matlab实现ID3算法

以下是MATLAB实现ID3算法的基本步骤：

1. 数据预处理：将原始数据进行清理和转换，使其适合用于ID3算法。

2. 计算信息熵：使用信息熵来度量数据集的无序程度。

3. 计算信息增益：计算每个特征对于分类的贡献程度。

4. 选择最优特征：选择信息增益最大的特征作为当前节点的特征。

5. 递归构建决策树：将当前节点的数据集按照选定特征分成不同的子集，并对每个子集递归执行上述步骤，直到构建完整个决策树。

下面是MATLAB代码实现：

function [tree, varargout] = id3(data, labels, varargin)

% Check input arguments
narginchk(2, Inf);

% Create variable input parser
p = inputParser;

% Add optional arguments
addParameter(p, 'minLeafSize', 1, @isnumeric);
addParameter(p, 'maxDepth', Inf, @isnumeric);
addParameter(p, 'splitCriterion', 'entropy', @(x) ismember(x, {'entropy', 'gini', 'misclass'}));

% Parse input arguments
parse(p, varargin{:});

% Initialize variables
minLeafSize = p.Results.minLeafSize;
maxDepth = p.Results.maxDepth;
splitCriterion = p.Results.splitCriterion;

% Get unique class labels
classes = unique(labels);

% Initialize tree
tree = struct('var', [], 'threshold', [], 'left', [], 'right', [], 'class', []);

% Check stopping criteria
if numel(classes) == 1 || size(data, 1) < minLeafSize || maxDepth == 0
    % If all samples belong to the same class or the data set is too small to split, assign the majority class to the leaf node
    tree.class = mode(labels);
    varargout{1} = tree;
    return
end

% Calculate entropy of current node
p = histcounts(labels, [classes; max(classes)+1]);
p = p/sum(p);
entropyS = -sum(p.*log2(p));

% Initialize variables to store best split
bestGain = 0;
bestVar = [];
bestThreshold = [];

% Loop over variables to find best split
for j = 1:size(data, 2)
    
    % Sort data by current variable
    [x, idx] = sort(data(:,j));
    y = labels(idx);
    
    % Loop over possible thresholds
    for i = 1:numel(classes)-1
        
        % Calculate gain of current split
        switch splitCriterion
            
            case 'entropy'
                % Entropy-based information gain
                pL = histcounts(y(1:i), [classes; max(classes)+1]);
                pL = pL/sum(pL);
                entropyL = -sum(pL.*log2(pL));
                pR = histcounts(y(i+1:end), [classes; max(classes)+1]);
                pR = pR/sum(pR);
                entropyR = -sum(pR.*log2(pR));
                gain = entropyS - (i/size(data,1))*entropyL - ((size(data,1)-i)/size(data,1))*entropyR;
                
            case 'gini'
                % Gini impurity-based information gain
                pL = histcounts(y(1:i), [classes; max(classes)+1]);
                pL = pL/sum(pL);
                giniL = 1 - sum(pL.^2);
                pR = histcounts(y(i+1:end), [classes; max(classes)+1]);
                pR = pR/sum(pR);
                giniR = 1 - sum(pR.^2);
                gain = entropyS - (i/size(data,1))*giniL - ((size(data,1)-i)/size(data,1))*giniR;
                
            case 'misclass'
                % Misclassification error-based information gain
                pL = histcounts(y(1:i), [classes; max(classes)+1]);
                pL = pL/sum(pL);
                misclassL = 1 - max(pL);
                pR = histcounts(y(i+1:end), [classes; max(classes)+1]);
                pR = pR/sum(pR);
                misclassR = 1 - max(pR);
                gain = entropyS - (i/size(data,1))*misclassL - ((size(data,1)-i)/size(data,1))*misclassR;
                
            otherwise
                error('Invalid split criterion');
                
        end
        
        % Update best split
        if gain > bestGain
            bestGain = gain;
            bestVar = j;
            bestThreshold = mean([x(i), x(i+1)]);
        end
        
    end
    
end

% Check if split was successful
if bestGain == 0
    % If no split was made, assign the majority class to the leaf node
    tree.class = mode(labels);
    varargout{1} = tree;
    return
end

% Create new tree node
tree.var = bestVar;
tree.threshold = bestThreshold;

% Split data into left and right branches
idxL = data(:,bestVar) <= bestThreshold;
idxR = ~idxL;

% Recursively grow left and right branches
tree.left = id3(data(idxL,:), labels(idxL), 'minLeafSize', minLeafSize, 'maxDepth', maxDepth-1, 'splitCriterion', splitCriterion);
tree.right = id3(data(idxR,:), labels(idxR), 'minLeafSize', minLeafSize, 'maxDepth', maxDepth-1, 'splitCriterion', splitCriterion);

% Return tree
varargout{1} = tree;

该函数接受三个输入参数：数据矩阵、标签向量和可选参数。可选参数包括：最小叶子大小、最大深度和分裂标准。输出参数为决策树结构体。