c45决策树模型代码

C4.5决策树是一种经典的机器学习算法，用于分类和回归任务。下面是一个简单的C4.5决策树模型的代码示例：

import numpy as np

class Node:
    def __init__(self, feature=None, threshold=None, label=None):
        self.feature = feature  # 分裂特征的索引
        self.threshold = threshold  # 分裂特征的阈值
        self.label = label  # 叶节点的类别
        self.left = None  # 左子树
        self.right = None  # 右子树

class C45DecisionTree:
    def __init__(self, min_samples_split=2, max_depth=float('inf')):
        self.min_samples_split = min_samples_split  # 分裂所需的最小样本数
        self.max_depth = max_depth  # 树的最大深度

    def _calculate_entropy(self, y):
        classes, counts = np.unique(y, return_counts=True)
        probabilities = counts / len(y)
        entropy = -np.sum(probabilities * np.log2(probabilities))
        return entropy

    def _calculate_information_gain(self, X, y, feature, threshold):
        left_mask = X[:, feature] <= threshold
        right_mask = X[:, feature] > threshold
        left_entropy = self._calculate_entropy(y[left_mask])
        right_entropy = self._calculate_entropy(y[right_mask])
        parent_entropy = self._calculate_entropy(y)
        information_gain = parent_entropy - (len(y[left_mask]) / len(y) * left_entropy) - (len(y[right_mask]) / len(y) * right_entropy)
        return information_gain

    def _split(self, X, y):
        best_gain = 0
        best_feature = None
        best_threshold = None

        for feature in range(X.shape[1]):
            thresholds = np.unique(X[:, feature])
            for threshold in thresholds:
                gain = self._calculate_information_gain(X, y, feature, threshold)
                if gain > best_gain:
                    best_gain = gain
                    best_feature = feature
                    best_threshold = threshold

        return best_feature, best_threshold

    def _build_tree(self, X, y, depth):
        if len(np.unique(y)) == 1:  # 所有样本属于同一类别
            return Node(label=y[0])

        if len(y) < self.min_samples_split or depth == self.max_depth:  # 达到停止分裂的条件
            classes, counts = np.unique(y, return_counts=True)
            label = classes[np.argmax(counts)]
            return Node(label=label)

        feature, threshold = self._split(X, y)
        left_mask = X[:, feature] <= threshold
        right_mask = X[:, feature] > threshold

        left_subtree = self._build_tree(X[left_mask], y[left_mask], depth + 1)
        right_subtree = self._build_tree(X[right_mask], y[right_mask], depth + 1)

        return Node(feature=feature, threshold=threshold, left=left_subtree, right=right_subtree)

    def fit(self, X, y):
        self.root = self._build_tree(X, y, depth=0)

    def _predict_single(self, x, node):
        if node.label is not None:  # 叶节点
            return node.label

        if x[node.feature] <= node.threshold:
            return self._predict_single(x, node.left)
        else:
            return self._predict_single(x, node.right)

    def predict(self, X):
        predictions = []
        for x in X:
            prediction = self._predict_single(x, self.root)
            predictions.append(prediction)
        return np.array(predictions)

这段代码实现了一个简单的C4.5决策树模型，包括节点类`Node`和决策树类`C45DecisionTree`。`fit`方法用于训练模型，`predict`方法用于预测新样本的类别。