python

　　算法流程参考了《统计学习与方法》

import numpy as np
import pandas as pd
from graphviz import Digraph


class BaseTree(object):
    def __init__(self, feature, label, title=None):
        """
        树基本属性
        :param feature: 特征列
        :param label: 目标列
        :param title: 标题列
        """
        self.root = {}
        self.feature = feature
        self.label = label
        self.title = title
        self.n_classes = tuple(set(label))
        self.n_features = len(feature)

        self._build_tree_(self.root, self.label, self.feature, self.title)

    def _build_tree_(self, n, label, feature, title):
        """
        递归构建决策树
        :param n: 对每一层来说该参数是树的当前节点 字典树
        :param label: 每一层递归中目标列会由于上一层中做出的选择而不断减小
        :param feature: 每一层递归中特征也会由于前一层中做出的选择而不断减小 对于一条路径来说 会减少特征列
        :param title: 标题原理同 label
        :return: 
        """
        if feature is not None:
            gain_feature = self._solve_gain_(label, feature, tuple(set(label)), len(feature))
            select_feature = np.argmax(gain_feature)
            selected_feature = feature[:, select_feature]
            states = set(selected_feature)
            n[title[select_feature]] = {}
            feature = np.delete(feature, select_feature, axis=1)
            title_ = np.delete(title, select_feature)
            for i, _ in enumerate(states):
                inx = np.where(selected_feature == _)[0]
                label_ = label[inx]
                if len(set(label_)) == 1:
                    n[title[select_feature]][str(label_[0])] = {}
                    continue
                feature_ = feature[inx]
                self._build_tree_(n[title[select_feature]], label_, feature_, title_)

    @staticmethod
    def _solve_entropy_(label, n_classes, n_features):
        """
        计算经验熵
        :param label: 
        :param n_classes: 
        :param n_features: 
        :return: 
        """
        sigma = 0.
        for _ in n_classes:
            p = len(np.where(label == _)[0]) / n_features
            sigma += (p * np.log2(p) if p != 0 else 0)
        return -sigma

    def _solve_conditional_entropy_(self, label, feature, n_classes):
        """
        计算条件熵
        :param label: 
        :param feature: 
        :param n_classes: 
        :return: 
        """
        group_states = [tuple(set(_)) for _ in feature.transpose()]
        n_features = len(feature)
        ans = []
        for i, branch in enumerate(group_states):
            res = 0.
            for state in branch:
                inx = np.where(feature[:, i] == state)[0]
                n_f = len(inx)
                sigma = self._solve_entropy_(label[inx], n_classes, n_f)
                res += n_f / n_features * sigma
            ans.append(res)
        return np.array(ans)

    def _solve_gain_(self, label, feature, n_classes, n_features):
        """
        计算信息增益
        :param label: 
        :param feature: 
        :param n_classes: 
        :param n_features: 
        :return: 
        """
        return self._solve_entropy_(label, n_classes, n_features)
               - self._solve_conditional_entropy_(label, feature, n_classes)

    def get_root(self):
        """
        获取决策树
        :return: 
        """
        return self.root


class DecisionTree(object):
    def __init__(self, title=None):
        self.tree = None
        self.title = title
        self.que = []
        self.nums = []
        self.count = 1

    def fit(self, X, y):
        """
        拟合接口
        :param X: 数据集的特征
        :param y: 数据集的目标
        :return: 
        """
        self.tree = BaseTree(X, y, self.title)

    def predict(self, X):
        pass

    def decision_tree_struct(self):
        """
        获取决策树
        :return: 
        """
        return self.tree.get_root()

    def _travl_dict_(self, dot, node):
        """
        层序遍历字典树以生成 graph
        :param dot: 
        :param node: 
        :return: 
        """
        for _ in node.keys():
            s = str(self.nums.pop(0) if self.nums else '0')
            self.que.append(node[_])
            for i, k in enumerate(node[_].keys()):
                dot.edge(_ + '_' + s, k + '_' + str(self.count),
                         label='Yes' if i & 1 else 'No')
                self.nums.append(self.count)
                self.count += 1
        if self.que:
            self._travl_dict_(dot, self.que.pop(0))

    def generate_graph(self):
        """
        生成决策树图
        :return: 
        """
        dot = Digraph(name='tree', node_attr={'shape': 'circle'}, format='png')
        self._travl_dict_(dot, self.tree.get_root())
        dot.render('decision.gv', view=True)


data = pd.read_csv('data.csv', encoding='gbk')
y = data['index'].astype(np.int)
train_x = data.drop(['index', 'name'], axis=1)
for _ in train_x.keys():
    train_x[_] = train_x[_].map({'是': 1, '否': 0})
title = list(train_x.keys())

dt = DecisionTree(title)
X = train_x.values.reshape((-1, len(title)))
dt.fit(X, y.values)
d = dt.decision_tree_struct()
print(d)
dt.generate_graph()

　　因为没有设置 graphviz 中文字体，所以无法正常显示，使用 index 代替了。
　　测试数据：

　　graphviz 查看生成的决策树结构：