基于MATLAB的SMOTE算法实现

一、SMOTE算法原理

核心思想：通过插值生成少数类新样本，解决数据不平衡问题

关键步骤：

确定少数类样本：识别数据集中样本量最少的类别
计算k近邻：对每个少数类样本计算k个最近邻
生成新样本：在样本与近邻间随机插值
数据集重构：合并原始数据与合成样本

二、MATLAB实现代码

2.1 基础二分类实现

function [X_resampled, y_resampled] = mySMOTE(X, y, k, ratio)
    % 参数说明：
    % X: 特征矩阵 (n_samples × n_features)
    % y: 标签向量 (n_samples × 1)
    % k: 近邻数
    % ratio: 过采样倍数
    
    % 找出少数类样本
    minority_class = mode(y);
    idx = y == minority_class;
    X_minority = X(idx, :);
    n_minority = size(X_minority, 1);
    
    % 计算k近邻
    [idx_knn, ~] = knnsearch(X_minority, X_minority, 'K', k+1);
    neighbors = idx_knn(:, 2:end);  % 排除自身
    
    % 生成新样本
    n_synthetic = round(ratio * n_minority);
    synthetic_samples = zeros(n_synthetic, size(X, 2));
    
    for i = 1:n_synthetic
        % 随机选择基样本
        base_idx = randi(n_minority);
        % 随机选择近邻
        neighbor_idx = neighbors(base_idx, randi(k));
        % 线性插值
        diff = X_minority(neighbor_idx, :) - X_minority(base_idx, :);
        gap = rand(1, size(X, 2));
        synthetic_samples(i, :) = X_minority(base_idx, :) + gap .* diff;
    end
    
    % 合并数据集
    X_resampled = [X; synthetic_samples];
    y_resampled = [y; repmat(minority_class, n_synthetic, 1)];
end

2.2 多分类扩展实现

function [X_resampled, y_resampled] = multiClassSMOTE(X, y, k, ratio)
    % 处理多分类不平衡问题
    classes = unique(y);
    X_resampled = X;
    y_resampled = y;
    
    for i = 1:length(classes)
        class = classes(i);
        idx = y == class;
        n_class = sum(idx);
        
        % 仅处理少数类
        if n_class < mean(y == classes) && n_class > 1
            X_minority = X(idx, :);
            [X_synthetic, y_synthetic] = mySMOTE(X_minority, class, k, ratio);
            X_resampled = [X_resampled; X_synthetic];
            y_resampled = [y_resampled; y_synthetic];
        end
    end
end

三、参数优化

参数	推荐范围	影响分析
k值	3-10	过小导致噪声敏感，过大降低多样性
过采样倍数	1-5	倍数过高导致过拟合
距离度量	欧氏/马氏	影响近邻选择准确性
平衡策略	过采样/欠采样	需结合欠采样避免类别反转

四、性能优化

4.1 数据预处理

% 特征标准化
scaler = fitpreprocess(X);
X_scaled = transform(scaler, X);

% 处理缺失值
X_clean = fillmissing(X, 'linear');

4.2 并行计算加速

% 启用并行池
parpool('local');

% 并行生成样本
parfor i = 1:num_cores
    % 分块处理数据
end

4.3 边界样本保护

% Tomek Links检测
[idx_tomek] = detect_tomek_links(X, y, k);
X_protected = X(~idx_tomek, :);

五、应用案例

5.1 医疗诊断数据集

% 加载数据
load('medical_data.mat');
X = data(:, 1:end-1);
y = data(:, end);

% 执行SMOTE
[X_balanced, y_balanced] = multiClassSMOTE(X, y, 5, 2);

% 模型训练
model = fitcsvm(X_balanced, y_balanced);

5.2 工业故障检测

% 参数设置
k = 7;        % 高维数据需增大k值
ratio = 3;    % 严重不平衡时提高倍数

% 执行过采样
[X_resampled, y_resampled] = mySMOTE(X_fault, y_fault, k, ratio);

% 交叉验证
cv = cvpartition(y_resampled, 'KFold', 5);
accuracy = crossval(@(XTrain,yTrain,XTest,yTest) ...
    sum(predict(fitcsvm(XTrain,yTrain), XTest) == yTest)/numel(yTest), ...
    X_resampled, y_resampled, 'partition', cv);
disp(['平均准确率: ', num2str(mean(accuracy))]);

参考代码 matlab下的实现smote算法 www.youwenfan.com/contentcni/65444.html

六、可视化分析

6.1 二维数据分布

% 生成示例数据
[X, y] = make_classification(1000, 2, 1, 2, 1, 0.5);

% 执行SMOTE
[X_balanced, y_balanced] = mySMOTE(X, y, 5, 2);

% 绘制分布
figure;
gscatter(X(:,1), X(:,2), y);
hold on;
gscatter(X_balanced(:,1), X_balanced(:,2), y_balanced);
title('SMOTE效果可视化');
legend('原始少数类', '原始多数类', '合成少数类');

6.2 决策边界对比

% 训练模型
model_original = fitcsvm(X, y);
model_balanced = fitcsvm(X_balanced, y_balanced);

% 生成网格
[x1Grid, x2Grid] = meshgrid(linspace(-5,5,50));
xGrid = [x1Grid(:), x2Grid(:)];

% 预测概率
[~,score_original] = predict(model_original, xGrid);
[~,score_balanced] = predict(model_balanced, xGrid);

% 绘制决策面
figure;
contourf(x1Grid, x2Grid, reshape(score_original(:,2),50,50), 'LineColor', 'none');
hold on;
gscatter(X(:,1), X(:,2), y);
title('原始数据决策边界');

figure;
contourf(x1Grid, x2Grid, reshape(score_balanced(:,2),50,50), 'LineColor', 'none');
hold on;
gscatter(X_balanced(:,1), X_balanced(:,2), y_balanced);
title('SMOTE平衡后决策边界');