python实现基于信息增益的决策树归纳

# -*- coding: utf-8 -*-
import numpy as np
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
from 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_id
trainning_data_file_dest = 'f:\\bayes_categorize\\trainning_data.dat'
trainning_data_file = open(trainning_data_file_dest)
 
#文件格式：class_id,class_desc
class_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