id3决策树算法的matlab实现
时间: 2023-06-19 21:05:05 浏览: 73
以下是ID3决策树算法的matlab实现,其中包括数据预处理、决策树生成和分类等步骤。
%数据预处理
data = [6, 180, 12, 0;
5.92, 190, 11, 0;
5.58, 170, 12, 0;
5.92, 165, 10, 0;
5, 100, 6, 1;
5.5, 150, 8, 1;
5.42, 130, 7, 1;
5.75, 150, 9, 1];
labels = {'Height','Weight','FootSize','Gender'};
%决策树生成
tree = createTree(data, labels);
%分类
test = [6, 130, 8];
result = classify(tree, labels, test);
%定义决策树生成函数
function tree = createTree(data, labels)
numFeatures = size(data, 2) - 1;
bestFeature = chooseBestFeature(data);
bestLabel = labels{bestFeature};
tree = struct('node',bestLabel,'children',[]);
uniqueVals = unique(data(:,bestFeature));
for i = 1:length(uniqueVals)
subData = data(data(:,bestFeature) == uniqueVals(i),:);
subLabels = labels;
subLabels(bestFeature) = [];
if length(unique(subData(:,end))) == 1
tree.children{i} = struct('node',unique(subData(:,end)),'children',[]);
elseif isempty(subLabels)
tree.children{i} = struct('node',mode(subData(:,end)),'children',[]);
else
tree.children{i} = createTree(subData, subLabels);
end
end
end
%定义信息增益函数
function [bestFeature] = chooseBestFeature(data)
numFeatures = size(data, 2) - 1;
baseEntropy = calcShannonEnt(data);
bestInfoGain = 0;
bestFeature = -1;
for i = 1:numFeatures
featList = data(:,i);
uniqueVals = unique(featList);
newEntropy = 0;
for j = 1:length(uniqueVals)
subData = data(featList == uniqueVals(j),:);
prob = size(subData, 1) / size(data, 1);
newEntropy = newEntropy - prob * calcShannonEnt(subData);
end
infoGain = baseEntropy - newEntropy;
if infoGain > bestInfoGain
bestInfoGain = infoGain;
bestFeature = i;
end
end
end
%定义计算信息熵函数
function [shannonEnt] = calcShannonEnt(data)
numEntries = size(data, 1);
labelCounts = tabulate(data(:,end));
probs = labelCounts(:,end) / numEntries;
shannonEnt = -sum(probs .* log2(probs));
end
%定义分类函数
function [result] = classify(tree, labels, test)
if ~isstruct(tree)
result = tree;
return
end
idx = find(strcmp(labels,tree.node));
for i = 1:length(tree.children)
if tree.children{i}.node == test(idx)
result = classify(tree.children{i}, labels, test);
return
end
end
result = mode(data(:,end));
end
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