決定ツリーID 3アルゴリズム実装

決定ツリーのID 3アルゴリズムは情報利得に基づいて最適な特徴を選択し,そこで自分で実現し,直接コードをアップロードする.

  1 """
  2 CreateTime    : 2019/3/3 22:19
  3 Author        : X
  4 Filename      : decision_tree.py
  5 """
  6 
  7 import pandas as pd
  8 from math import log2
  9 
 10 
 11 def create_data_set():
 12     """Create 8 * 3 data set. two feature."""
 13     data_set = [['long', 'thick', 'man'],
 14                 ['short', 'thick', 'man'],
 15                 ['short', 'thick', 'man'],
 16                 ['long', 'thin', 'woman'],
 17                 ['short', 'thin', 'woman'],
 18                 ['short', 'thick', 'woman'],
 19                 ['long', 'thick', 'woman'],
 20                 ['long', 'thick', 'woman']]
 21     labels = ['hair', 'sound']
 22     return data_set, labels
 23 
 24 
 25 def calculate_entropy(data_set):
 26     """Calculate entropy by data set label.
 27        formula: H(X) = -3/8*log(3/8, 2) - -5/8*log(5/8, 2)"""
 28     data_len = data_set.shape[0]
 29     entropy = 0
 30     for size in data_set.groupby(data_set.iloc[:, -1]).size():
 31         p_label = size/data_len
 32         entropy -= p_label * log2(p_label)
 33     return entropy
 34 
 35 
 36 def get_best_feature(data_set):
 37     """Get the best feature by infoGain.
 38        formula: InfoGain(X, Y) = H(X) - H(X|Y)
 39                 H(X|Y) = sum(P(X) * H(Yx))"""
 40     best_feature = -1
 41     base_entropy = calculate_entropy(data_set)
 42     best_info_gain = 0
 43     len_data = data_set.shape[0]
 44     for i in range(data_set.shape[1] - 1):
 45         new_entropy = 0
 46         for _, group in data_set.groupby(data_set.iloc[:, i]):
 47             p_label = group.shape[0]/len_data
 48             new_entropy += p_label * calculate_entropy(group)
 49         info_gain = base_entropy - new_entropy
 50         if info_gain > best_info_gain:
 51             best_feature = i
 52             best_info_gain = info_gain
 53     return best_feature
 54 
 55 
 56 def majority_cnt(class_list):
 57     """When only class label, return the max label."""
 58     majority_class = class_list.groupby(
 59         class_list.iloc[:, -1]).size().sort_values().index[-1]
 60     return majority_class
 61 
 62 
 63 def create_tree(data_set, labels):
 64     """data_set: DataFrame"""
 65     class_list = data_set.values[:, -1]
 66     class_list_set = set(class_list)
 67     if len(class_list_set) == 1:
 68         return list(class_list)[0]
 69     if len(data_set.values[0]) == 1:
 70         return majority_cnt(data_set)
 71     best_feature = get_best_feature(data_set)
 72     best_feature_label = labels[best_feature]
 73     del labels[best_feature]
 74     my_tree = {best_feature_label: {}}
 75     for name, group in data_set.groupby(data_set.iloc[:, best_feature]):
 76         group.drop(columns=[best_feature], axis=1, inplace=True)
 77         my_tree[best_feature_label][name] = create_tree(group, labels)
 78     return my_tree
 79 
 80 
 81 def classify(test_data, my_tree):
 82     if not test_data:
 83         return 'Not found class.'
 84     for key, tree in my_tree.items():
 85         if key != test_data[0]:
 86             return classify(test_data, tree)
 87         else:
 88             if isinstance(tree, dict):
 89                 del test_data[0]
 90                 return classify(test_data, tree)
 91             else:
 92                 return tree
 93 
 94 
 95 if __name__ == '__main__':
 96     DATA_SET, LABELS = create_data_set()
 97     TREE = create_tree(pd.DataFrame(DATA_SET), LABELS)
 98     import json
 99     print(json.dumps(TREE, indent=4))
100     print(classify(["thick", "long"], TREE))

C4.5アルゴリズムは、情報利得率に基づいて最適特徴を選択するものであり、すなわちID 3アルゴリズムに基づいて情報利得率を求めればよく、情報利得をlabelベースの特徴Xのエントロピーで除算する.
ここでは実装コードは与えられず,自分で実装することは理解を深めることを意味する.