义基尼不纯度计算过程
    def _calculate_gini_impurity(self, y, y1, y2):
        p = len(y1) / len(y)
        gini = calculate_gini(y)
	# 基尼不纯度
        gini_impurity = p * calculate_gini(y1) + (1-p) * calculate_gini(y2)
        return gini_impurity
    
    ### 多数投票
    def _majority_vote(self, y):
        most_common = None
        max_count = 0
        for label in np.unique(y):
            # 统计多数
            count = len(y[y == label])
            if count > max_count:
                most_common = label
                max_count = count
        return most_common
    
    # 分类树拟合
    def fit(self, X, y):
        self.impurity_calculation = self._calculate_gini_impurity
        self._leaf_value_calculation = self._majority_vote
        super(ClassificationTree, self).fit(X, y)

		
### CART回归树
class RegressionTree(BinaryDecisionTree):
	# 计算方差减少量
    def _calculate_variance_reduction(self, y, y1, y2):
        var_tot = np.var(y, axis=0)
        var_y1 = np.var(y1, axis=0)
        var_y2 = np.var(y2, axis=0)
        frac_1 = len(y1) / len(y)
        frac_2 = len(y2) / len(y)
        # 计算方差减少量
        variance_reduction = var_tot - (frac_1 * var_y1 + frac_2 * var_y2)
        return sum(variance_reduction)

    # 节点值取平均
    def _mean_of_y(self, y):
        value = np.mean(y, axis=0)
        return value if len(value) > 1 else value[0]

    # 回归树拟合
    def fit(self, X, y):
        self.impurity_calculation = self._calculate_variance_reduction
        self._leaf_value_calculation = self._mean_of_y
        super(RegressionTree, self).fit(X, y)