1. 环境准备和数据加载
matlab
复制代码
% 添加BNT工具箱到路径
addpath(genpath('bnt'));
% 生成示例数据
% 假设有3个输入特征和1个分类输出
n_samples = 1000;
n_features = 3;
n_classes = 3;
% 生成特征数据
X = randn(n_samples, n_features);
% 生成类别标签（基于特征的某种关系）
true_weights = [2, -1, 0.5];
y_scores = X * true_weights' + randn(n_samples, 1)*0.5;
y = discretize(y_scores, [-inf, -0.5, 0.5, inf]);
% 划分训练集和测试集
train_ratio = 0.7;
n_train = floor(n_samples * train_ratio);
X_train = X(1:n_train, :);
y_train = y(1:n_train);
X_test = X(n_train+1:end, :);
y_test = y(n_train+1:end);
2. 构建贝叶斯网络结构
matlab
复制代码
function dag = create_classification_bnet(n_features, n_classes)
% 创建有向无环图
% 节点1: 类别变量
% 节点2-n_features+1: 特征变量
dag = zeros(n_features + 1, n_features + 1);
% 类别节点指向所有特征节点
class_node = 1;
for i = 1:n_features
feature_node = i + 1;
dag(class_node, feature_node) = 1;
end
fprintf('构建了包含%d个特征的分类网络\n', n_features);
end
3. 参数学习和模型训练
matlab
复制代码
function bnet = train_bayesian_classifier(X_train, y_train, n_classes)
[n_samples, n_features] = size(X_train);
% 创建网络结构
dag = create_classification_bnet(n_features, n_classes);
ns = ones(1, n_features + 1);
ns(1) = n_classes; % 类别节点的状态数
% 离散化连续特征（简单示例使用3个区间）
for i = 1:n_features
ns(i+1) = 3; % 每个特征离散化为3个状态
end
% 创建贝叶斯网络
bnet = mk_bnet(dag, ns);
% 设置节点类型
bnet.CPD{1} = tabular_CPD(bnet, 1); % 类别先验
for i = 1:n_features
bnet.CPD{i+1} = tabular_CPD(bnet, i+1); % 特征条件概率
end
% 准备训练数据
data = cell(n_features + 1, n_samples);
% 类别数据
data(1, :) = num2cell(y_train');
% 特征数据（离散化）
for i = 1:n_features
feature_data = X_train(:, i);
% 等宽离散化
edges = linspace(min(feature_data), max(feature_data), 4);
disc_data = discretize(feature_data, edges);
data(i+1, :) = num2cell(disc_data');
end
% 参数学习
bnet = learn_params(bnet, data);
fprintf('贝叶斯分类器训练完成\n');
end
4. 预测函数
matlab
复制代码
function [predictions, probabilities] = bayesian_predict(bnet, X_test, n_classes)
[n_test, n_features] = size(X_test);
% 离散化测试数据
test_data = cell(n_features + 1, n_test);
test_data(1, :) = {[]}; % 类别未知
for i = 1:n_features
feature_data = X_test(:, i);
edges = linspace(min(feature_data), max(feature_data), 4);
disc_data = discretize(feature_data, edges);
test_data(i+1, :) = num2cell(disc_data');
end
% 创建推理引擎
engine = jtree_inf_engine(bnet);
predictions = zeros(n_test, 1);
probabilities = zeros(n_test, n_classes);
for i = 1:n_test
% 设置证据
evidence = test_data(:, i);
% 进行推理
[engine, loglik] = enter_evidence(engine, evidence);
% 查询类别节点的后验概率
marg = marginal_nodes(engine, 1);
probabilities(i, :) = marg.T;
[~, predictions(i)] = max(marg.T);
end
end
5. 完整的工作流程
matlab
复制代码
function main_multiple_input_classification()
% 主函数：多输入分类预测
% 1. 准备数据
fprintf('准备数据...\n');
[X, y, X_train, y_train, X_test, y_test] = prepare_data();
% 2. 训练模型
fprintf('训练贝叶斯分类器...\n');
n_classes = length(unique(y));
bnet = train_bayesian_classifier(X_train, y_train, n_classes);
% 3. 预测
fprintf('进行预测...\n');
[predictions, probabilities] = bayesian_predict(bnet, X_test, n_classes);
% 4. 评估模型
fprintf('评估模型性能...\n');
evaluate_model(y_test, predictions, probabilities);
% 5. 可视化结果
visualize_results(X_test, y_test, predictions, probabilities);
end
function [X, y, X_train, y_train, X_test, y_test] = prepare_data()
% 生成更真实的数据
n_samples = 2000;
n_features = 4;
% 生成特征数据
X = zeros(n_samples, n_features);
% 特征1: 正态分布
X(:,1) = randn(n_samples, 1);
% 特征2: 均匀分布
X(:,2) = rand(n_samples, 1) * 10;
% 特征3: 与特征1相关
X(:,3) = 0.5 * X(:,1) + randn(n_samples, 1) * 0.5;
% 特征4: 分类特征
X(:,4) = randi(3, n_samples, 1);
% 基于特征的复杂关系生成类别
scores = 2*X(:,1) - 1.5*X(:,2) + 0.8*X(:,3) + 0.5*(X(:,4)-2);
noise = randn(n_samples, 1) * 0.3;
y_scores = scores + noise;
% 分为3类
y = discretize(y_scores, [-inf, -2, 2, inf]);
% 划分数据集
train_ratio = 0.7;
n_train = floor(n_samples * train_ratio);
X_train = X(1:n_train, :);
y_train = y(1:n_train);
X_test = X(n_train+1:end, :);
y_test = y(n_train+1:end);
end
function evaluate_model(y_true, y_pred, probabilities)
% 计算准确率
accuracy = sum(y_true == y_pred) / length(y_true);
fprintf('准确率: %.4f\n', accuracy);
% 混淆矩阵
cm = confusionmat(y_true, y_pred);
fprintf('混淆矩阵:\n');
disp(cm);
% 各类别准确率
for i = 1:max(y_true)
class_idx = (y_true == i);
class_acc = sum(y_true(class_idx) == y_pred(class_idx)) / sum(class_idx);
fprintf('类别 %d 准确率: %.4f\n', i, class_acc);
end
% 平均概率
mean_prob = mean(max(probabilities, [], 2));
fprintf('平均预测置信度: %.4f\n', mean_prob);
end
function visualize_results(X_test, y_test, predictions, probabilities)
% 可视化结果
figure;
% 只使用前两个特征进行可视化
if size(X_test, 2) >= 2
subplot(2, 2, 1);
gscatter(X_test(:,1), X_test(:,2), y_test, 'rgb', 'o');
title('真实类别');
xlabel('特征1'); ylabel('特征2');
subplot(2, 2, 2);
gscatter(X_test(:,1), X_test(:,2), predictions, 'rgb', 'x');
title('预测类别');
xlabel('特征1'); ylabel('特征2');
subplot(2, 2, 3);
correct = (y_test == predictions);
gscatter(X_test(:,1), X_test(:,2), correct, 'br', 'o*');
title('分类结果 (蓝色:正确, 红色:错误)');
xlabel('特征1'); ylabel('特征2');
subplot(2, 2, 4);
confidence = max(probabilities, [], 2);
scatter(X_test(:,1), X_test(:,2), 50, confidence, 'filled');
colorbar;
title('预测置信度');
xlabel('特征1'); ylabel('特征2');
end
end
6. 高级功能：连续特征处理
matlab
复制代码
function bnet = train_with_continuous_features(X_train, y_train, n_classes)
% 使用连续特征的高斯节点
[n_samples, n_features] = size(X_train);
% 创建网络结构
dag = create_classification_bnet(n_features, n_classes);
% 节点大小：类别节点离散，特征节点连续
discrete_nodes = 1;
continuous_nodes = 2:(n_features+1);
ns = ones(1, n_features + 1);
ns(discrete_nodes) = n_classes;
% 创建混合网络
bnet = mk_bnet(dag, ns, 'discrete', discrete_nodes);
% 设置CPD
bnet.CPD{1} = tabular_CPD(bnet, 1); % 离散类别节点
for i = continuous_nodes
% 高斯节点，均值依赖于父节点（类别）
bnet.CPD{i} = gaussian_CPD(bnet, i, 'cov_type', 'diag');
end
% 准备数据
data = cell(n_features + 1, n_samples);
data(1, :) = num2cell(y_train');
for i = 1:n_features
data{i+1, :} = num2cell(X_train(:, i)');
end
% 参数学习
bnet = learn_params(bnet, data);
end