# 决策树ID3算法python实现

HelloData

step1:计算香农熵

``````from math import log
import operator

# 计算香农熵
def calculate_entropy(data):
label_counts = {}
for feature_data in data:
laber = feature_data[-1]  # 最后一行是laber
if laber not in label_counts.keys():
label_counts[laber] = 0
label_counts[laber] += 1

count = len(data)
entropy = 0.0

for key in label_counts:
prob = float(label_counts[key]) / count
entropy -= prob * log(prob, 2)
return entropy``````

step2.计算某个feature的信息增益的方法

``````# 计算某个feature的信息增益
# index:要计算信息增益的feature 对应的在data 的第几列
# data 的香农熵
def calculate_relative_entropy(data, index, entropy):
feat_list = [number[index] for number in data]  # 得到某个特征下所有值（某列）
uniqual_vals = set(feat_list)
new_entropy = 0
for value in uniqual_vals:
sub_data = split_data(data, index, value)
prob = len(sub_data) / float(len(data))
new_entropy += prob * calculate_entropy(sub_data)  # 对各子集香农熵求和
relative_entropy = entropy - new_entropy  # 计算信息增益
return relative_entropy``````

step3.选择最大信息增益的feature

``````# 选择最大信息增益的feature
def choose_max_relative_entropy(data):
num_feature = len(data[0]) - 1
base_entropy = calculate_entropy(data)#香农熵
best_infor_gain = 0
best_feature = -1
for i in range(num_feature):
info_gain=calculate_relative_entropy(data, i, base_entropy)
#最大信息增益
if (info_gain > best_infor_gain):
best_infor_gain = info_gain
best_feature = i

return best_feature``````

step4.构建决策树

``````def create_decision_tree(data, labels):
class_list=[example[-1] for example in data]
# 类别相同，停止划分
if class_list.count(class_list[-1]) == len(class_list):
return class_list[-1]
# 判断是否遍历完所有的特征时返回个数最多的类别
if len(data[0]) == 1:
return most_class(class_list)
# 按照信息增益最高选取分类特征属性
best_feat = choose_max_relative_entropy(data)
best_feat_lable = labels[best_feat] # 该特征的label
decision_tree = {best_feat_lable: {}} # 构建树的字典
del(labels[best_feat]) # 从labels的list中删除该label
feat_values = [example[best_feat] for example in data]
unique_values = set(feat_values)
for value in unique_values:
sub_lables=labels[:]
# 构建数据的子集合，并进行递归
decision_tree[best_feat_lable][value] = create_decision_tree(split_data(data, best_feat, value), sub_lables)
return decision_tree``````

``````# 当遍历完所有的特征时返回个数最多的类别
def most_class(classList):
class_count={}
for vote in classList:
if vote not in class_count.keys():class_count[vote]=0
class_count[vote]+=1
sorted_class_count=sorted(class_count.items,key=operator.itemgetter(1),reversed=True)
return sorted_class_count[0][0]

# 工具函数输入三个变量（待划分的数据集，特征，分类值）返回不含划分特征的子集
def split_data(data, axis, value):
ret_data=[]
for feat_vec in data:
if feat_vec[axis]==value :
reduce_feat_vec=feat_vec[:axis]
reduce_feat_vec.extend(feat_vec[axis+1:])
ret_data.append(reduce_feat_vec)
return ret_data``````

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