matlab基于粗糙集理论的属性约简算法代码

以下是一个基于粗糙集理论的属性约简算法的MATLAB代码示例：

function [reducted_features, accuracy] = rough_set(attribute_matrix, decision_matrix)
% attribute_matrix - 属性矩阵，每一列代表一个属性
% decision_matrix - 决策矩阵，每一行代表一个样本的决策
% reducted_features - 约简后的属性集合
% accuracy - 约简后的分类准确率

[num_samples, num_features] = size(attribute_matrix);
num_decisions = length(unique(decision_matrix));

% 初始化属性重要度向量
importance_vector = zeros(1, num_features);

% 计算属性重要度
for i = 1:num_features
    % 计算属性i的决策关联度
    positive_samples = find(attribute_matrix(:, i) == 1);
    negative_samples = find(attribute_matrix(:, i) == 0);
    num_positive_samples = length(intersect(positive_samples, find(decision_matrix == 1)));
    num_negative_samples = length(intersect(negative_samples, find(decision_matrix == 0)));
    positive_ratio = num_positive_samples / length(positive_samples);
    negative_ratio = num_negative_samples / length(negative_samples);
    decision_association = abs(positive_ratio - negative_ratio);
    
    % 计算属性i的条件熵
    conditional_entropy = 0;
    for j = 1:num_decisions
        decision_samples = find(decision_matrix == j);
        num_decision_samples = length(decision_samples);
        num_decision_and_attribute_samples = length(intersect(decision_samples, positive_samples));
        if num_decision_and_attribute_samples == 0
            continue;
        end
        decision_attribute_ratio = num_decision_and_attribute_samples / num_decision_samples;
        conditional_entropy = conditional_entropy - decision_attribute_ratio * log2(decision_attribute_ratio);
    end
    
    % 计算属性i的重要度
    importance_vector(i) = decision_association * conditional_entropy;
end

% 对属性重要度进行排序，并选择前k个作为约简后的属性集合
[~, indices] = sort(importance_vector, 'descend');
reducted_features = indices(1:round(num_features / 2));

% 计算约简后的分类准确率
attribute_matrix_reduced = attribute_matrix(:, reducted_features);
decision_matrix_reduced = decision_matrix;
classifier = fitcknn(attribute_matrix_reduced, decision_matrix_reduced, 'NumNeighbors', 3);
accuracy = sum(predict(classifier, attribute_matrix_reduced) == decision_matrix_reduced) / num_samples;
end

该算法的思路是计算每个属性的重要度，然后按重要度从高到低排序选择一部分属性作为约简后的属性集合。在本例中，我们选择了重要度前50%的属性作为约简后的属性集合，并使用K近邻分类器计算了约简后的分类准确率。