本文实例为大家分享了基于信息增益的决策树归纳的Python实现代码，供大家参考，具体内容如下

# -*- coding: utf-8 -*-import numpy as npimport matplotlib.mlab as mlabimport matplotlib.pyplot as pltfrom copy import copy #加载训练数据#文件格式：属性标号，是否连续【yes|no】，属性说明attribute_file_dest = 'F:\\bayes_categorize\\attribute.dat'attribute_file = open(attribute_file_dest) #文件格式：rec_id,attr1_value,attr2_value,...，attrn_value,class_idtrainning_data_file_dest = 'F:\\bayes_categorize\\trainning_data.dat'trainning_data_file = open(trainning_data_file_dest) #文件格式：class_id,class_descclass_desc_file_dest = 'F:\\bayes_categorize\\class_desc.dat'class_desc_file = open(class_desc_file_dest) root_attr_dict = {}for line in attribute_file : line = line.strip() fld_list = line.split(',') root_attr_dict[int(fld_list[0])] = tuple(fld_list[1:]) class_dict = {}for line in class_desc_file : line = line.strip() fld_list = line.split(',') class_dict[int(fld_list[0])] = fld_list[1] trainning_data_dict = {}class_member_set_dict = {}for line in trainning_data_file : line = line.strip() fld_list = line.split(',') rec_id = int(fld_list[0]) a1 = int(fld_list[1]) a2 = int(fld_list[2]) a3 = float(fld_list[3]) c_id = int(fld_list[4]) if c_id not in class_member_set_dict : class_member_set_dict[c_id] = set() class_member_set_dict[c_id].add(rec_id) trainning_data_dict[rec_id] = (a1 , a2 , a3 , c_id) attribute_file.close()class_desc_file.close()trainning_data_file.close() class_possibility_dict = {}for c_id in class_member_set_dict : class_possibility_dict[c_id] = (len(class_member_set_dict[c_id]) + 0.0)/len(trainning_data_dict) #等待分类的数据data_to_classify_file_dest = 'F:\\bayes_categorize\\trainning_data_new.dat'data_to_classify_file = open(data_to_classify_file_dest)data_to_classify_dict = {}for line in data_to_classify_file : line = line.strip() fld_list = line.split(',') rec_id = int(fld_list[0]) a1 = int(fld_list[1]) a2 = int(fld_list[2]) a3 = float(fld_list[3]) c_id = int(fld_list[4]) data_to_classify_dict[rec_id] = (a1 , a2 , a3 , c_id)data_to_classify_file.close() '''决策树的表达结点的需求：1、指示出是哪一种分区 一共3种 一是离散穷举 二是连续有分裂点 三是离散有判别集合 零是叶子结点2、保存分类所需信息3、子结点列表每个结点用Tuple类型表示元素一是整形，取值123 分别对应两种分裂类型元素二是集合类型 对于1保存所有的离散值 对于2保存分裂点 对于3保存判别集合 对于0保存分类结果类标号元素三是dict key对于1来说是某个的离散值 对于23来说只有12两种 对于2来说1代表小于等于分裂点对于3来说1代表属于判别集合''' #对于一个成员列表，计算其熵#公式为 Info_D = - sum(pi * log2 (pi)) pi为一个元素属于Ci的概率，用|Ci|/|D|计算 ，对所有分类求和def get_entropy( member_list ) : #成员总数 mem_cnt = len(member_list) #首先找出member中所包含的分类 class_dict = {} for mem_id in member_list : c_id = trainning_data_dict[mem_id][3] if c_id not in class_dict : class_dict[c_id] = set() class_dict[c_id].add(mem_id) tmp_sum = 0.0 for c_id in class_dict : pi = ( len(class_dict[c_id]) + 0.0 ) / mem_cnt tmp_sum += pi * mlab.log2(pi) tmp_sum = -tmp_sum return tmp_sum def attribute_selection_method( member_list , attribute_dict ) : #先计算原始的熵 info_D = get_entropy(member_list) max_info_Gain = 0.0 attr_get = 0 split_point = 0.0 for attr_id in attribute_dict : #对于每一个属性计算划分后的熵 #信息增益等于原始的熵减去划分后的熵 info_D_new = 0 #如果是连续属性 if attribute_dict[attr_id][0] == 'yes' : #先得到memberlist中此属性的取值序列，把序列中每一对相邻项的中值作为划分点计算熵 #找出其中最小的，作为此连续属性的划分点 value_list = [] for mem_id in member_list : value_list.append(trainning_data_dict[mem_id][attr_id - 1]) #获取相邻元素的中值序列 mid_value_list = [] value_list.sort() #print value_list last_value = None for value in value_list : if value == last_value : continue if last_value is not None : mid_value_list.append((last_value+value)/2) last_value = value #print mid_value_list #对于中值序列做循环 #计算以此值做为划分点的熵 #总的熵等于两个划分的熵乘以两个划分的比重 min_info = 1000000000.0 total_mens = len(member_list) + 0.0 for mid_value in mid_value_list : #小于mid_value的mem less_list = [] #大于 more_list = [] for tmp_mem_id in member_list : if trainning_data_dict[tmp_mem_id][attr_id - 1] <= mid_value : less_list.append(tmp_mem_id) else : more_list.append(tmp_mem_id) sum_info = len(less_list)/total_mens * get_entropy(less_list) \ + len(more_list)/total_mens * get_entropy(more_list) if sum_info < min_info : min_info = sum_info split_point = mid_value info_D_new = min_info #如果是离散属性 else : #计算划分后的熵 #采用循环累加的方式 attr_value_member_dict = {} #键为attribute value , 值为memberlist for tmp_mem_id in member_list : attr_value = trainning_data_dict[tmp_mem_id][attr_id - 1] if attr_value not in attr_value_member_dict : attr_value_member_dict[attr_value] = [] attr_value_member_dict[attr_value].append(tmp_mem_id) #将每个离散值的熵乘以比重加到这上面 total_mens = len(member_list) + 0.0 sum_info = 0.0 for a_value in attr_value_member_dict : sum_info += len(attr_value_member_dict[a_value])/total_mens \ * get_entropy(attr_value_member_dict[a_value]) info_D_new = sum_info info_Gain = info_D - info_D_new if info_Gain > max_info_Gain : max_info_Gain = info_Gain attr_get = attr_id #如果是离散的 #print 'attr_get ' + str(attr_get) if attribute_dict[attr_get][0] == 'no' : return (1 , attr_get , split_point) else : return (2 , attr_get , split_point) #第三类先不考虑 def get_decision_tree(father_node , key , member_list , attr_dict ) : #最终的结果是新建一个结点，并且添加到father_node的sub_node_dict，对key为键 #检查memberlist 如果都是同类的，则生成一个叶子结点，set里面保存类标号 class_set = set() for mem_id in member_list : class_set.add(trainning_data_dict[mem_id][3]) if len(class_set) == 1 : father_node[2][key] = (0 , (1 , class_set) , {} ) return #检查attribute_list，如果为空，产生叶子结点，类标号为memberlist中多数元素的类标号 #如果几个类的成员等量，则打印提示，并且全部添加到set里面 if not attr_dict : class_cnt_dict = {} for mem_id in member_list : c_id = trainning_data_dict[mem_id][3] if c_id not in class_cnt_dict : class_cnt_dict[c_id] = 1 else : class_cnt_dict[c_id] += 1 class_set = set() max_cnt = 0 for c_id in class_cnt_dict : if class_cnt_dict[c_id] > max_cnt : max_cnt = class_cnt_dict[c_id] class_set.clear() class_set.add(c_id) elif class_cnt_dict[c_id] == max_cnt : class_set.add(c_id) if len(class_set) > 1 : print 'more than one class !' father_node[2][key] = (0 , (1 , class_set ) , {} ) return #找出最好的分区方案 ， 暂不考虑第三种划分方法 #比较所有离散属性和所有连续属性的所有中值点划分的信息增益 split_criterion = attribute_selection_method(member_list , attr_dict) #print split_criterion selected_plan_id = split_criterion[0] selected_attr_id = split_criterion[1] #如果采用的是离散属性做为分区方案，删除这个属性 new_attr_dict = copy(attr_dict) if attr_dict[selected_attr_id][0] == 'no' : del new_attr_dict[selected_attr_id] #建立一个结点new_node，father_node[2][key] = new_node #然后对new node的每一个key , sub_member_list， #调用 get_decision_tree(new_node , new_key , sub_member_list , new_attribute_dict) #实现递归 ele2 = ( selected_attr_id , set() ) #如果是1 , ele2保存所有离散值 if selected_plan_id == 1 : for mem_id in member_list : ele2[1].add(trainning_data_dict[mem_id][selected_attr_id - 1]) #如果是2，ele2保存分裂点 elif selected_plan_id == 2 : ele2[1].add(split_criterion[2]) #如果是3则保存判别集合，先不管 else : print 'not completed' pass new_node = ( selected_plan_id , ele2 , {} ) father_node[2][key] = new_node #生成KEY，并递归调用 if selected_plan_id == 1 : #每个attr_value是一个key attr_value_member_dict = {} for mem_id in member_list : attr_value = trainning_data_dict[mem_id][selected_attr_id - 1 ] if attr_value not in attr_value_member_dict : attr_value_member_dict[attr_value] = [] attr_value_member_dict[attr_value].append(mem_id) for attr_value in attr_value_member_dict : get_decision_tree(new_node , attr_value , attr_value_member_dict[attr_value] , new_attr_dict) pass elif selected_plan_id == 2 : #key 只有12 , 小于等于分裂点的是1 ， 大于的是2 less_list = [] more_list = [] for mem_id in member_list : attr_value = trainning_data_dict[mem_id][selected_attr_id - 1 ] if attr_value <= split_criterion[2] : less_list.append(mem_id) else : more_list.append(mem_id) #if len(less_list) != 0 : get_decision_tree(new_node , 1 , less_list , new_attr_dict) #if len(more_list) != 0 : get_decision_tree(new_node , 2 , more_list , new_attr_dict) pass #如果是3则保存判别集合，先不管 else : print 'not completed' pass def get_class_sub(node , tp ) : # attr_id = node[1][0] plan_id = node[0] key = 0 if plan_id == 0 : return node[1][1] elif plan_id == 1 : key = tp[attr_id - 1] elif plan_id == 2 : split_point = tuple(node[1][1])[0] attr_value = tp[attr_id - 1] if attr_value <= split_point : key = 1 else : key = 2 else : print 'error' return set() return get_class_sub(node[2][key] , tp ) def get_class(r_node , tp) : #tp为一组属性值 if r_node[0] != -1 : print 'error' return set() if 1 in r_node[2] : return get_class_sub(r_node[2][1] , tp) else : print 'error' return set() if __name__ == '__main__' : root_node = ( -1 , set() , {} ) mem_list = trainning_data_dict.keys() get_decision_tree(root_node , 1 , mem_list , root_attr_dict ) #测试分类器的准确率 diff_cnt = 0 for mem_id in data_to_classify_dict : c_id = get_class(root_node , data_to_classify_dict[mem_id][0:3]) if tuple(c_id)[0] != data_to_classify_dict[mem_id][3] : print tuple(c_id)[0] print data_to_classify_dict[mem_id][3] print 'different' diff_cnt += 1 print diff_cnt

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