一、核心代码实现框架
1. 数据预处理模块
% 数据标准化（Z-score） function X_norm = preprocess(X) mu = mean(X,1); sigma = std(X,0,1); X_norm = (X - mu) ./ sigma; end % 离散化处理（适用于连续特征） function X_disc = discretize(X, n_bins) X_disc = zeros(size(X)); for i=1:size(X,2) edges = linspace(min(X(:,i)), max(X(:,i)), n_bins+1); X_disc(:,i) = discretize(X(:,i), edges); end end 2. 互信息计算核心函数
function mi = compute_mutual_info(X, Y) % 离散特征互信息计算（基于直方图） n = size(X,1); [joint, edges_x, edges_y] = histcounts2(X, Y); P_joint = joint / n; P_x = histcounts(X, edges_x) / n; P_y = histcounts(Y, edges_y) / n; % 避免零概率问题 P_joint(P_joint < eps) = eps; P_x(P_x < eps) = eps; P_y(P_y < eps) = eps; mi = sum(sum(P_joint .* log2(P_joint ./ (P_x' * P_y)))); end % 条件互信息计算（蒙特卡洛近似） function cond_mi = compute_conditional_mi(X, Y, S) n = size(X,1); k = 100; % 蒙特卡洛采样次数 mi_sum = 0; for i=1:k idx = randperm(n, k); X_samp = X(idx,:); Y_samp = Y(idx); S_samp = S(idx,:); cond_mi = cond_mi + compute_mutual_info(X_samp, Y_samp) ... - compute_mutual_info(S_samp, Y_samp); end cond_mi = cond_mi / k; end 3. mRMR特征选择主程序
function [selected, scores] = mrmr_feature_selection(X, Y, k) % 输入参数： % X: n×p特征矩阵 % Y: n×1目标变量 % k: 选择特征数 [n,p] = size(X); selected = []; remaining = 1:p; % 计算初始互信息 mi = arrayfun(@(i) compute_mutual_info(X(:,i), Y), 1:p); % 选择首个特征 [~, idx] = max(mi); selected = [selected, idx]; remaining(remaining == idx) = []; % 迭代选择后续特征 for t=2:k max_score = -inf; best_feat = 0; for i=remaining % 计算条件互信息 cond_mi = 0; for j=selected cond_mi = cond_mi + compute_conditional_mi(X(:,i), Y, X(:,j)); end cond_mi = cond_mi / length(selected); % 计算mRMR评分 score = compute_mutual_info(X(:,i), Y) - cond_mi; if score > max_score max_score = score; best_feat = i; end end selected = [selected, best_feat]; remaining(remaining == best_feat) = []; end scores = compute_mutual_info(X, Y); end 二、优化
1. 计算效率提升
并行计算加速：利用MATLAB并行工具箱加速条件互信息计算
parfor i=1:length(remaining) % 并行计算每个候选特征的评分 end近似算法：使用k近邻（k-NN）替代精确概率估计
function mi = mi_knn(X, Y, k) n = size(X,1); mi = 0; for i=1:n % 使用k-NN估计联合分布 [idx] = knnsearch(X, X(i,:), 'K', k+1); P_joint = histcounts2(X(idx(2:end),:), Y(idx(2:end))); P_x = histcounts(X(i,:), linspace(min(X(:,1)), max(X(:,1)), k)); P_y = histcounts(Y(i), linspace(min(Y), max(Y), k)); mi = mi + log2(sum(P_joint(:)) / (sum(P_x)*sum(P_y))); end mi = mi / n; end
2. 高维数据处理
特征预筛选：先使用卡方检验筛选前50%特征
function idx = preselect_chi2(X, Y, ratio) h = chi2gof(X, 'Expected', mean(X,1), 'Alpha', 0.05); [~, order] = sort(h.p, 'descend'); idx = order(1:round(ratio*size(X,2))); end分块计算：将特征矩阵分块处理（每块100个特征）
block_size = 100; num_blocks = ceil(p / block_size); for b=1:num_blocks start_idx = (b-1)*block_size +1; end_idx = min(b*block_size, p); % 处理每个特征块 end
三、典型应用案例
1. 基因表达数据分析
% 加载数据 load('gene_expression.mat'); X = gene_data(:,2:end); % 去除样本ID列 Y = gene_data(:,1); % 疾病标签 % 数据预处理 X_norm = preprocess(X); X_disc = discretize(X_norm, 10); % mRMR特征选择 [selected, scores] = mrmr_feature_selection(X_disc, Y, 20); % 结果可视化 bar(scores(selected)); xlabel('特征索引'); ylabel('互信息值'); title('mRMR特征重要性排序'); 2. 图像纹理特征选择
% 提取局部二值模式(LBP)特征 features = extractLBPFeatures(im2single(images)); % 应用mRMR降维 [selected, ~] = mrmr_feature_selection(features, labels, 50); % 使用SVM进行分类 model = fitcsvm(features(:,selected), labels); 参考代码 mRMR算法 www.youwenfan.com/contentale/63850.html
四、扩展工具箱推荐
Statistics and Machine Learning Toolbox： 内置
fscmrmr函数实现快速mRMR计算 支持并行计算加速Deep Learning Toolbox：
结合深度特征提取+特征选择
示例代码：
layers = [imageInputLayer([28 28 1]) convolution2dLayer(3,16,'Padding','same') reluLayer maxPooling2dLayer(2,'Stride',2) fullyConnectedLayer(10) classificationLayer];
Image Processing Toolbox： 提供HOG、LBP等特征提取函数 支持图像特征自动降维
实际应用中建议优先使用内置函数fscmrmr进行快速验证，再根据需求定制优化算法。对于超大规模数据，可结合Hadoop/Matlab Parallel Server实现分布式计算。