MATLAB 实现基分类器为决策树的 AdaBoost

最新推荐文章于 2025-12-19 16:12:26 发布

原创最新推荐文章于 2025-12-19 16:12:26 发布 · 95 阅读

1 ·

CC 4.0 BY-SA版权

文章标签：

#matlab #决策树 #开发语言

特点：

基学习器：单层决策树（decision stump，深度=1）
支持二分类/多类
输出：训练准确率、测试准确率、特征重要性

一、主文件 demo_AdaBoost_DT.m

%% 0. 环境
clear; clc; close all;

%% 1. 加载数据（鸢尾花 3 类，取前两类做二分类）
load fisheriris
X = meas(1:100, :);               % 100×4
Y = species(1:100);               % 前两类
Y = grp2idx(Y);                   % 转 1/2

%% 2. 划分训练/测试
cv = cvpartition(Y, 'HoldOut', 0.3);
XTrain = X(cv.training, :);
YTrain = Y(cv.training);
XTest  = X(cv.test, :);
YTest  = Y(cv.test);

%% 3. 参数
nLearner = 100;                   % 提升轮数

%% 4. 训练 AdaBoost-DecisionTree
[model, trainScore] = adaBoostTrain(XTrain, YTrain, nLearner);

%% 5. 测试
yPred = adaBoostPredict(model, XTest);
accTest = mean(yPred == YTest);
fprintf('测试准确率 = %.2f %%\n', accTest*100);

%% 6. 特征重要性
bar(model.featureImportance); xlabel('特征'); ylabel('重要性');
title('AdaBoost-DecisionTree 特征重要性');

二、训练函数 adaBoostTrain.m

function [model, score] = adaBoostTrain(X, Y, nLearner)
[n, p] = size(X);
classList = unique(Y);  nClass = numel(classList);
% 初始化权重
w = ones(n, 1) / n;
learner = struct();
for m = 1:nLearner
    % 1. 训练单层决策树（decision stump）
    [node, err] = decisionStump(X, Y, w);
    % 2. 计算基学习器权重 α
    alpha = log((1-err)/max(err,1e-12));
    % 3. 更新样本权重
    yHat = stumpPredict(node, X);
    match = (yHat == Y);
    w = w .* exp(alpha .* (1-match));
    w = w / sum(w);               % 归一化
    % 4. 保存
    learner(m).node   = node;
    learner(m).alpha  = alpha;
    learner(m).err    = err;
end
model.learner = learner;
model.nClass  = nClass;
model.featureImportance = computeImportance(learner, p);
% 训练集得分
score = adaBoostPredict(model, X);
end

三、决策树桩 decisionStump.m

function [node, err] = decisionStump(X, Y, w)
[n, p] = size(X);
bestErr = inf;
for d = 1:p
    x = X(:, d);
    [~, ~, thresh] = unique(x);
    for t = thresh(2:end)               % 遍历所有可能阈值
        left  = x <= t;
        right = ~left;
        % 多数投票
        yLeft  = mode(Y(left));
        yRight = mode(Y(right));
        yHat   = yLeft;
        yHat(right) = yRight;
        err = sum(w .* (yHat ~= Y));
        if err < bestErr
            bestErr = err;
            node.dimension = d;
            node.threshold = t;
            node.yLeft  = yLeft;
            node.yRight = yRight;
        end
    end
end
err = bestErr;
end

四、预测函数 adaBoostPredict.m

function yPred = adaBoostPredict(model, X)
[n, ~] = size(X);
nLearner = numel(model.learner);
score = zeros(n, model.nClass);
for m = 1:nLearner
    node  = model.learner(m).node;
    alpha = model.learner(m).alpha;
    yHat  = stumpPredict(node, X);
    for k = 1:model.nClass
        score(:, k) = score(:, k) + alpha * (yHat == k);
    end
end
[~, yPred] = max(score, [], 2);
end