使用Matlab进行SVM多分类

众所周知，普通的SVM只适合用于二分类，需要进行相应的改进才能使其适用于多分类任务。
本文将着重介绍如何让使用Matlab软件对数据进行SVM多分类。
原理就不详细介绍了，传送门

1. 二分类

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clear,clc 
%% 二分类 
%训练数据20×2,20行代表20个训练样本点，第一列代表横坐标，第二列纵坐标 
Train_Data =[-3 0;4 0;4 -2;3 -3;-3 -2;1 -4;-3 -4;0 1;-1 0;2 2;3 3;-2 -1;-4.5 -4;2 -1;5 -4;-2 2;-2 -3;0 2;1 -2;2 0]; 
%共20行，代表训练数据对应点属于哪一类(1类,-1类) 
Train_labels =[1 -1 -1 -1 1 -1 1 1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1]'; TestData = [3 -1;3 1;-2 1;-1 -2;2 -3;-3 -3]; %测试数据 
classifier = fitcsvm(Train_Data,Train_labels); %train 
test_labels = predict(classifier ,TestData); % test

这里 test_labels 就是最后的分类结果

2. 多分类（不调用工具箱）

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%% 多分类 
TrainingSet=[ 1 10;2 20;3 30;4 40;5 50;6 66;3 30;4.1 42];%训练数据 
TestSet=[3 34; 1 14; 2.2 25; 6.2 63];%测试数据 
GroupTrain=[1;1;2;2;3;3;2;2];%训练标签 
results =my_MultiSvm(TrainingSet, GroupTrain, TestSet); 
disp('multi class problem'); 
disp(results);

results为最终的分类结果，上述中有用到 my_MultiSvm.m() 函数，以下是my_MultiSvm.m函数的全部内容

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function [y_predict,models] = my_MultiSvm(X_train, y_train, X_test) 
% multi svm % one vs all 模型 
% Input: % X_train: n*m矩阵 n为训练集样本数 m为特征数 
% y_train: n*1向量 为训练集label，支持任意多种类 
% X_test: n*m矩阵 n为测试集样本数 m为特征数 
% Output: % y_predict: n*1向量 测试集的预测结果 
y_labels = unique(y_train); 
n_class = size(y_labels, 1); 
models = cell(n_class, 1); % 训练n个模型 
for i = 1:n_class 
    class_i_place = find(y_train == y_labels(i)); 
    svm_train_x = X_train(class_i_place,:); 
    sample_num = numel(class_i_place); 
    class_others = find(y_train ~= y_labels(i)); 
    randp = randperm(numel(class_others)); 
    svm_train_minus = randp(1:sample_num)'; 
    svm_train_x = [svm_train_x; X_train(svm_train_minus,:)]; 
    svm_train_y = [ones(sample_num, 1); -1*ones(sample_num, 1)]; 
    disp(['生成模型：', num2str(i)]) 
    models{i} = fitcsvm(svm_train_x, svm_train_y); 
end 
test_num = size(X_test, 1); 
y_predict = zeros(test_num, 1);
% 对每条数据，n个模型分别进行预测，选择label为1且概率最大的一个作为预测类别 
for i = 1:test_num 
    if mod(i, 100) == 0 
        disp(['预测个数：', num2str(i)]) 
    end 
    bagging = zeros(n_class, 1); 
    for j = 1:n_class 
        model = models{j}; 
        [label, rat] = predict(model, X_test(i,:)); 
        bagging(j) = bagging(j) + rat(2); 
    end 
    [maxn, maxp] = max(bagging); 
    y_predict(i) = y_labels(maxp); 
end 
end

3.多分类(调用libsvm工具箱)

【这个工具箱总是出现奇怪的问题，不是很推荐】

以下代码是调用matlab工具箱libsvm的一种方法

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TrainingSet=[ 1 10;2 20;3 30;4 40;5 50;6 66;3 30;4.1 42];%训练数据 
TestSet=[3 34; 1 14; 2.2 25; 6.2 63];%测试数据 
GroupTrain=[1;1;2;2;3;3;2;2];%训练标签 
GroupTest=[1;2;1;3];%测试标签 %svm分类 
model = svmtrain(GroupTrain,TrainingSet); % SVM网络预测 
[predict_label] = svmpredict(GroupTest,TestSet,model);

之所以放到最后，是因为需要在matlab安装libsvm的工具箱，具体方法可参看此链接在Matlab中安装LibSVM工具箱

以上内容转载改进自这里

2024-4-23
【最近在尝试用SVM做通信信号分选，仿真实验的时候碰到了题目问题，写篇Blog记录一下解决过程】
最后记录一下我的解决代码：

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%% 使用支持向量机SVM进行分类
% 分开训练数据和测试数据
numTrain = DataSet;  
numTest = size(features, 1) - numTrain;
svmTraining = features(1:numTrain, :);
svmTrainingLabel = featureLabels(1:numTrain, :);
svmTest = features(numTrain+1:end, :);
svmTestLabel = featureLabels(numTrain+1:end, :);
% histogram(svmTestLabel,'BarWidth',0.5);
% 随机重排
randp = randperm(size(svmTraining,1));
svmTraining = svmTraining(randp,:);
svmTrainingLabel = svmTrainingLabel(randp,:);
randp = randperm(size(svmTest,1));
svmTest = svmTest(randp,:);
svmTestLabel = svmTestLabel(randp,:);

LabelSet = unique(svmTrainingLabel);
LabelSet = string(LabelSet);
NumClass = size(LabelSet, 1);
svmModels = cell(NumClass, 1);
% 训练NumClass个模型，每个模型针对一种调制类型，将是与不是作为判断数据导入svm进行二分类
for i = 1:NumClass
    class_i_place = find(svmTrainingLabel == LabelSet(i));
    svm_train_x = svmTraining(class_i_place, :);
    sample_num1 = numel(class_i_place);
    sample_num2 = min(numel(class_i_place), numTrain-sample_num1);
    class_others = find(svmTrainingLabel ~= LabelSet(i));
    randp = randperm(numel(class_others));
    svm_train_minus = randp(1:sample_num2)';
    svm_train_x = [svm_train_x; svmTraining(svm_train_minus, :)];
    svm_train_y = [ones(sample_num1, 1); -1 * ones(sample_num2, 1)];
    fprintf('正在生成%s类的模型，进度%d/%d\n', LabelSet(i), i, NumClass)
    svmModels{i} = fitcsvm(svm_train_x, svm_train_y);
end
svmTestPred = strings(numTest, 1);
% 对每条数据，n个模型分别进行预测，选择label为1且概率最大的一个作为预测类别
for i = 1:numTest
    bagging = zeros(NumClass, 1);
    for j = 1:NumClass
        model = svmModels{j};
        [~, rat] = predict(model, svmTest(i, :));
        bagging(j) = rat(2);
    end
    [maxn, maxp] = max(bagging);
    svmTestPred(i) = LabelSet(maxp);
end
svmTestPred = categorical(svmTestPred);
testAccuracy = mean(svmTestPred == svmTestLabel);
disp("Test accuracy:" +testAccuracy * 100 + " %")
figure
cm = confusionchart(svmTestLabel, svmTestPred);
cm.Title = 'Confusion Matrix for SVM    Accuracy: ' + string(testAccuracy*100) + ' %';
cm.RowSummary = 'row-normalized';
cm.Parent.Position = [cm.Parent.Position(1:2), 740, 424];
saveas(gcf, 'confusion_matrix_restruct.png');