Adaboost用matlab实现

Matlab机器学习工具箱中的集成学习技术随着人工智能领域的发展和机器学习技术的不断推进，集成学习作为一种重要的机器学习方法，正在被广泛应用于各个领域。

在Matlab机器学习工具箱中，集成学习技术得到了很好的支持和实现。

本文将详细介绍Matlab机器学习工具箱中的集成学习技术，并探讨其在实际问题中的应用。

一、集成学习简介集成学习是一种将多个学习器进行适当组合的机器学习方法。

它通过对多个学习器的预测结果进行投票或加权平均等方式，获得更准确、更稳定的预测结果。

集成学习的核心思想是“三个臭皮匠胜过一个诸葛亮”，通过组合多个学习器的优势，从而实现更好的分类或回归效果。

在Matlab机器学习工具箱中，集成学习技术被封装在ensemble子库中。

该子库提供了多种集成学习算法的实现，包括AdaBoost、Bagging、随机森林等。

同时，Matlab还提供了相关的函数和工具，方便用户进行集成学习的模型训练、预测和评估。

二、AdaBoost算法AdaBoost是集成学习中最经典的算法之一，也是Matlab机器学习工具箱中支持的算法之一。

AdaBoost的核心思想是通过迭代的方式训练一系列弱分类器，并根据它们的性能进行加权组合，获得精确的分类器。

具体算法流程如下：1. 初始化数据权重：给每个样本一个初始权重，初始权重可以是相同的或根据样本分布设定。

2. 训练弱分类器：使用当前数据权重训练一个弱分类器，通常是使用一个简单的分类算法，比如决策树。

3. 更新样本权重：根据分类器的性能更新样本的权重，被错误分类的样本权重会得到增加，被正确分类的样本权重会得到减少。

4. 组合弱分类器：对每个弱分类器根据其分类性能进行加权组合，形成最终的分类器。

通过这种方式，AdaBoost能够不断改进分类器的性能，从而提高整体的预测准确率。

在Matlab中，可以使用ensemble子库中的adaboost函数来实现AdaBoost算法。

三、Bagging算法Bagging是另一种常见的集成学习算法，也是Matlab机器学习工具箱中支持的算法之一。

30个智能算法matlab代码以下是30个使用MATLAB编写的智能算法的示例代码： 1. 线性回归算法：matlab.x = [1, 2, 3, 4, 5];y = [2, 4, 6, 8, 10];coefficients = polyfit(x, y, 1);predicted_y = polyval(coefficients, x);2. 逻辑回归算法：matlab.x = [1, 2, 3, 4, 5];y = [0, 0, 1, 1, 1];model = fitglm(x, y, 'Distribution', 'binomial'); predicted_y = predict(model, x);3. 支持向量机算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3];y = [1, 1, -1, -1, -1];model = fitcsvm(x', y');predicted_y = predict(model, x');4. 决策树算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; y = [0, 0, 1, 1, 1];model = fitctree(x', y');predicted_y = predict(model, x');5. 随机森林算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; y = [0, 0, 1, 1, 1];model = TreeBagger(50, x', y');predicted_y = predict(model, x');6. K均值聚类算法：matlab.x = [1, 2, 3, 10, 11, 12]; y = [1, 2, 3, 10, 11, 12]; data = [x', y'];idx = kmeans(data, 2);7. DBSCAN聚类算法：matlab.x = [1, 2, 3, 10, 11, 12]; y = [1, 2, 3, 10, 11, 12]; data = [x', y'];epsilon = 2;minPts = 2;[idx, corePoints] = dbscan(data, epsilon, minPts);8. 神经网络算法：matlab.x = [1, 2, 3, 4, 5];y = [0, 0, 1, 1, 1];net = feedforwardnet(10);net = train(net, x', y');predicted_y = net(x');9. 遗传算法：matlab.fitnessFunction = @(x) x^2 4x + 4;nvars = 1;lb = 0;ub = 5;options = gaoptimset('PlotFcns', @gaplotbestf);[x, fval] = ga(fitnessFunction, nvars, [], [], [], [], lb, ub, [], options);10. 粒子群优化算法：matlab.fitnessFunction = @(x) x^2 4x + 4;nvars = 1;lb = 0;ub = 5;options = optimoptions('particleswarm', 'PlotFcn',@pswplotbestf);[x, fval] = particleswarm(fitnessFunction, nvars, lb, ub, options);11. 蚁群算法：matlab.distanceMatrix = [0, 2, 3; 2, 0, 4; 3, 4, 0];pheromoneMatrix = ones(3, 3);alpha = 1;beta = 1;iterations = 10;bestPath = antColonyOptimization(distanceMatrix, pheromoneMatrix, alpha, beta, iterations);12. 粒子群-蚁群混合算法：matlab.distanceMatrix = [0, 2, 3; 2, 0, 4; 3, 4, 0];pheromoneMatrix = ones(3, 3);alpha = 1;beta = 1;iterations = 10;bestPath = particleAntHybrid(distanceMatrix, pheromoneMatrix, alpha, beta, iterations);13. 遗传算法-粒子群混合算法：matlab.fitnessFunction = @(x) x^2 4x + 4;nvars = 1;lb = 0;ub = 5;gaOptions = gaoptimset('PlotFcns', @gaplotbestf);psOptions = optimoptions('particleswarm', 'PlotFcn',@pswplotbestf);[x, fval] = gaParticleHybrid(fitnessFunction, nvars, lb, ub, gaOptions, psOptions);14. K近邻算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; y = [0, 0, 1, 1, 1];model = fitcknn(x', y');predicted_y = predict(model, x');15. 朴素贝叶斯算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; y = [0, 0, 1, 1, 1];model = fitcnb(x', y');predicted_y = predict(model, x');16. AdaBoost算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3];y = [0, 0, 1, 1, 1];model = fitensemble(x', y', 'AdaBoostM1', 100, 'Tree'); predicted_y = predict(model, x');17. 高斯混合模型算法：matlab.x = [1, 2, 3, 4, 5]';y = [0, 0, 1, 1, 1]';data = [x, y];model = fitgmdist(data, 2);idx = cluster(model, data);18. 主成分分析算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; coefficients = pca(x');transformed_x = x' coefficients;19. 独立成分分析算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; coefficients = fastica(x');transformed_x = x' coefficients;20. 模糊C均值聚类算法：matlab.x = [1, 2, 3, 4, 5; 1, 2, 2, 3, 3]; options = [2, 100, 1e-5, 0];[centers, U] = fcm(x', 2, options);21. 遗传规划算法：matlab.fitnessFunction = @(x) x^2 4x + 4; nvars = 1;lb = 0;ub = 5;options = optimoptions('ga', 'PlotFcn', @gaplotbestf);[x, fval] = ga(fitnessFunction, nvars, [], [], [], [], lb, ub, [], options);22. 线性规划算法：matlab.f = [-5; -4];A = [1, 2; 3, 1];b = [8; 6];lb = [0; 0];ub = [];[x, fval] = linprog(f, A, b, [], [], lb, ub);23. 整数规划算法：matlab.f = [-5; -4];A = [1, 2; 3, 1];b = [8; 6];intcon = [1, 2];[x, fval] = intlinprog(f, intcon, A, b);24. 图像分割算法：matlab.image = imread('image.jpg');grayImage = rgb2gray(image);binaryImage = imbinarize(grayImage);segmented = medfilt2(binaryImage);25. 文本分类算法：matlab.documents = ["This is a document.", "Another document.", "Yet another document."];labels = categorical(["Class 1", "Class 2", "Class 1"]);model = trainTextClassifier(documents, labels);newDocuments = ["A new document.", "Another new document."];predictedLabels = classifyText(model, newDocuments);26. 图像识别算法：matlab.image = imread('image.jpg');features = extractFeatures(image);model = trainImageClassifier(features, labels);newImage = imread('new_image.jpg');newFeatures = extractFeatures(newImage);predictedLabel = classifyImage(model, newFeatures);27. 时间序列预测算法：matlab.data = [1, 2, 3, 4, 5];model = arima(2, 1, 1);model = estimate(model, data);forecastedData = forecast(model, 5);28. 关联规则挖掘算法：matlab.data = readtable('data.csv');rules = associationRules(data, 'Support', 0.1);29. 增强学习算法：matlab.environment = rlPredefinedEnv('Pendulum');agent = rlDDPGAgent(environment);train(agent);30. 马尔可夫决策过程算法：matlab.states = [1, 2, 3];actions = [1, 2];transitionMatrix = [0.8, 0.1, 0.1; 0.2, 0.6, 0.2; 0.3, 0.3, 0.4];rewardMatrix = [1, 0, -1; -1, 1, 0; 0, -1, 1];policy = mdpPolicyIteration(transitionMatrix, rewardMatrix);以上是30个使用MATLAB编写的智能算法的示例代码，每个算法都可以根据具体的问题和数据进行相应的调整和优化。

A d a b o o s t算法多类问题M a t l a b实现一种adaboost多类分类算法Matlab实现一、adaboost算法简介Adaboost算法的主要思想是给定一个训练集(x1,y1),…,(xm,ym),其中xi属于某个域或者实例空间X，yi=-1或者+1。

初始化时Adaboost指定训练集上的分布为1/m,并按照该分布调用弱学习器对训练集上的分布，并按照该分布调用弱学习器对训练集进行训练，每次训练后，根据训练结果更新训练集上的分布，并按照新的样本分布进行训练。

反复迭代T轮，最终得到一个估计序列h1,..,hT,每个估计都具有一定的权重，最终的估计H是采用权重投票方式获得。

Adaboost算法的伪代码如图1所示。

图1、Adaboost算法二、多类问题从上面的流程可以看出，Adaboost算法是针对二类问题的。

但是我们面对的问题很多都是不是简单的非0即1，而是多类问题。

常见的就是解决方法，就是把多类问题转换成二类问题。

用的比较多就是两种组合方法，OAA和OAO，我这里就是采用对这种方法的结合，实现adaboost算法对多类问题的分类。

目前需要对7类问题进行分类，依次编号：0、1、2、3、4、5、6。

特征向量 28个。

样本总数 840个；OAA分类器的个数 7 个OAO分类器的个数 7（7-1）/2 = 21个。

弱分类器的个数 K= 10；弱分类用BP神经网络算法的思路：Step1、把数据分成训练集和测试集Step 2、训练OAA、OAO分类器；Step3、保存相应的分类器和投票权重；Step4、测试样本，预测所以OAA分类器的权重；Step5、选择OAA预测值中最大的两个Step6、选用OAO分类器对选取预测权重最大的两个类进行预测；Step7、输出测试结果；注：为了统一，在训练OAO分类器是，把类别序列在前的类为正样本，输出+1，类别序列号在后面的为负样本，输出为-1。

测试强分类器的识别率为：0.93左右。

adaboost算法程序matlabAdaboost算法是一种常用的集成学习方法，广泛应用于分类问题中。

它的核心思想是通过集成多个弱分类器，来构建一个强分类器，从而提高整体分类的准确性。

本文将介绍Adaboost算法的原理和主要步骤，并使用Matlab编写一个简单的Adaboost算法程序。

Adaboost算法的原理非常简单，它通过迭代的方式，每次训练一个弱分类器，并根据分类结果调整样本权重，使得分类错误的样本在下一轮训练中得到更多的关注。

最终，将所有弱分类器的结果进行加权投票，得到最终的分类结果。

Adaboost算法的主要步骤如下：1. 初始化样本权重。

将所有样本的权重初始化为相等值，通常为1/N，其中N为样本数量。

2. 迭代训练弱分类器。

在每一轮迭代中，根据当前样本权重训练一个弱分类器。

弱分类器可以是任何分类算法，如决策树、支持向量机等。

3. 计算分类误差率。

根据当前弱分类器的分类结果，计算分类误差率。

分类误差率定义为分类错误的样本权重之和。

4. 更新样本权重。

根据分类误差率，更新样本权重。

分类错误的样本权重会增加，而分类正确的样本权重会减少。

5. 计算弱分类器权重。

根据分类误差率，计算当前弱分类器的权重。

分类误差率越小的弱分类器权重越大，反之越小。

6. 更新样本权重分布。

根据弱分类器的权重，更新样本权重分布。

分类错误的样本权重会增加，而分类正确的样本权重会减少。

7. 终止条件判断。

如果达到预定的迭代次数或分类误差率满足终止条件，则停止迭代。

8. 构建强分类器。

将所有弱分类器的结果进行加权投票，得到最终的分类结果。

权重越大的弱分类器对分类结果的贡献越大。

接下来，我们使用Matlab编写一个简单的Adaboost算法程序。

假设我们有一个二分类问题的训练集，包含N个样本和D个特征。

我们使用决策树作为弱分类器。

我们需要定义一些参数，如迭代次数和弱分类器数量。

然后，我们初始化样本权重和弱分类器权重。

MATLAB_智能算法30个案例分析1.线性回归：使用MATLAB的回归工具箱，对给定的数据集进行线性回归分析，获取拟合的直线方程。

2.逻辑回归：使用MATLAB的分类工具箱，对给定的数据集进行逻辑回归分析，建立分类模型。

3.K均值聚类：使用MATLAB的聚类工具箱，对给定的数据集进行K 均值聚类算法，将数据集分为多个簇。

4.支持向量机：使用MATLAB的SVM工具箱，对给定的数据集进行支持向量机算法，建立分类或回归模型。

5.决策树：使用MATLAB的分类工具箱，对给定的数据集进行决策树分析，建立决策模型。

6.随机森林：使用MATLAB的分类和回归工具箱，对给定的数据集进行随机森林算法，集成多个决策树模型。

7. AdaBoost：使用MATLAB的分类工具箱，对给定的数据集进行AdaBoost算法，提升分类性能。

8.遗传算法：使用MATLAB的全局优化工具箱，利用遗传算法进行优化问题的求解。

9.粒子群优化：使用MATLAB的全局优化工具箱，利用粒子群优化算法进行优化问题的求解。

10.模拟退火算法：使用MATLAB的全局优化工具箱，利用模拟退火算法进行优化问题的求解。

11.神经网络：使用MATLAB的神经网络工具箱，构建和训练多层感知机模型。

12.卷积神经网络：使用MATLAB的深度学习工具箱，构建和训练卷积神经网络模型。

13.循环神经网络：使用MATLAB的深度学习工具箱，构建和训练循环神经网络模型。

14.长短期记忆网络：使用MATLAB的深度学习工具箱，构建和训练长短期记忆网络模型。

15.GAN（生成对抗网络）：使用MATLAB的深度学习工具箱，构建和训练生成对抗网络模型。

16.自编码器：使用MATLAB的深度学习工具箱，构建和训练自编码器模型。

17.强化学习：使用MATLAB的强化学习工具箱，构建和训练强化学习模型。

18.关联规则挖掘：使用MATLAB的数据挖掘工具箱，发现数据中的关联规则。

一、CatBoost简介CatBoost是一种用于机器学习的开源梯度提升库，由Yandex开发。

它专门针对类别特征进行优化，能够自动处理类别特征的编码，从而减少了许多特性工程的工作量。

CatBoost能够快速训练模型，具有出色的性能，并且在大规模数据集上表现出色。

二、Matlab代码中使用CatBoost的优势1. 支持类别特征编码在传统的机器学习模型中，类别特征通常需要进行独热编码或者标签编码等处理，而CatBoost能够自动处理类别特征的编码，极大地减少了特性工程的工作量。

2. 快速训练模型由于CatBoost是专门针对大规模数据集进行优化的，因此在处理大规模数据集时，CatBoost能够比传统的机器学习模型更快速地训练模型。

3. 出色的性能CatBoost在各种机器学习任务上都展现出了出色的性能，尤其是在处理类别特征较多的数据集时，CatBoost能够更好地发挥其优势。

三、在Matlab中使用CatBoost的方法在Matlab中使用CatBoost，需要先安装CatBoost库，并在Matlab中载入CatBoost库。

接下来，可以使用CatBoost库提供的各种函数进行模型的训练和预测。

以下是一个简单的示例代码：```Matlab导入数据data = load('data.csv');X = data(:, 1:end-1);y = data(:, end);创建CatBoost模型mdl = fitcensemble(X, y, 'Method', 'catboost', 'Learners', 'tree', 'NumLearningCycles', 100);进行预测pred = predict(mdl, X);```以上代码示例中，首先导入数据，然后使用CatBoost库提供的fitcensemble函数创建CatBoost模型，最后使用predict函数进行预测。

Adaboost算法和BP算法都是常用的机器学习算法，在应用中有着广泛的应用。

本文将分别介绍Adaboost和BP算法的原理，然后给出它们在Matlab中的代码实现。

1. Adaboost算法原理Adaboost（Adaptive Boosting）算法是一种集成学习方法，它通过训练多个弱分类器，然后将这些弱分类器进行组合，构成一个强分类器。

Adaboost算法的基本思想是每一轮训练都调整数据分布，使得前一轮分类错误的样本在下一轮中受到更多的关注，以此来提高分类的准确性。

Adaboost的算法流程如下：1. 初始化训练数据的权值分布，使得每个样本的权值相等。

2. 对于每一轮训练，根据当前的数据权值分布训练一个弱分类器。

3. 计算该弱分类器的分类错误率，并根据错误率调整样本的权值分布。

4. 根据弱分类器的权重，更新最终的分类器。

5. 重复步骤2-4，直到达到预定的训练轮数或者分类误差达到要求。

2. BP算法原理BP（Back Propagation）算法是一种常用的神经网络训练算法，它通过利用梯度下降法来不断调整神经网络的权值，使得网络的输出尽可能接近于期望的输出。

BP算法的基本思想是通过计算误差的梯度来调整网络中每一个连接的权值，以最小化网络的总误差。

BP算法的算法流程如下：1. 初始化神经网络的权值，可以使用随机值来进行初始化。

2. 对于每一个训练样本，通过正向传播计算网络的输出，并计算输出与期望输出之间的误差。

3. 通过反向传播计算每个权值的梯度，并根据梯度下降法来调整权值。

4. 重复步骤2-3，直到达到预定的训练轮数或者网络的误差达到要求。

3. Adaboost的Matlab代码实现以下是Adaboost算法在Matlab中的代码实现：```function [strongClassifier, alpha] = adaboost(X, y, T)N = size(X, 1); 样本数D = ones(N, 1)/N; 初始化样本权值分布weakClassifiers = cell(1, T); 初始化弱分类器数组alpha = zeros(1, T); 初始化弱分类器权重数组for t = 1:T训练一个弱分类器[weakClassifier, error, h] = tr本人nWeakClassifier(X, y, D);if error >= 0.5break; 弱分类器误差大于0.5，停止训练end更新弱分类器权重alpha(t) = 0.5 * log((1-error)/error);更新样本权值分布D = D .* exp(-alpha(t) * y .* h);D = D / sum(D);保存弱分类器和权重weakClassifiers{t} = weakClassifier;end构建强分类器strongClassifier.weakClassifiers = weakClassifiers; strongClassifier.alpha = alpha;end```4. BP算法的Matlab代码实现以下是BP算法在Matlab中的代码实现：```function [W1, W2] = tr本人nBP(X, y, hiddenSize, lr, epochs) inputSize = size(X, 2);outputSize = size(y, 2);W1 = randn(inputSize, hiddenSize); 输入层到隐藏层的权值矩阵W2 = randn(hiddenSize, outputSize); 隐藏层到输出层的权值矩阵for epoch = 1:epochsfor i = 1:size(X, 1)正向传播z1 = X(i, :) * W1;a1 = sigmoid(z1);z2 = a1 * W2;a2 = sigmoid(z2);计算误差error = y(i, :) - a2;反向传播d2 = error .* dsigmoid(z2);d1 = (d2 * W2') .* dsigmoid(z1);更新权值W2 = W2 + lr * a1' * d2;W1 = W1 + lr * X(i, :)' * d1;endendend```以上分别介绍了Adaboost算法和BP算法的原理，以及它们在Matlab中的代码实现。

Boost升压电路及MATLAB仿真一、设计要求1.输入电压（VIN）:12V2.输出电压（VO）：18V3.输出电流（IN）:5A4.电压纹波：0.1V5.开关频率设置为50KHz需设计一个闭环控制电路，输入电压在10—14V或负载电流在2—5A范围变化时，稳态输出能够保持在18V 。

根据设计要求很显然是要设计一个升压电路即Boost电路。

Boost电路又称为升压型电路,是一种开关直流升压电路，它可以是输出电压比输入电压高。

其工作过程包括电路启动时的瞬态工作过程和电路稳定后的稳态工作过程。

二、主电路设计图1主电路2.1 Boost电路的工作原理Boost升压电路电感的作用：是将电能和磁场能相互转换的能量转换器件，当MOS开关管闭合后，电感将电能转换为磁场能储存起来，当MOS断开后电感将储存的磁场能转换为电场能，且这个能量在和输入电源电压叠加后通过二极管和电容的滤波后得到平滑的直流电压提供给负载，由于这个电压是输入电源电压和电感的磁场能转换为电能的叠加后形成的，所以输出电压高于输入电压，既升压过程的完成。

Boost升压电路的肖特基二极管主要起隔离作用，即在MOS开关管闭合时，肖特基二极管的正极电压比负极的电压低，此时二极管反向截止，使此电感的储能过程不影响输出端电容对负载的正常供电；因在MOS管断开时，两种叠加后的能量通过二极向负载供电，此时二极管正向导通，要求其正向压降越小越好，尽量使更多的能量供给到负载端。

闭合开关会引起通过电感的电流增加。

打开开关会促使电流通过二极管流向输出电容因储存来自电感的电流，多个开关周期以后输出电容的电压升高，结果输出电压高于输入电压。

接下来分两部分对Boost电路作具体介绍即充电过程和放电过程。

充电过程在充电过程中，开关闭合（三极管导通），等效电路如图二，开关（三极管）处用导线代替。

这时，输入电压流过电感。

二极管防止电容对地放电。

由于输入是直流电，所以电感上的电流以一定的比率线性增加，这个比率跟电感大小有关。

GML AdaBoost Matlab Toolbox ManualThis manual describes the usage of GML AdaBoost matlab toolbox, and is organized as follows: in the first section will introduce you to the basic concept of the toolbox, then we give an example script that uses the toolbox, section 3 speaks about all available functions and classes and section 4 is Q and A. Introduction (1)Implemented algorithms (2)Available weak learners (2)CART (2)Additional functionalities (3)Authors (4)Library structure and usage (4)Functions and Classes (4)function [Learners, Weights, {final_hyp}] = RealAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn, final_hyp}) (4)function [Learners, Weights, {final_hyp}] = GentleAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn}) (5)function [Learners, Weights, {final_hyp}] = ModestAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn}) (5)function Result = Classify(Learners, Weights, Data) (5)function code = TranslateToC (Learners, Weights, fid) (5)@tree_node_w : (6)@crossvalidation : (6)Example scripts (7)Example_1 script (7)Comments on the script (7)Example_2 script (7)Comments on the script (9)Example_3 script (9)Comments on the script (11)TrainAndSave script (11)Comments on the script (11)Q and A: (11)What version of Matlab should I have for the toolbox to work? (11)Is this toolbox free to use? (12)I found a bug! (12)How should I represent my data to use it in toolbox? (12)How to load my data from txt file to use it in your toolbox? (12)Can I regulate false positive to false negative rate? (12)What is the best way to analyze the resulting committee? (12)Can I use constructed committee in C++ application? (12)Reference (12)IntroductionGML AdaBoost Matlab Toolbox is set of matlab functions and classes implementing a family of classification algorithms, known as Boosting.Implemented algorithmsSo far we have implemented 3 different boosting schemes: Real AdaBoost, Gentle AdaBoost and Modest AdaBoost.Real AdaBoost (see [2] for full description) is the generalization of a basic AdaBoost algorithm first introduced by Fruend and Schapire [1]. Real AdaBoost should be treated as a basic “hardcore” boosting algorithm.Gentle AdaBoost is a more robust and stable version of real AdaBoost (see [3] for full description). So far, it has been the most practically efficient boosting algorithm, used, for example, in Viola-Jones object detector [4]. Our experiments show, that Gentle AdaBoost performs slightly better then Real AdaBoost on regular data, but is considerably better on noisy data, and much more resistant to outliers.Modest AdaBoost (see [5] for a full description) – regularized tradeoff of AdaBoost, mostly aimed for better generalization capability and resistance to overfitting. Our experiments show, that in terms of test error and overfitting this algorithm outperforms both Real and Gentle AdaBoost.Available weak learnersNow a tree learner is available (there was only stumps in version 0.1). You can define the number of maximum splits that would be done during the training. You can still use a stump learner – it’s just a tree with only one split.CARTCART is an acronym for Classification and Regression Trees. Here, we will describe an algorithm for using and building a CART decision tree for classification task.Decision tree is a tree graph, with leaves representing the classification result and nodes representing some predicate. Branches of the tree are marked true or false. Classification process in case of decision tree is a process of tree traverse. We start from root and descend further, until we reach the leaf – the value associated with the leaf is the class of the presented sample. At each step we compute the value of the predicate associated with current node. We choose next node (or leaf) that is connected with current by the branch with the value of current nodes predicate.Figure 1. CART example.Let ()()m m y x y x S ,,...,,11= be a sequence of training examples, where each j x belongs to the domain or instance space n R X ∈ (real valued vector with dimensionality n ()j n j j x x x ,...,1=), and each label j y belongs to a finite label space Y . We will consider binary classification task, where {}1,1+−=Y .In toolbox we use the following algorithm for construction a node of CART:1. For each and all n dimensions find the threshold, that separates S with least error;2. Choose dimension i with least error, and construct the node:a. With predicate Θ>i x ;b. Branches true/false, that are connected with leafs, that have respectiveclassification.Let “error of leaf” be the probability of a sample being misclassified if during the tree traverse we stop at this leaf. To construct the whole tree the following algorithm is used:1. Construct root node;2. Choose leave with largest error;3. Construct node, using only those training samples, that are associated with chosen leaf;4. Replace chosen leaf with constructed node;5. Repeat 2-4 until all leafs have zero error, or predefined number of steps done.To make CART able to learn on weighted training data we only have to evaluate all errors according to weights.Additional functionalitiesAlongside with 3 Boosting algorithms we also provide a class that should give you an easy way to make a cross-validation test.AuthorsThis toolbox was implemented by Alexander Vezhnevets – an undergraduate student of Moscow State University. If you have any questions or suggestions, please mail me:vezhnick@Library structure and usageLibrary provides a set of functions that implement classifier boosting procedures. Weak learners (classifiers) are implemented as class, while boosting procedures are implemented as global functions.We provide CART (classification trees) as weak learners. Class “tree_node_w” implements CART. Number of maximum splits (tree depth) is passed as constructor parameter. User should create class object with desired number of splits and pass it to the boosting function.Boosting procedure (GentleAdaBoost, ModestAdaBoost, RealAdaBoost) constructs boosted classifier committee using training set represented by matrix of training samples and their respective labels (see function descriptions for more details).Cell array of weak classifiers and a vector of their weights represent boosted committee. Actually, each node of CART trees constructed during the training process is represented as an individual weak classifier. Thus a tree with 4 nodes would be represented as a cell array of 4 nodes and 4 respective numbers in vector of weights.Constructed committee can be saved to text file. This file can be used for analyzes of constructed committee C++ code provided that can load saved committee from file and perform classification with it. See TranslateToC function.Functions and Classesfunction [Learners, Weights, {final_hyp}] = RealAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn, final_hyp})Boosts a weak learner WeakLrn using Real AdaBoost algorithm with Max_Iter iterations on dataset given in Data and Labels.Arguments:•WeakLrn - weak learner•Data - training data. Should be DxN matrix, where D is the dimensionality of data, and N is the number of training samples;•Labels - training labels. Should be 1xN matrix, where N is the number of training samples, any label is either +1 or –1;•Max_Iter - number of iterations;•OldW - weights of already built committee (used for further training of already built commitee). Optional parameter;•OldLrn - learners of already built committee (used for further training of already built committee). Optional parameter;•final_hyp - output for training data of already built committee (used to speed up further training of already built committee). Optional parameter.Return:•Learners - cell array of constructed learners. Each learner is a node of CART tree represented by object of tree_node_w class;•Weights - weights of learners. This vector has the same size as Learners and represents weight of each learner in final committee;•final_hyp - output for training data.function [Learners, Weights, {final_hyp}] = GentleAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn})Boosts a weak learner WeakLrn using Gentle AdaBoost algorithm with Max_Iter iterations on dataset given in Data and Labels. The parameters semantic is the same as in RealAdaBoost function.function [Learners, Weights, {final_hyp}] = ModestAdaBoost(WeakLrn, Data, Labels, Max_Iter, {OldW, OldLrn})Boosts a weak learner WeakLrn using Modest AdaBoost algorithm with Max_Iter iterations on dataset given in Data and Labels. The parameters semantics are the same as in RealAdaBoost function.function Result = Classify(Learners, Weights, Data)Classifies Data using boosted assembly of Learners with respective Weights. Result will contain real numbers; the signum of those numbers represents the class, and its absolute magnitude is the “confidence” of the decision. To obtain classification one should take signum of Result. To regulate the rate of false positive / false negative Result could be compared with some threshold. Increasing threshold would reduce false positive rate, but will also increase false negative. Example:Confidence = Classify(Learners, Weights, X); % obtaining real valued resultsTetta = 0.2; % TP/FP regulating thresholdY = sign(Confidence - Tetta); % obtaining classificationfunction code = TranslateToC (Learners, Weights, fid)Use this function to save constructed classifiers for further use in C++ applications. C++ codes that loads saved committee is provided (see C++ directory for code and example usage). File has the following format:<TN><W> <N > <D> <T> <Ts> {<D> <T> <Ts> }<W> <N > <D> <T> <Ts> {<D> <T> <Ts> }…<end>Where:TN – total number of weak classifiers;W – weight of weak classifier;N – number of thresholds representing weak classifier (in CART each node can be represented as the set of thresholds);D – thresholds dimension;T – threshold value;Ts – threshold sing. It’s either –1 or +1, resembling if the sample should be greater or lesser than threshold to be classified positive.Arguments:•Learners - learners of committee to be saved;•Weights - weights of committee to be saved;•fid - opened file id (use fopen to make one).Return:•code - equals 1 if everything was alright.@tree_node_w :A class that implements a classification tree weak learner. This is the most popular weak learner for the boosting algorithms. It splits data by a set of hyper planes orthogonal to coordinate axis. We use a greedy splitting rule – at each step we perform a split, which best lowers the total tree error.Class methods:function tree_node = tree_node_w(max_splits) – constructor. Call to make the object,max_splits specifies the maximum amount of tree splits during training.function nodes = train(node, dataset, labels, weights) – trains a tree to fit dataset in to labels, with respect to weights. nodes – is a cell array that contains terminal tree nodes. Arguments:•node - object of tree_node_w class (initialized properly);•dataset - training data;•labels - training labels;•weights - weights of training data. Needed for boosting procedure;Return:•nodes - tree is represented as a cell array of its nodes.function y = calc_output(tree_node, XData) – classifies XData with tree_node and stores result in y.Arguments:•tree_node - classification tree node;•XData - data that will be classified.Return:•y - +1, if XData belongs to tree node, -1 otherwise (y is a vector)@crossvalidation :A class that helps to perform a crossvalidation. It works like a storage class, you should pass the data alongside with labels and the class automatically splits it into the specified number of subsets. You can then access any fold you want.Class methods:function this = crossvalidation(folds) – constructor. Use to create an object with specified number of folds.function this = Initialize(this, Data, Labels) – initializes the object. Data and Labels will be split in to the specified in constructor number of folds and stored within the class. Data should be a NK× matrix, where K is the instance space dimensionality and N is the number of training samples; Labels must be N1 matrix.×function [Data, Labels] = GetFold(this, N) – returns Data and Labels of fold N stored in this.function [Data, Labels] = CatFold(this, Data, Labels, N) – concatenates the fold N to Data and Labels.Example scriptsExample_1 script% Step1: reading Data from the filefile_data = load('Ionosphere.txt');Data = file_data(:,1:end-1)';Labels = file_data(:, end)';Labels = Labels*2 - 1;MaxIter = 200; % boosting iterations% Step2: splitting data to training and control setTrainData = Data(:,1:2:end);TrainLabels = Labels(1:2:end);ControlData = Data(:,2:2:end);ControlLabels = Labels(2:2:end);% Step3: constructing weak learnerweak_learner = tree_node_w(3); % pass the number of tree splits to the constructor% Step4: training with Gentle AdaBoost[RLearners RWeights] = GentleAdaBoost(weak_learner, TrainData, TrainLabels, MaxIter);% Step5: training with Modest AdaBoost[MLearners MWeights] = ModestAdaBoost(weak_learner, TrainData, TrainLabels, MaxIter);% Step6: evaluating on control setResultR = sign(Classify(RLearners, RWeights, ControlData));ResultM = sign(Classify(MLearners, MWeights, ControlData));% Step7: calculating errorErrorR = sum(ControlLabels ~= ResultR)ErrorM = sum(ControlLabels ~= ResultM)Comments on the scriptStep 1 – data is loaded from txt file. Each line of which is a data sample (feature vector). Last element of line is the class marker (it is 0/1 in example, so that is why “Labels = Labels*2 - 1;” line is required);Step 2 – we split data in two subsets; half goes to control set, half to training set;Step 3 – here we construct a tree weak learner, which would be used for boosting. We pass the max number of splits (1 = stump);Step 4 and 5 – we boost weak learners with two different algorithms, using training set;Step 6 – calculating classifiers output on control set;Step 7 – calculating error.Example_2 script% Step1: reading Data from the filefile_data = load('Ionosphere.txt');Data = file_data(:,1:end-1)';Labels = file_data(:, end)';Labels = Labels*2 - 1;MaxIter = 100; % boosting iterations% Step2: splitting data to training and control setTrainData = Data(:,1:2:end);TrainLabels = Labels(1:2:end);ControlData = Data(:,2:2:end);ControlLabels = Labels(2:2:end);% and initializing matrices for storing step errorRAB_control_error = zeros(1, MaxIter);MAB_control_error = zeros(1, MaxIter);GAB_control_error = zeros(1, MaxIter);% Step3: constructing weak learnerweak_learner = tree_node_w(3); % pass the number of tree splits to the constructor% and initializing learners and weights maticesGLearners = [];GWeights = [];RLearners = [];RWeights = [];NuLearners = [];NuWeights = [];% Step4: iterativly running the trainingfor lrn_num = 1 : MaxIterclc;disp(strcat('Boosting step: ', num2str(lrn_num),'/', num2str(MaxIter)));%training gentle adaboost[GLearners GWeights] = GentleAdaBoost(weak_learner, TrainData, TrainLabels, 1, GWeights, GLearners);%evaluating control errorGControl = sign(Classify(GLearners, GWeights, ControlData));GAB_control_error(lrn_num) = GAB_control_error(lrn_num) + sum(GControl ~= ControlLabels) / length(ControlLabels);%training real adaboost[RLearners RWeights] = RealAdaBoost(weak_learner, TrainData, TrainLabels, 1, RWeights, RLearners);%evaluating control errorRControl = sign(Classify(RLearners, RWeights, ControlData));RAB_control_error(lrn_num) = RAB_control_error(lrn_num) + sum(RControl ~= ControlLabels) / length(ControlLabels);%training modest adaboost[NuLearners NuWeights] = ModestAdaBoost(weak_learner, TrainData, TrainLabels, 1, NuWeights, NuLearners);%evaluating control errorNuControl = sign(Classify(NuLearners, NuWeights, ControlData));MAB_control_error(lrn_num) = MAB_control_error(lrn_num) + sum(NuControl~= ControlLabels) / length(ControlLabels);end% Step4: displaying graphsfigure, plot(GAB_control_error);hold on;plot(MAB_control_error, 'r');plot(RAB_control_error, 'g');hold off;legend('Gentle AdaBoost', 'Modest AdaBoost', 'Real AdaBoost');xlabel('Iterations');ylabel('Test Error');Comments on the scriptThis script implements iterative training of boosted committee. At step 4 we start a cycle in which training is done. For each iteration control error is stored and afterwards control error graphs are displayed. Note, that while training we pass committees constructed on previous steps to boosting function – this is done to speed up the process.Example_3 scriptfile_data = load('Ionosphere.txt');%transforming data to toolbox formatsFullData = file_data(:,1:end-1)';FullLabels = file_data(:, end)';FullLabels = FullLabels*2 - 1;MaxIter = 100; % boosting iterationsCrossValidationFold = 5; % number of cross-validation foldsweak_learner = tree_node_w(2); % constructing weak learner% initializing matrices for storing step errorRAB_control_error = zeros(1, MaxIter);MAB_control_error = zeros(1, MaxIter);GAB_control_error = zeros(1, MaxIter);% constructing object for cross-validationCrossValid = crossvalidation(CrossValidationFold);% initializing it with dataCrossValid = Initialize(CrossValid, FullData, FullLabels);NuWeights = [];% for all foldsfor n = 1 : CrossValidationFoldTrainData = [];TrainLabels = [];ControlData = [];ControlLabels = [];% getting current fold[ControlData ControlLabels] = GetFold(CrossValid, n);% concatinating other folds into the training setfor k = 1:CrossValidationFoldif(k ~= n)[TrainData TrainLabels] = CatFold(CrossValid, TrainData, TrainLabels, k);endendGLearners = [];GWeights = [];RLearners = [];RWeights = [];NuLearners = [];NuWeights = [];%training and storing the error for each stepfor lrn_num = 1 : MaxIterclc;disp(strcat('Cross-validation step: ',num2str(n), '/',num2str(CrossValidationFold), '. Boosting step: ', num2str(lrn_num),'/', num2str(MaxIter)));%training gentle adaboost[GLearners GWeights] = GentleAdaBoost(weak_learner, TrainData, TrainLabels, 1, GWeights, GLearners);%evaluating control errorGControl = sign(Classify(GLearners, GWeights, ControlData));GAB_control_error(lrn_num) = GAB_control_error(lrn_num) +sum(GControl ~= ControlLabels) / length(ControlLabels);%training real adaboost[RLearners RWeights] = RealAdaBoost(weak_learner, TrainData, TrainLabels, 1, RWeights, RLearners);%evaluating control errorRControl = sign(Classify(RLearners, RWeights, ControlData));RAB_control_error(lrn_num) = RAB_control_error(lrn_num) +sum(RControl ~= ControlLabels) / length(ControlLabels);%training modest adaboost[NuLearners NuWeights] = ModestAdaBoost(weak_learner, TrainData, TrainLabels, 1, NuWeights, NuLearners);%evaluating control errorNuControl = sign(Classify(NuLearners, NuWeights, ControlData));MAB_control_error(lrn_num) = MAB_control_error(lrn_num) +sum(NuControl ~= ControlLabels) / length(ControlLabels);endend%saving results%save(strcat(name,'_result'),'RAB_control_error', 'MAB_control_error','CrossValidationFold', 'MaxIter', 'name', 'CrossValid');% displaying graphsfigure, plot(GAB_control_error / CrossValidationFold );hold on;plot(MAB_control_error / CrossValidationFold , 'r');plot(RAB_control_error / CrossValidationFold, 'g');hold off;legend('Gentle AdaBoost', 'Modest AdaBoost', 'Real AdaBoost');title(strcat(num2str(CrossValidationFold), ' fold cross-validation'));xlabel('Iterations');ylabel('Test Error');Comments on the scriptThis script implements iterative training of boosted committee with cross-validation . The only difference from Example_2 is the use of @crossvalidation class.TrainAndSave scriptfile_data = load('Ionosphere.txt');Data = file_data(:,1:end-1)';Labels = file_data(:, end)';Labels = Labels*2 - 1;% Data = Data';% Labels = Labels';weak_learner = tree_node_w(2);% Step1: training with Gentle AdaBoost[RLearners RWeights] = RealAdaBoost(weak_learner, Data, Labels, 200);% Step2: training with Modest AdaBoost[MLearners MWeights] = ModestAdaBoost(weak_learner, Data, Labels, 200);fid = fopen('RealBoost.txt','w');TranslateToC(RLearners, RWeights, fid);fclose(fid);fid = fopen('ModestBoost.txt','w');TranslateToC(MLearners, MWeights, fid);fclose(fid);Comments on the scriptThis script illustrates TranslateToC function usage. This script is much similar to Example_1. Q and A:What version of Matlab should I have for the toolbox to work?We don’t use any version specific functions, so it should work with most versions of Matlab. It will work on Matlab 6 and Matlab 7 for sure.Is this toolbox free to use?Yes. You can use it in any way you want and you don’t have to pay anyone. Although you must mention that you used our toolbox, if you publish any results that were obtained using it.I found a bug!Please mail me, so I can fix it. avezhnevets@graphics.cs.msu.ruHow should I represent my data to use it in toolbox?It should be a NK× matrix, where K is the instance space dimensionality and N is the number of training samples; and a vector (N1 matrix) with labels (-1, +1).×How to load my data from txt file to use it in your toolbox?You can use any method, that matlab provides. For most of txt files “load('data.txt');” should work fine.Can I regulate false positive to false negative rate?Yes. See description of “Classify” function.What is the best way to analyze the resulting committee?We advice you to save committee using “TranslateToC” function and analyze the txt file. Its format is described in “Library structure and usage” section.Can I use constructed committee in C++ application?Yes. See TranslateToC function and TrainAndSave example.Reference[1]Y Freund and R. E. Schapire. Game theory, on-line prediction and boosting. In Proceedings of the Ninth AnnualConference on Computational Learning Theory, pages 325–332, 1996.[2]R.E. Schapire and Y. Singer Improved boosting algorithms using confidence-rated predictions. Machine Learning,37(3):297-336, December 1999.[3]Jerome Friedman, Trevor Hastie, and Robert Tibshirani. Additive logistic regression: A statistical view of boosting.TheAnnals of Statistics, 38(2):337–374, April 2000.[4]P. Viola and M. Jones. Robust Real-time Object Detection.In Proc. 2nd Int'l Workshop on Statistical and ComputationalTheories of Vision -- Modeling, Learning, Computing and Sampling, Vancouver, Canada, July 2001.[5] A. Vezhnevets and V. Vezhnevets. Modest AdaBoost – teaching AdaBoost to generalize better. Graphicon 2005.[6]Newman, D.J. & Hettich, S. & Blake, C.L. & Merz, C.J. (1998). UCI Repository of machine learning databases[/~mlearn/MLRepository.html]. Irvine, CA: University of California, Department of Information and Computer Science.。

matlab多分类方法Matlab是一种常用的科学计算软件，广泛应用于工程、数学、物理等领域的数据分析和模型建立。

在机器学习中，多分类问题是一个重要的研究方向。

本文将介绍一些常用的Matlab多分类方法，并探讨它们的优缺点。

1. 逻辑回归（Logistic Regression）逻辑回归是一种广义线性模型，常用于解决二分类问题。

通过对输入数据进行线性组合并经过sigmoid函数映射（将输出限制在0到1之间），可以得到分类结果。

在Matlab中，可以使用fitglm函数实现逻辑回归，并利用分类评估指标（如准确率、查准率和查全率）来评估模型的性能。

2. 支持向量机（Support Vector Machine）支持向量机是一种常用的分类算法，在多分类问题中也有广泛的应用。

它通过找到一个最优超平面将不同类别的样本分开，从而实现分类。

在Matlab中，可以使用fitcecoc函数实现支持向量机的多分类，其中cecoc表示错误纠错输出码。

支持向量机在处理高维数据和非线性问题上表现较好，但对于大规模数据集可能计算复杂度较高。

3. 决策树（Decision Tree）决策树是一种基于树状结构的分类方法，通过一系列的特征判断逐步分类数据。

在Matlab中，可以使用fitctree函数实现决策树算法。

决策树易于理解和解释，但容易产生过拟合，并且对于噪声较大的数据可能不稳定。

4. 集成学习（Ensemble Learning）集成学习通过组合多个基分类器的预测结果，提高分类的准确性和鲁棒性。

常见的集成学习方法包括随机森林（Random Forest）和Adaboost。

在Matlab中，可以使用TreeBagger函数实现随机森林，在fitensemble函数中选择Adaboost算法。

集成学习适用于高维数据和复杂分类问题，能够有效地减少过拟合。

5. 神经网络（Neural Network）神经网络是一种模拟生物神经系统工作原理的机器学习算法。

Matlab中Adaboost算法的代码实现Adaboost(Adaptive Boosting)是一种利用弱分类器构建强分类器的机器学习算法。

它通过迭代训练一系列弱分类器，并根据它们的表现动态调整样本权重，从而得到一个强分类器。

在Matlab中，可以利用现有的工具箱或自己编写代码实现Adaboost算法，下面将介绍如何使用Matlab进行Adaboost算法的代码实现。

1. 准备数据集需要准备用于训练和测试的数据集。

数据集通常包括特征矩阵和标签向量，其中特征矩阵的每一行代表一个样本的特征向量，标签向量表示每个样本的类别。

在Matlab中，可以使用table或array等数据结构来表示数据集。

2. 初始化权重在Adaboost算法中，每个样本都有一个权重，初始时可以将所有样本的权重设为相等值。

在Matlab中，可以使用ones函数创建一个全为1的权重向量。

3. 训练弱分类器接下来，需要进行迭代训练，每一轮训练都会得到一个新的弱分类器。

在Matlab中，可以使用现有的分类器函数，比如fitctree、fitcsvm 等，也可以根据具体情况自定义弱分类器的训练函数。

4. 计算分类器权重每个弱分类器都有一个权重，表示它在最终分类器中的重要程度。

在Matlab中，可以根据分类器的表现和误差率来计算权重。

5. 更新样本权重根据弱分类器的表现，需要更新每个样本的权重。

在Matlab中，可以根据Adaboost算法的更新规则，按照公式计算新的样本权重。

6. 构建强分类器经过多轮训练后，可以得到一系列弱分类器和对应的权重，将它们组合起来得到最终的强分类器。

在Matlab中，可以使用cell数组或结构体来保存弱分类器和权重，然后根据它们构建强分类器的预测函数。

7. 测试分类器可以将得到的强分类器应用到新的数据集上进行测试。

在Matlab中，可以利用训练好的分类器函数对新样本进行预测，并计算准确率、精确率、召回率等指标进行评估。

如何在MATLAB中使用机器学习算法一、介绍MATLAB与机器学习算法MATLAB是一种专业的科学计算软件，被广泛应用于各个领域中的数据分析、模型建立和算法调试等任务。

机器学习算法是近年来兴起的一类基于数据的算法，可以用于从数据中自动发现模式、进行预测和分类等任务。

在这篇文章中，我们将介绍如何在MATLAB中使用机器学习算法。

二、数据预处理在使用机器学习算法之前，首先需要进行数据预处理。

数据预处理包括数据清洗、特征选择、特征缩放等步骤。

MATLAB提供了丰富的函数和工具箱来实现这些预处理任务。

例如，可以使用`readtable`函数读取数据，并使用`table`数据结构存储数据。

然后，可以使用`fillmissing`函数对数据缺失值进行填充。

此外，MATLAB还提供了`featureSelection`和`featureScaling`等函数来进行特征选择和特征缩放。

三、监督学习算法监督学习算法是一类使用带有标签的训练数据来训练模型的算法。

监督学习算法包括线性回归、逻辑回归、支持向量机等。

在MATLAB中，可以使用`fitlm`函数进行线性回归分析。

该函数可以通过最小二乘法拟合线性模型，并给出相应的系数和拟合优度等信息。

此外，还可以使用`fitcsvm`函数实现支持向量机算法，该函数根据输入数据的标签进行分类训练。

四、无监督学习算法无监督学习算法是一类从无标签数据中发现模式的算法，主要包括聚类算法和降维算法。

在MATLAB中，可以使用`kmeans`函数实现k-means聚类算法。

该函数根据数据点之间的距离进行聚类，并给出每个数据点所属的聚类标签。

此外，还可以使用`pca`函数实现主成分分析算法，该函数将数据投影到新的坐标系中，以降低数据的维度。

五、集成学习算法集成学习算法是一种将多个单一模型组合成一个更强大的模型的算法。

常用的集成学习算法包括随机森林和Adaboost算法。

在MATLAB中，可以使用`TreeBagger`函数实现随机森林算法。

MATLAB_智能算法30个案例分析MATLAB是一种强大的数值计算和编程工具，教育和科研领域中广泛应用于数据分析、机器学习和智能算法的研究。

在本文中，我们将介绍30个MATLAB智能算法的案例分析，并探讨其用途和优势。

分析的案例包括分类、回归、聚类、神经网络和遗传算法等不同类型的智能算法。

1. K均值聚类：利用MATLAB中的kmeans函数对一组数据进行聚类分析，得到不同的簇。

2. 随机森林：利用MATLAB中的TreeBagger函数构建一个随机森林分类器，并通过测试数据进行分类预测。

3. 人工神经网络：使用MATLAB中的feedforwardnet函数构建一个人工神经网络，并通过训练集进行预测。

4. 遗传算法：利用MATLAB中的ga函数对一个优化问题进行求解，找到最优解。

5. 支持向量机：使用MATLAB中的svmtrain和svmclassify函数构建一个支持向量机分类器，并进行分类预测。

6. 极限学习机：使用MATLAB中的elmtrain和elmpredict函数构建一个极限学习机分类器，并进行分类预测。

7. 逻辑回归：使用MATLAB中的mnrfit和mnrval函数构建一个逻辑回归模型，并进行预测。

8. 隐马尔可夫模型：使用MATLAB中的hmmtrain和hmmdecode函数构建一个隐马尔可夫模型，对一系列观测数据进行预测。

9. 神经进化算法：利用MATLAB中的ne_train函数构建一个基于神经进化算法的神经网络分类器，并进行分类预测。

10. 朴素贝叶斯分类器：使用MATLAB中的NaiveBayes对象构建一个朴素贝叶斯分类器，并进行分类预测。

11. 高斯过程回归：使用MATLAB中的fitrgp函数构建一个高斯过程回归模型，并进行回归预测。

12. 最小二乘支持向量机：使用MATLAB中的fitcsvm函数构建一个最小二乘支持向量机分类器，并进行分类预测。

13. 遗传网络：利用MATLAB中的ngenetic函数构建一个基于遗传算法和人工神经网络的分类器，并进行分类预测。

boost变换器matlab课程设计一、课程目标知识目标：1. 掌握BOOST变换器的基本工作原理及其数学模型；2. 理解MATLAB/Simulink环境下进行BOOST变换器仿真分析的步骤与方法；3. 学会应用MATLAB软件对BOOST变换器的性能进行参数化设计和分析。

技能目标：1. 能够运用MATLAB/Simulink构建BOOST变换器的仿真模型；2. 能够通过MATLAB编程实现对BOOST变换器性能数据的处理和分析；3. 能够独立完成对BOOST变换器的性能优化与故障诊断。

情感态度价值观目标：1. 培养学生对电力电子技术学习的兴趣，激发学生的探究欲望；2. 增强学生的团队合作意识，提高学生在团队中沟通协调的能力；3. 培养学生严谨的科学态度，使学生具备良好的工程素养。

课程性质：本课程为实践性较强的专业课，旨在帮助学生将理论知识与实际应用相结合，提高学生的动手能力和创新能力。

学生特点：学生已具备一定的电力电子技术基础和MATLAB编程能力，具有较强的学习兴趣和探究欲望。

教学要求：教师应注重理论与实践相结合，充分调动学生的积极性，引导学生主动参与课堂讨论和实践活动，提高学生的实际操作能力。

同时，关注学生的学习进度，确保课程目标的实现。

通过课程学习，使学生在知识、技能和情感态度价值观方面取得具体的学习成果。

二、教学内容1. BOOST变换器原理回顾：包括BOOST变换器的基本结构、工作原理、开关器件的作用及其控制方式。

相关教材章节：电力电子技术第三章第二节。

2. MATLAB/Simulink仿真环境介绍：介绍MATLAB/Simulink软件的基本操作、仿真模型构建方法及仿真参数设置。

相关教材章节：MATLAB仿真与应用第四章。

3. BOOST变换器仿真模型构建：利用MATLAB/Simulink构建BOOST变换器的仿真模型，并进行仿真实验。

相关教材章节：电力电子技术第三章第三节。

Adaboost用matlab实现一例。

Mathworks网站找到的。

可以直接复制下面代码到matlab中，不过会缺少两个图形。

或者把下面每个函数（共6个）分别放在6个m文件中，然后运行demo文件。

说明----------目录中包含一下文件。

1. ADABOOST_te.m2. ADABOOST_tr.m3. demo.m4. likelihood2class.m5. threshold_te.m6. threshold_tr.m本工程的目的是为被称做AdaBoost的学习算法提供一个源文件，以提高用户定义的分类的性能。

要使用adaboost，首先两个函数必须用合适的参数运行。

对于每个源文件的解释都可以通过"help"命令得到。

要看它们是如何工作的，运行demo.m，即>> demo。

demo.m中的前三行说明了训练集和测试集的长度以及若分类器的数量。

要发现bug，请马上向作者发送一封邮件。

Cuneyt Mertayake mail: cuneyt.mertayak@版本：1.0 日期：03/09/2008%% DEMONSTRATION OF ADABOOST_tr and ADABOOST_te%% Just type "demo" to run the demo.%% Using adaboost with linear threshold classifier% for a two class classification problem.%% Bug Reporting: Please contact the author for bug reporting and comments.%% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007% Creating the training and testing sets%tr_n = 200;te_n = 200;weak_learner_n = 20;tr_set = abs(rand(tr_n,2))*100;te_set = abs(rand(te_n,2))*100;tr_labels = (tr_set(:,1)-tr_set(:,2) > 0) + 1;te_labels = (te_set(:,1)-te_set(:,2) > 0) + 1;% Displaying the training and testing setsfigure;subplot(2,2,1);hold on; axis square;indices = tr_labels==1;plot(tr_set(indices,1),tr_set(indices,2),'b*');indices = ~indices;plot(tr_set(indices,1),tr_set(indices,2),'r*');title('Training set');subplot(2,2,2);hold on; axis square;indices = te_labels==1;plot(te_set(indices,1),te_set(indices,2),'b*');indices = ~indices;plot(te_set(indices,1),te_set(indices,2),'r*');title('Testing set');% Training and testing error ratestr_error = zeros(1,weak_learner_n);te_error = zeros(1,weak_learner_n);for i=1:weak_learner_nadaboost_model = ADABOOST_tr(@threshold_tr,@threshold_te,tr_set,tr_labels,i);[L_tr,hits_tr] = ADABOOST_te(adaboost_model,@threshold_te,tr_set,tr_labels);tr_error(i) = (tr_n-hits_tr)/tr_n;[L_te,hits_te] = ADABOOST_te(adaboost_model,@threshold_te,te_set,te_labels);te_error(i) = (te_n-hits_te)/te_n;endsubplot(2,2,3);plot(1:weak_learner_n,tr_error);axis([1,weak_learner_n,0,1]);title('Training Error');xlabel('weak classifier number');ylabel('error rate');grid on;subplot(2,2,4); axis square;plot(1:weak_learner_n,te_error);axis([1,weak_learner_n,0,1]);title('Testing Error');xlabel('weak classifier number');ylabel('error rate');grid on;function adaboost_model = ADABOOST_tr(tr_func_handle, te_func_handle, train_set, labels, no_of_hypothesis)%% ADABOOST TRAINING: A META-LEARNING ALGORITHM% adaboost_model = ADABOOST_tr(tr_func_handle,te_func_handle,% train_set,labels,no_of_hypothesis)%% 'tr_func_handle' and 'te_func_handle' are function handles for% training and testing of a weak learner, respectively. The weak learner% has to support the learning in weighted datasets. The prototypes% of these functions has to be as follows.%% model = train_func(train_set,sample_weights,labels)% train_set: a TxD-matrix where each row is a training sample in% a D dimensional feature space.% sample_weights: a Tx1 dimensional vector, the i-th entry% of which denotes the weight of the i-th sample.% labels: a Tx1 dimensional vector, the i-th entry of which% is the label of the i-th sample.% model: the output model of the training phase, which can% consists of parameters estimated.%% [L,hits,error_rate] = test_func(model,test_set,sample_weights,true_labels)% model: the output of train_func% test_set: a KxD dimensional matrix, each of whose row is a% testing sample in a D dimensional feature space.% sample_weights: a Dx1 dimensional vector, the i-th entry% of which denotes the weight of the i-th sample.% true_labels: a Dx1 dimensional vector, the i-th entry of which % is the label of the i-th sample.% L: a Dx1-array with the predicted labels of the samples.% hits: number of hits, calculated with the comparison of L and% true_labels.% error_rate: number of misses divided by the number of samples. %%% 'train_set' contains the samples for training and it is NxD matrix% where N is the number of samples and D is the dimension of the% feature space. 'labels' is an Nx1 matrix containing the class% labels of the samples. 'no_of_hypothesis' is the number of weak% learners to be used.%% The output 'adaboost_model' is a structure with the fields% - 'weights': 1x'no_of_hypothesis' matrix specifying the weights% of the resulted weighted majority voting combination% - 'parameters': 1x'no_of_hypothesis' structure matrix specifying% the special parameters of the hypothesis that is% created at the corresponding iteration of% learning algorithm%% Specific Properties That Must Be Satisfied by The Function pointed% by 'func_handle'% ------------------------------------------------------------------%% Note: Labels must be positive integers from 1 upto the number of classes.% Node-2: Weighting is done as specified in AIMA book, Stuart Russell et.al. (sec edition) %% Bug Reporting: Please contact the author for bug reporting and comments.%% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007%adaboost_model = struct('weights',zeros(1,no_of_hypothesis),...'parameters',[]); %cell(1,no_of_hypothesis));sample_n = size(train_set,1);samples_weight = ones(sample_n,1)/sample_n;for turn=1:no_of_hypothesisadaboost_model.parameters{turn} = tr_func_handle(train_set,samples_weight,labels);[L,hits,error_rate] = te_func_handle(adaboost_model.parameters{turn},...train_set,samples_weight,labels);if(error_rate==1)error_rate=1-eps;elseif(error_rate==0)error_rate=eps;end% The weight of the turn-th weak classifieradaboost_model.weights(turn) = log10((1-error_rate)/error_rate);C=likelihood2class(L);t_labeled=(C==labels); % true labeled samples% Importance of the true classified samples is decreased for the next weak classifier samples_weight(t_labeled) = samples_weight(t_labeled)*...((error_rate)/(1-error_rate));% Normalizationsamples_weight = samples_weight/sum(samples_weight);end% Normalizationadaboost_model.weights=adaboost_model.weights/sum(adaboost_model.weights);function [L,hits] = ADABOOST_te(adaboost_model,te_func_handle,test_set,...true_labels)%% ADABOOST TESTING%% [L,hits] = ADABOOST_te(adaboost_model,te_func_handle,train_set,% true_labels)%% 'te_func_handle' is a handle to the testing function of a% learning (weak) algorithm whose prototype is shown below.%% [L,hits,error_rate] = test_func(model,test_set,sample_weights,true_labels) % model: the output of train_func% test_set: a KxD dimensional matrix, each of whose row is a% testing sample in a D dimensional feature space.% sample_weights: a Dx1 dimensional vector, the i-th entry% of which denotes the weight of the i-th sample.% true_labels: a Dx1 dimensional vector, the i-th entry of which% is the label of the i-th sample.% L: a Dx1-array with the predicted labels of the samples.% hits: number of hits, calculated with the comparison of L and% true_labels.% error_rate: number of misses divided by the number of samples. %% It is the corresponding testing% module of the function that is specified in the training phase.% 'test_set' is a NxD matrix where N is the number of samples% in the test set and D is the dimension of the feature space.% 'true_labels' is a Nx1 matrix specifying the class label of% each corresponding sample's features (each row) in 'test_set'.% 'adaboost_model' is the model that is generated by the function% 'ADABOOST_tr'.%% 'L' is the likelihoods that are assigned by the 'ADABOOST_te'.% 'hits' is the number of correctly predicted labels.%% Specific Properties That Must Be Satisfied by The Function pointed% by 'func_handle'% ------------------------------------------------------------------%% Notice: Labels must be positive integer values from 1 upto the number classes.%% Bug Reporting: Please contact the author for bug reporting and comments.%% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007%hypothesis_n = length(adaboost_model.weights);sample_n = size(test_set,1);class_n = length(unique(true_labels));temp_L = zeros(sample_n,class_n,hypothesis_n); % likelihoods for each weak classifier% for each weak classifier, likelihoods of test samples are collectedfor i=1:hypothesis_n[temp_L(:,:,i),hits,error_rate] = te_func_handle(adaboost_model.parameters{i},...test_set,ones(sample_n,1),true_labels);temp_L(:,:,i) = temp_L(:,:,i)*adaboost_model.weights(i);endL = sum(temp_L,3);hits = sum(likelihood2class(L)==true_labels);function model = threshold_tr(train_set, sample_weights, labels)%% TRAINING THRESHOLD CLASSIFIER%% Training of the basic linear classifier where seperation hyperplane% is perpedicular to one dimension.%% model = threshold_tr(train_set, sample_weights, labels)% train_set: an NxD-matrix, each row is a training sample in the D dimensional feature% space.% sample_weights: an Nx1-vector, each entry is the weight of the corresponding training sample% labels: Nx1 dimensional vector, each entry is the corresponding label (either 1 or 2)%% model: the ouput model. It consists of% 1) min_error: training error% 2) min_error_thr: threshold value% 3) pos_neg: whether up-direction shows the positive region (label:2, 'pos') or% the negative region (label:1, 'neg')%% Bug Reporting: Please contact the author for bug reporting and comments.%% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007model = struct('min_error',[],'min_error_thr',[],'pos_neg',[],'dim',[]);sample_n = size(train_set,1);min_error = sum(sample_weights);min_error_thr = 0;pos_neg = 'pos';% for each dimensionfor dim=1:size(train_set,2)sorted = sort(train_set(:,dim),1,'ascend');% for each interval in the specified dimensionfor i=1:(sample_n+1)if(i==1)thr = sorted(1)-0.5;elseif(i==sample_n+1)thr = sorted(sample_n)+0.5;elsethr = (sorted(i-1)+sorted(i))/2;endind1 = train_set(:,dim) < thr;ind2 = ~ind1;tmp_err = sum(sample_weights((labels.*ind1)==2)) + sum(sample_weights((labels.*ind2)==1));if(tmp_err < min_error)min_error = tmp_err;min_error_thr = thr;pos_neg = 'pos';model.dim = dim;endind1 = train_set(:,dim) < thr;ind2 = ~ind1;tmp_err = sum(sample_weights((labels.*ind1)==1)) + sum(sample_weights((labels.*ind2)==2));if(tmp_err < min_error)min_error = tmp_err;min_error_thr = thr;pos_neg = 'neg';model.dim = dim;endendendmodel.min_error = min_error;model.min_error_thr = min_error_thr;model.pos_neg = pos_neg;function [L,hits,error_rate] = threshold_te(model,test_set,sample_weights,true_labels)%% TESTING THRESHOLD CLASSIFIER%% Testing of the basic linear classifier where seperation hyperplane is% perpedicular to one dimension.%% [L,hits,error_rate] = threshold_te(model,test_set,sample_weights,true_labels)%% model: the model that is outputed from threshold_tr. It consists of% 1) min_error: training error% 2) min_error_thr: threshold value% 3) pos_neg: whether up-direction shows the positive region (label:2, 'pos') or% the negative region (label:1, 'neg')% test_set: an NxD-matrix, each row is a testing sample in the D dimensional feature% space.% sample_weights: an Nx1-vector, each entry is the weight of the corresponding test sample% true_labels: Nx1 dimensional vector, each entry is the corresponding label (either 1 or 2) %% L: an Nx2-matrix showing likelihoods of each class% hits: the number of hits% error_rate: the error rate with the sample weights%%% Bug Reporting: Please contact the author for bug reporting and comments.%% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007feat = test_set(:,model.dim);if(strcmp(model.pos_neg,'pos'))ind = (feat>model.min_error_thr)+1;elseind = (feat<model.min_error_thr)+1;endhits = sum(ind==true_labels);error_rate = sum(sample_weights(ind~=true_labels));L = zeros(length(feat),2);L(ind==1,1) = 1;L(ind==2,2) = 1;function classes = likelihood2class(likelihoods)%% LIKELIHOODS TO CLASSES%% classes = likelihood2class(likelihoods)%% Find the class assignment of the samples from the likelihoods% 'likelihoods' an NxD matrix where N is the number of samples and% D is the dimension of the feature space. 'likelihoods(i,j)' is% the i-th samples likelihood of belonging to class-j.%% 'classes' contains the class index of the each sample maximum likelihood %% Bug Reporting: Please contact the author for bug reporting and comments. %% Cuneyt Mertayak% email: cuneyt.mertayak@% version: 1.0% date: 21/05/2007%[sample_n,class_n] = size(likelihoods);maxs = (likelihoods==repmat(max(likelihoods,[],2),[1,class_n]));classes=zeros(sample_n,1);for i=1:sample_nclasses(i) = find(maxs(i,:),1);end。

AdaBoost 算法中寻找最优阈值分类器的代码优化AdaBoost 每一轮的训练获得一个当前权重条件下的最优阈值。

% 逐步求精的方法获取第j 个特征值上的最优分类器 % 输入:% X 训练样本,rows X cols 维矩阵,rows 个样本，每个样本cols 个特征值 % Y 每个样本所属类别的标识,向量,长度为rows % rows 样本容量% weight 权重向量,存放当前每个样本的权重值 % j 当前查找最佳弱分类器的特征列 % 输出:% bestError %搜索到第j 列最佳弱分类器得到的最小错误率 % bestThresh %搜索到第j 列最佳弱分类器的阈值% bestBias %搜索到第j 列最佳弱分类器的偏置 %% 迭代4次,每次将区间划分为12个小段 %% 调用格式为 [bestError,bestThresh,bestBias]=findBestWeakLearner(X,Y ,rows,weight,j) % 最后更新 2007-03-25function [bestError,bestThresh,bestBias]=findBestWeakLearner(X,Y ,rows,weight,j) % 检查输入特征向量与类标需为列向量iptcheckinput(X,{'logical','numeric'},{'2d','nonempty','real'},mfilename, 'X', 1); iptcheckinput(Y ,{'logical','numeric'},{'column','nonempty','integer'},mfilename, 'Y', 2);iteration=4; % 迭代次数sectNum=12; % 每次迭代,将搜索区域划分的片段 maxFea=max(X(:,j)); % 搜索空间的最大值 minFea=min(X(:,j)); % 搜索空间的最小值 step=(maxFea-minFea)/(sectNum-1); % 每次搜索的递增量bestError=rows; % 初值:最好的分类器错误率for iter=1:iteration % 迭代iteration 次,范围逐步缩小,寻找最优值 tempError=rows; % 初值:第iter 次迭代的分类器错误率 for i=1:sectNum % 第iter 次迭代的搜索次数 thresh=minFea+(i-1)*step; % 第i 次搜索的阈值 for p=1:-2:-1 % ！这个循环可去掉 h=zeros(rows,1); %每个样本对弱分类器的输出 for ii=1:rows %！这个循环可向量化 if((p*X(ii,j))<(p*thresh)) h(ii)=1; else h(ii)=0; end end %end for 列向量为特征，行向量为样本方向real adaboost ?rows:样本容量j†F 是同一个样本中的第几个特征% end if iierror=sum(weight(find(h~=Y))); % 第iter 次迭代第i 次搜索加权错误率%！ 这段属冗余代码if(error<tempError) % 第iter 次迭代最优的错误率 阈值 偏置 tempError=error; % 第iter 次迭代最小的错误率 tempThresh=thresh; % 第iter 次迭代最小错误分类情况下的阈值tempBias=p; % 第iter 次迭代最小错误分类情况下的偏置 end end%end for p end%end for iif(tempError<bestError) % 迭代获取的最优错误率 阈值 偏置 bestError=tempError; bestThresh=tempThresh; bestBias=tempBias; end %将搜索范围缩小,继续进行搜索span=(maxFea-minFea)/8; % 搜索范围减为原有的1/4 maxFea=tempThresh+span; % 减少搜索范围后搜索空间的最大值 minFea=tempThresh-span; % 减少搜索范围后搜索空间的最小值step=(maxFea-minFea)/(sectNum-1);% 减少搜索范围后每次搜索的递增量 end在将循环向量化，并删除一些重复的赋值运算后。

一种adaboost多类分类算法Matlab实现一、adaboost算法简介Adaboost算法的主要思想是给定一个训练集(x1,y1),…,(xm,ym),其中xi属于某个域或者实例空间X，yi=-1或者+1。

初始化时Adaboost指定训练集上的分布为1/m,并按照该分布调用弱学习器对训练集上的分布，并按照该分布调用弱学习器对训练集进行训练，每次训练后，根据训练结果更新训练集上的分布，并按照新的样本分布进行训练。

反复迭代T轮，最终得到一个估计序列h1,..,hT,每个估计都具有一定的权重，最终的估计H是采用权重投票方式获得。

Adaboost算法的伪代码如图1所示。

图1、Adaboost算法二、多类问题从上面的流程可以看出，Adaboost算法是针对二类问题的。

但是我们面对的问题很多都是不是简单的非0即1，而是多类问题。

常见的就是解决方法，就是把多类问题转换成二类问题。

用的比较多就是两种组合方法，OAA和OAO，我这里就是采用对这种方法的结合，实现adaboost算法对多类问题的分类。

目前需要对7类问题进行分类，依次编号：0、1、2、3、4、5、6。

特征向量28个。

样本总数840个；OAA分类器的个数7 个OAO分类器的个数7（7-1）/2 = 21个。

弱分类器的个数K= 10；弱分类用BP神经网络算法的思路：Step1、把数据分成训练集和测试集Step 2、训练OAA、OAO分类器；Step3、保存相应的分类器和投票权重；Step4、测试样本，预测所以OAA分类器的权重；Step5、选择OAA预测值中最大的两个Step6、选用OAO分类器对选取预测权重最大的两个类进行预测；Step7、输出测试结果；注：为了统一，在训练OAO分类器是，把类别序列在前的类为正样本，输出+1，类别序列号在后面的为负样本，输出为-1。

测试强分类器的识别率为：0.93左右。

三、小结其实这个主要的思想就是用差异的样本和差异的分类器，组合较好的分类器器，提升样本的准确性和鲁邦性。

MATLAB 神经⽹络（5）基于BP_Adaboost 的强分类器设计——公司财务预警建模5.1 案例背景5.1.1 BP_Adaboost 模型Adaboost 算法的思想是合并多个“弱”分类器的输出以产⽣有效分类。

其主要步骤为：⾸先给出弱学习算法和样本空间(X ,Y )，从样本空间中找出m 组训练数据，每组训练数据的权重都是1m 。

然后⽤弱学习算法迭代运算T 次，每次运算后都按照分类结果更新训练数据权重分布，对于分类失败的训练个体赋予较⼤权重，下次迭代运算时更加关注这些训练个体。

弱分类器通过反复迭代得到⼀个分类函数序列f 1,f 2,...,f T ，每个分类函数赋予⼀个权重，分类结果越好的函数，其对应权重越⼤。

T 次迭代之后，最终强分类函数F 由弱分类函数加权得到。

BP_Adaboost 模型即BP 神经⽹络作为弱分类器，反复训练BP 神经⽹络预测样本输出，通过Adaboost 算法得到多个BP 神经⽹络弱分类器组成的强分类器。

5.1.2 公司财务预警系统介绍公司财务预警系统是为了防⽌公司财务系统运⾏偏离预期⽬标⽽建⽴的报警系统，具有针对性和预测性等特点。

它通过公司的各项指标综合评价并预测公司财务状况、发展趋势和变化，为决策者科学决策提供智⼒⽀持。

评价指标：成分费⽤利润率、资产营运能⼒、公司总资产、总资产增长率、流动⽐率、营业现⾦流量、审计意见类型、每股收益、存货周转率和资产负债率5.2模型建⽴算法步骤如下：1. 数据初始化和⽹络初始化。

从样本空间中随机选择m 组训练数据，初始化测试数据的分布权值D t (i )=1m ，根据样本输⼊输出维数确定神经⽹络结构，初始化BP 神经⽹络权值和阈值。

2. 若分类器预测。

训练第t 个弱分类器时，⽤训练数据训练BP 神经⽹络并且预测训练数据输出，得到预测序列g (t )的预测误差e t ，误差和e t 的计算公式为e t =∑i D t (i )i =1,2,…,m (g (t )≠y )3. 计算预测序列权重。