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.csdn.net/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。
该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.csdn.net/leafage_m/article/details/80137305
文章来源: 决策树―西瓜书课后题4.3―MATLAB代码