ID3很不错的讲解（matlab程序实现）

clc;
clear all;
close all;


%% 导入数据
%data = [1,1,1;1,1,1;1,0,0;0,1,0;0,1,0];

data = [0,2,0,0,0;
    0,2,0,1,0;
    1,2,0,0,1;
    2,1,0,0,1;
    2,0,1,0,1;
    2,0,1,1,0;
    1,0,1,1,1;
    0,1,0,0,0;
    0,0,1,0,1;
    2,1,1,0,1;
    0,1,1,1,1;
    1,1,0,1,1;
    1,2,1,0,1;
    2,1,0,1,0];
% data = {‘sunny‘,‘hot‘,‘high‘,‘week‘,‘no‘;
%              ‘sunny‘,‘hot‘,‘high‘,‘strong‘,‘no‘;
%              ‘overcast‘,‘hot‘,‘high‘,‘week‘,‘yes‘;
%              ‘rain‘,‘midd‘,‘high‘,‘week‘,‘yes‘;
%              ‘rain‘,‘cool‘,‘nomal‘,‘week‘,‘yes‘;
%              ‘rain‘,‘cool‘,‘nomal‘,‘strong‘,‘no‘;
%              ‘overcast‘,‘cool‘,‘nomal‘,‘strong‘,‘yes‘;
%              ‘sunny‘,‘midd‘,‘high‘,‘week‘,‘no‘;
%              ‘sunny‘,‘cool‘,‘nomal‘,‘week‘,‘yes‘;
%              ‘rain‘,‘midd‘,‘nomal‘,‘week‘,‘yes‘;
%              ‘sunny‘,‘midd‘,‘nomal‘,‘strong‘,‘yes‘;
%              ‘overcast‘,‘midd‘,‘high‘,‘strong‘,‘yes‘;
%              ‘overcast‘,‘hot‘,‘nomal‘,‘week‘,‘yes‘;
%              ‘rain‘,‘midd‘,‘high‘,‘strong‘,‘no‘};
%sunuy-0,overcast-1,rain-2;--hot-2,midd-1,cool-2---high-0,nomal-1--week-0,strong-1,no-0,yes-1

%% 生成决策树
make_tree(data);

function  make_tree(train_data)
%input                 train_data          训练数据
%output               

[m,n] = size(train_data);
disp(‘original data‘);
disp(train_data);
class_list = train_data(:,n);
class_first = 1;

for i = 2:m
   if train_data(i,n) ==  class_list(1,:)
%    if strcmp(train_data(i,n),class_list(1,:))
        class_first = class_first + 1;
    end
end

%% 退出程序条件
if class_first == m || n == 1
    disp(‘final data‘);
    disp(train_data);
    return;
end

%% 建立决策树
bestfeat = choose_bestfeat(train_data);

disp([‘bestfeature:‘,num2str(bestfeat)]);

featvalue = unique(train_data(:,bestfeat));

featvalue_num = length(featvalue);

for i = 1:featvalue_num
    make_tree(splitData(train_data,bestfeat,featvalue(i,:)));
    disp(‘--------------------------------------------‘);
end
end

function [best_feature] = choose_bestfeat(data)
%input                 data                        输入数据
%output               bestfeature             选择特征值

[m,n] = size(data);
feature_num = n - 1;
baseentropy = calc_entropy(data);

best_gain = 0;
best_feature = 0;

%% 挑选最佳特征位
for j =1:feature_num
    feature_temp = unique(data(:,j));
    num_f = length(feature_temp);
    new_entropy = 0;
    for i = 1:num_f
        subSet = splitData(data, j, feature_temp(i,:));
        [m_s,n_s] = size(subSet);
        prob = m_s./m;
        new_entropy = new_entropy + prob * calc_entropy(subSet);
    end
    inf_gain = baseentropy - new_entropy;
    if inf_gain > best_gain
        best_gain = inf_gain;
        best_feature = j;
    end
end
end

function [entropy] = calc_entropy(train_data)
%input                 train_data          训练数据
%output               entropy             熵值

[m,n] = size(train_data);

%% 得到类的项并统计每个类的个数
label_value = train_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

%% 计算熵值
label_number (:,2) = label_number(:,2) ./ m;
entropy = 0;
entropy = sum(-label_number(:,2).*log2 (label_number(:,2)));

end

function [subSet] = splitData(data, j, value)
%input                 data              训练数据
%input                  j                   对应第j个属性
%input                 value             第j个属性对应的特征值
%output               sunset              熵值

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

function [subSet] = splitData(data, j, value)
%input                 data              训练数据
%input                  j                   对应第j个属性
%input                 value             第j个属性对应的特征值
%output               sunset              熵值

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