Python机器学习算法之决策树算法的实现与优缺点

import numpy as np
import math
from collections import Counter

# 创建数据
def create_data():
    X1 = np.random.rand(50, 1)*100
    X2 = np.random.rand(50, 1)*100
    X3 = np.random.rand(50, 1)*100
    
    def f(x):
        return 2 if x > 70 else 1 if x > 40 else 0
    
    y = X1 + X2 + X3
    Y = y > 150
    Y = Y + 0
    r = map(f, X1)
    X1 = list(r)
    
    r = map(f, X2)
    X2 = list(r)
    
    r = map(f, X3)
    X3 = list(r)
    x = np.c_[X1, X2, X3, Y]
    return x, ['courseA', 'courseB', 'courseC']


# 计算集合信息熵的函数
def calculate_info_entropy(dataset):
    n = len(dataset)
    # 我们用Counter统计一下Y的数量
    labels = Counter(dataset[:, -1])
    entropy = 0.0
    # 套用信息熵公式
    for k, v in labels.items():
        prob = v / n
        entropy -= prob * math.log(prob, 2)
    return entropy

# 实现拆分函数
def split_dataset(dataset, idx):
  	# idx是要拆分的特征下标
    splitData = defaultdict(list)
    for data in dataset:
      	# 这里删除了idx这个特征的取值，因为用不到了
        splitData[data[idx]].append(np.delete(data, idx))
    return list(splitData.values()), list(splitData.keys())

# 实现特征的选择函数
def choose_feature_to_split(dataset):
    n = len(dataset[0])-1
    m = len(dataset)
    # 切分之前的信息熵
    entropy = calculate_info_entropy(dataset)
    bestGain = 0.0
    feature = -1
    for i in range(n):
      	# 根据特征i切分
        split_data, _ = split_dataset(dataset, i)
        new_entropy = 0.0
        # 计算切分后的信息熵
        for data in split_data:
            prob = len(data) / m
            new_entropy += prob * calculate_info_entropy(data)
        # 获取信息增益
        gain = entropy - new_entropy
        if gain > bestGain:
            bestGain = gain
            feature = i
    return feature

# 决策树创建函数
def create_decision_tree(dataset, feature_names):
    dataset = np.array(dataset)
    counter = Counter(dataset[:, -1])
    # 如果数据集值剩下了一类，直接返回
    if len(counter) == 1:
        return dataset[0, -1]
    
    # 如果所有特征都已经切分完了，也直接返回
    if len(dataset[0]) == 1:
        return counter.most_common(1)[0][0]
    
    # 寻找最佳切分的特征
    fidx = choose_feature_to_split(dataset)
    fname = feature_names[fidx]
    
    node = {fname: {}}
    feature_names.remove(fname)
    
    # 递归调用，对每一个切分出来的取值递归建树
    split_data, vals = split_dataset(dataset, fidx)
    for data, val in zip(split_data, vals):
        node[fname][val] = create_decision_tree(data, feature_names[:])
    return node

# 决策树节点预测函数
def classify(node, feature_names, data):
  	# 获取当前节点判断的特征
    key = list(node.keys())[0]
    node = node[key]
    idx = feature_names.index(key)
    
    # 根据特征进行递归
    pred = None
    for key in node:
      	# 找到了对应的分叉
        if data[idx] == key:
          	# 如果再往下依然还有子树，那么则递归，否则返回结果
            if isinstance(node[key], dict):
                pred = classify(node[key], feature_names, data)
            else:
                pred = node[key]
                
    # 如果没有对应的分叉，则找到一个分叉返回
    if pred is None:
        for key in node:
            if not isinstance(node[key], dict):
                pred = node[key]
                break
    return pred