決策樹 ID3演算法

id3演算法通過計算每個屬性的資訊增益，認為資訊增益越大屬性越優，每次劃分選取資訊增益最大的屬性為劃分標準，重複這個過程，直到構成一棵決策樹。資訊熵是描述事件給我們的驚訝程度，如果所有事件的概率均等，那熵值大，驚訝程度低。如果有一事件的概率極高而其他極低，熵值便低，驚訝程度大。其計算公式如下：

資訊增益描述某個事件發生前後資訊熵的變化。

在id3裡面可以理解為引入特徵之後資訊熵的變化（這句話純屬個人理解，如果不對請指正）。其計算公式如下：

其中n表示分類的數目。data.txt

young myope no reduced no lenses young myope no normal soft young myope yes reduced no lenses young myope yes normal hard young hyper no reduced no lenses young hyper no normal soft young hyper yes reduced no lenses young hyper yes normal hard pre myope no reduced no lenses pre myope no normal soft pre myope yes reduced no lenses pre myope yes normal hard pre hyper no reduced no lenses pre hyper no normal soft pre hyper yes reduced no lenses pre hyper yes normal no lenses presbyopic myope no reduced no lenses presbyopic myope no normal no lenses presbyopic myope yes reduced no lenses presbyopic myope yes normal hard presbyopic hyper no reduced no lenses presbyopic hyper no normal soft presbyopic hyper yes reduced no lenses presbyopic hyper yes normal no lenses

label.txt

age	prescript	astigmatic	tearrate

#encoding: utf-8
import math
def cal_shannon_ent(data):
data_num = len(data)
cnt = {}
for feat_vec in data:
tmp_class = feat_vec[-1]
if tmp_class not in cnt.keys():
cnt[tmp_class] = 0
cnt[tmp_class] += 1
shannon_ent = 0.0
for key in cnt:
p = float(cnt[key]) / data_num
shannon_ent -= p * math.log(p, 2)
return shannon_ent
def split_data(data, index, value):
ret_data = 
for feat_vec in data:
if feat_vec[index] == value:
remain_feat_vec = feat_vec[:index]
remain_feat_vec.extend(feat_vec[index + 1:])
return ret_data
def get_best_feat(data):
base_ent = cal_shannon_ent(data)
feat_num = len(data[0]) - 1
best_info_gain = 0.0
best_feat = -1
for i in range(feat_num):
values = [j[i] for j in data]
unique_values = set(values)
new_ent = 0.0
for value in unique_values:
sub_data = split_data(data, i, value)
p = float(len(sub_data)) / len(data)
new_ent += p * cal_shannon_ent(sub_data) #
info_gain = base_ent - new_ent
if info_gain > best_info_gain:
best_info_gain = info_gain
best_feat = i
return best_feat
def get_major_class(class_list):
cnt = {}
maxx = -1
major_class = -1
for _class in class_list:
if _class not in cnt.keys():
cnt[_class] = 0
cnt[_class] += 1
if(cnt[_class] > maxx):
maxx = cnt[_class]
major_class = _class
return major_class
def create_tree_id3(data, label):
class_list = [i[-1] for i in data]
if class_list.count(class_list[0]) == len(class_list):
return class_list[0]
if len(data[0]) == 1:
return get_major_class(class_list)
best_feat = get_best_feat(data)
best_feat_label = label[best_feat]
ret_tree = }
del(label[best_feat])
values = [i[best_feat] for i in data]
unique_values = set(values)
for value in unique_values:
sub_label = label[:] #
ret_tree[best_feat_label][value] = create_tree_id3(split_data(data, best_feat, value), sub_label)
return ret_tree
if __name__=="__main__":
# data = [[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
# label = ['no su***cing', 'flippers']
fr = open('data.txt')
data = [line.strip().split('\t') for line in fr.readlines()]
fr = open('label.txt')
label = [line.strip().split('\t') for line in fr.readlines()][0]
print create_tree_id3(data, label)

}, 'myope': 'hard'}}, 'no': }, 'young': 'soft'}}}}}}

決策樹 ID3演算法

決策樹 ID3演算法

決策樹ID3演算法

決策樹 ID3演算法

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