当前位置：首页 > news >正文

基于MATLAB的线性判别分析（LDA）人脸识别实现

news 2025/9/10 8:09:22

一、系统架构设计

二、核心代码实现

1. 数据加载与预处理

%% 数据加载（假设图片已转换为10304维向量）
load('face_dataset.mat'); % 包含train_data, train_labels, test_data, test_labels% 数据归一化
train_data = double(train_data)/255;
test_data = double(test_data)/255;% 类别统计
unique_labels = unique(train_labels);
num_classes = length(unique_labels);

2. LDA模型训练

function [W, projected_train, projected_test] = train_LDA(train_data, train_labels, num_components)% 计算全局均值mu = mean(train_data, 2);% 初始化散度矩阵Sw = zeros(size(train_data,1));Sb = zeros(size(train_data,1));% 类别遍历for i = 1:num_classesidx = (train_labels == unique_labels(i));Ni = sum(idx);% 类内散度mu_i = mean(train_data(:,idx), 2);Sw = Sw + (train_data(:,idx) - mu_i) * (train_data(:,idx) - mu_i)';% 类间散度Sb = Sb + Ni * (mu_i - mu) * (mu_i - mu)';end% 求解广义特征值问题[V, D] = eig(Sb, Sw);[~, idx] = sort(diag(D), 'descend');W = V(:, idx(1:num_components));% 特征投影projected_train = W' * train_data;projected_test = W' * test_data;
end

3. 分类器实现（最近邻分类）

function accuracy = evaluate_classifier(train_proj, train_labels, test_proj, test_labels)% 构建KNN分类器mdl = fitcknn(train_proj', train_labels, 'NumNeighbors', 3, 'Distance', 'euclidean');% 预测predicted_labels = predict(mdl, test_proj');% 计算准确率accuracy = sum(predicted_labels == test_labels)/length(test_labels);
end

三、完整实现流程

%% 参数设置
num_components = 50; % 投影维度%% 模型训练
[W, train_proj, test_proj] = train_LDA(train_data, train_labels, num_components);%% 性能评估
accuracy = evaluate_classifier(train_proj, train_labels, test_proj, test_labels);
fprintf('分类准确率: %.2f%%
', accuracy*100);%% 可视化（二维投影）
figure;
gscatter(train_proj(1,:), train_proj(2,:), train_labels);
hold on;
plot(test_proj(1,:), test_proj(2,:), 'kx', 'MarkerSize', 10);
title('LDA投影可视化');
xlabel('第一判别分量');
ylabel('第二判别分量');
legend('训练样本', '测试样本');

推荐代码Linear Discriminant Analysis算法 www.youwenfan.com/contentcsg/51460.html

四、关键优化策略

1. 正则化处理（防止矩阵奇异）

% 添加正则化项
epsilon = 1e-6;
Sw_inv = inv(Sw + eye(size(Sw))*epsilon);

2. 核LDA扩展（处理非线性可分数据）

% 使用高斯核函数
K = kernel_matrix(train_data, 'rbf', 0.1);
[W_ker] = train_kernel_LDA(K, train_labels, num_components);

3. 多类扩展（C>2场景）

% 修改散度矩阵计算
for i = 1:num_classesmu_i = mean(train_data(:,train_labels==unique_labels(i)), 2);Sw = Sw + (train_data(:,train_labels==unique_labels(i)) - mu_i) * ...(train_data(:,train_labels==unique_labels(i)) - mu_i)';Sb = Sb + size(train_data,2)/num_classes * (mu_i - mu) * ...(mu_i - mu)';
end