决策树—西瓜书课后题4.3—MATLAB代码

题目：编程实现基于信息熵进行划分选择的决策树算法，并为西瓜数据集3.0上（P84表4.3）中的数据生成一棵决策树；

代码：

clc;
clear all;

[num,txt]=xlsread('D:\机器学习\WaterMelon_3.0.xlsx');
data=txt(2:end,[2:7,10]);
[rows,cols] = size(data);
for i=1:rows
    for j=1:cols
        %离散值：Discrete_value
        D_value(i,j)=string2num(data(i,j));
    end
end
%连续值：Continue_value
C_value=[num(:,[8,9]),D_value(:,7)];
make_tree(D_value,C_value);

%%
%建树
function  make_tree(data,data1)

  [m,n] = size(data);
  [m1,n1] = size(data1);
  disp('/');
  disp('待分数据集');
  disp(data);
  disp(data1);
  label = data(:,n);
  same_class_num = length(find(data(:,n) ==  label(1,1)));
  %退出递归条件
  if same_class_num  == m ||( n == 1 && n1 == 1)
     disp('划分后的数据子集');
     disp(data);
     disp(data1);
     return;
  end
  [best_feature,midle_data]= choose_bestfeature(data,data1);
  if best_feature<=6
     disp("待分数据集的最佳特征序号为");
     disp(best_feature);
     disp("属于待分离散数据集");
  elseif best_feature>6
         disp("待分数据集的最佳特征序号为");
         disp(best_feature-6);
         disp("属于待分连续数据集");
         disp("最佳增益时的二分点值");
         disp(midle_data);
  end
  %选中特征为离散特征时递归处理
  if best_feature<=6
     C2D_value=ones(size(data1,1),1);
     featvalue = unique(data(:,best_feature));
     featvalue_num = length(featvalue);
     for i=1:featvalue_num
         [subdata,subdata1] = splitData1(data,data1,best_feature,featvalue(i,1),C2D_value);
         make_tree(subdata,subdata1);
     end
  end
  %选中特征为离散特征时递归处理
  if best_feature>6
     C2D_value=C2Dtranlate(data1,best_feature-6,midle_data);
     featvalue = unique(C2D_value);
     featvalue_num = length(featvalue);
     for i=1:featvalue_num
         [subdata,subdata1] = splitData1(data,data1,best_feature,featvalue(i,1),C2D_value);
         make_tree(subdata,subdata1);
     end
  end
  
end

%%
%选择最佳特征
function [best_feature,midle_data]= choose_bestfeature(data,data1)

  [m,n] = size(data);
  Root_entropy = calc_entropy(data);
  midle_data = 0;
  best_gain = 0;
  best_feature = 0;
  
% 对于每一列特征
  for j=1:n-1
      feature_value = unique(data(:,j));
      num_f = length(feature_value);
      new_entropy = 0;
      for i=1:num_f
          subdata=splitData(data,j,feature_value(i,1));
          [m_s,n_s]=size(subdata);
          prob=m_s./m;
          new_entropy = new_entropy + prob * calc_entropy(subdata);
      end
      inf_gain=Root_entropy - new_entropy;
      if inf_gain > best_gain
        best_gain = inf_gain;
        best_feature = j;
      end
   end
   if size(data1,2)>=2
      for i=1:size(data1,2)-1
          [C_best_gain ,midle_data]=C_value_bestgain(data1,i);
          if C_best_gain > best_gain
             best_gain =  C_best_gain;
             best_feature = i+6;
         end
      end
   end

end
%%
%计算连续值特征的信息熵值
function [best_gain,midle_data]= C_value_bestgain(C_value,j)

  [m,n]=size(C_value);
  C_value_sort=sortrows(C_value,j);
  best_gain = 0;
  for i= 1:m-1
      midle_seris(i,j) = (C_value_sort(i,j)+C_value_sort(i+1,j))/2; 
      C2D_value = C2Dtranlate(C_value,j,midle_seris(i,j));
      C2D_value1 =[C2D_value,C_value(:,n)];
      [m1,n1] = size(C2D_value1);
      baseentropy = calc_entropy(C_value);
      feature_value = unique(C2D_value1(:,j));
      num_f = length(feature_value);
      new_entropy = 0;
      for t= 1:num_f
        subdata = splitData(C2D_value1 , j, feature_value(t,1));
        [m_s,n_s] = size(subdata);
        prob = m_s./m1;
        new_entropy = new_entropy + prob * calc_entropy(subdata);
      end
      inf_gain = baseentropy - new_entropy;
    
      if inf_gain > best_gain
         best_gain = inf_gain ; 
         midle_data = midle_seris(i,j);
      end  
  end
  
end

%%
%计算信息熵
function [entropy]= calc_entropy(data)

  [m,n] = size(data);
  label_value = data(:,n);
  label = unique(label_value);
  label_number = zeros(length(label),2);
  label_number(:,1) = label';
  for i= 1:length(label)
      label_number(i,2) = sum(label_value == label(i));
  end
  label_number (:,2) = label_number(:,2) ./ m;
  entropy = 0;
  entropy = sum(-label_number(:,2).*log2 (label_number(:,2)));
  
end

%%
%分离数据集为子数据集（对离散数据集和连续数据集），用于递归运算
function [subdata,subdata1]= splitData1(data,data1,j,value,c2d_value)

  subdata = data;
  subdata1 = data1;
  if j<=6
     subdata(:,j) = [];
     k = 0;
     for i= 1:size(data,1)
         if data(i,j) ~= value
            subdata(i-k,:) =[];
            subdata1(i-k,:) =[];
            k = k + 1;
         end
     end
     
   elseif j>6
          j=j-6;
          subdata1(:,j) = [];
          k = 0;
          for i= 1:size(data1,1)
              if c2d_value(i) ~= value
              subdata1(i-k,:) =[];
              subdata(i-k,:) =[];
              k = k + 1;
              end    
          end
    end
    
end

%%
%分离数据集为子数据集（对离散数据集），用于过程计算
function [subdata]= splitData(data, j, value)

  subdata = data;
  subdata(:,j) = [];
  k = 0;
  for i= 1:size(data,1)
      if data(i,j) ~= value
         subdata(i-k,:) =[];
         k = k + 1;
      end
  end
  
end

%%
%连续值转化离散值
function  [C2D_value]= C2Dtranlate(C_value,j,midle_data)

  [m,n] = size(C_value);
  for k= 1:m
      if C_value(k,j)< midle_data
         C2D_value(k,j)=0;
      elseif C_value(k,j)> midle_data
             C2D_value(k,j)=1;   
      end     
  end
  
end

%%
%处理原字符数据为矩阵表达
function num= string2num(string)

   if strcmp(string,'浅白') ||strcmp(string,'硬挺') ||strcmp(string,'清脆')||strcmp(string,'模糊')||strcmp(string,'平坦')||strcmp(string,'软粘')||strcmp(string,'否')
      num=0;
   elseif strcmp(string,'青绿') ||strcmp(string,'稍蜷') ||strcmp(string,'沉闷')||strcmp(string,'稍糊')||strcmp(string,'稍凹')||strcmp(string,'硬滑')||strcmp(string,'是')
      num=1;
   else
      num=2;
   end
   
end

生成决策树：

 

西瓜数据集Excel文件到这里去找：

https://blog.youkuaiyun.com/macunshi/article/details/80756016

我的代码是参考这位https://www.cnblogs.com/Kermit-Li/p/4503427.html博客里代码改进的，原ID3只能处理如色泽、根蒂、敲声、纹理等离散值，不能处理密度、含糖率这样的连续值，我在原代码的基础上增加了对连续值的处理。

上面的博客里有对离散值属性信息增益的计算过程，而对连续值的计算过程详解见这位的博客：

https://blog.youkuaiyun.com/leafage_m/article/details/80137305