使用交叉验证和 F1 分数选择 SVM 参数

Question

我需要在 SVM 中调整 C 和 Sigma 时跟踪 F1 分数， 例如下面的代码跟踪准确度，我需要将其更改为 F1-Score 但我无法做到…….

%# read some training data
[labels,data] = libsvmread('./heart_scale');

%# grid of parameters
folds = 5;
[C,gamma] = meshgrid(-5:2:15, -15:2:3);

%# grid search, and cross-validation
cv_acc = zeros(numel(C),1);
    for i=1:numel(C)
cv_acc(i) = svmtrain(labels, data, ...
                sprintf('-c %f -g %f -v %d', 2^C(i), 2^gamma(i), folds));
end

%# pair (C,gamma) with best accuracy
[~,idx] = max(cv_acc);

%# now you can train you model using best_C and best_gamma
best_C = 2^C(idx);
best_gamma = 2^gamma(idx);
%# ...

我看过以下两个链接

Retraining after Cross Validation with libsvm

10 fold cross-validation in one-against-all SVM (using LibSVM)

我明白我必须首先在训练数据上找到最佳的 C 和 gamma/sigma 参数，然后使用这两个值进行 LEAVE-ONE-OUT 交叉验证分类实验， 所以我现在想要的是首先进行网格搜索以调整 C 和 sigma。 请我更喜欢使用 MATLAB-SVM 而不是 LIBSVM。 下面是我的 LEAVE-ONE-OUT 交叉验证分类代码。

... clc
 clear all
close all
a = load('V1.csv');
X = double(a(:,1:12));
Y = double(a(:,13));
% train data
datall=[X,Y];
A=datall;
n = 40;
ordering = randperm(n);
B = A(ordering, :);  
good=B; 
input=good(:,1:12);
target=good(:,13);
CVO = cvpartition(target,'leaveout',1);  
cp = classperf(target);                      %# init performance tracker
svmModel=[];
for i = 1:CVO.NumTestSets                                %# for each fold
trIdx = CVO.training(i);              
teIdx = CVO.test(i);                   
%# train an SVM model over training instances

svmModel = svmtrain(input(trIdx,:), target(trIdx), ...
       'Autoscale',true, 'Showplot',false, 'Method','ls', ...
      'BoxConstraint',0.1, 'Kernel_Function','rbf', 'RBF_Sigma',0.1);
%# test using test instances
pred = svmclassify(svmModel, input(teIdx,:), 'Showplot',false);
%# evaluate and update performance object
cp = classperf(cp, pred, teIdx); 
end
%# get accuracy
accuracy=cp.CorrectRate*100
sensitivity=cp.Sensitivity*100
specificity=cp.Specificity*100
PPV=cp.PositivePredictiveValue*100
NPV=cp.NegativePredictiveValue*100
%# get confusion matrix
%# columns:actual, rows:predicted, last-row: unclassified instances
cp.CountingMatrix
recallP = sensitivity;
recallN = specificity;
precisionP = PPV;
precisionN = NPV;
f1P = 2*((precisionP*recallP)/(precisionP + recallP));
f1N = 2*((precisionN*recallN)/(precisionN + recallN));
aF1 = ((f1P+f1N)/2);

我已更改代码 但我犯了一些错误，我得到了错误，

a = load('V1.csv');
X = double(a(:,1:12));
Y = double(a(:,13));
% train data
datall=[X,Y];
A=datall;
n = 40;
ordering = randperm(n);
B = A(ordering, :);  
good=B; 
inpt=good(:,1:12);
target=good(:,13);
k=10;
cvFolds = crossvalind('Kfold', target, k);   %# get indices of 10-fold CV
cp = classperf(target);                      %# init performance tracker
svmModel=[];
for i = 1:k 
    testIdx = (cvFolds == i);    %# get indices of test    instances
trainIdx = ~testIdx;   
C = 0.1:0.1:1; 
S = 0.1:0.1:1; 
fscores = zeros(numel(C), numel(S)); %// Pre-allocation
for c = 1:numel(C)   
for s = 1:numel(S)
    vals = crossval(@(XTRAIN, YTRAIN, XVAL, YVAL)(fun(XTRAIN, YTRAIN, XVAL, YVAL, C(c), S(c))),inpt(trainIdx,:),target(trainIdx));
    fscores(c,s) = mean(vals);
end
end
 end

[cbest, sbest] = find(fscores == max(fscores(:)));
C_final = C(cbest);
S_final = S(sbest);    

.......

还有功能.....

.....
function fscore = fun(XTRAIN, YTRAIN, XVAL, YVAL, C, S)
svmModel = svmtrain(XTRAIN, YTRAIN, ...
   'Autoscale',true, 'Showplot',false, 'Method','ls', ...
  'BoxConstraint', C, 'Kernel_Function','rbf', 'RBF_Sigma', S);

   pred = svmclassify(svmModel, XVAL, 'Showplot',false);

   cp = classperf(YVAL, pred)
   %# get accuracy
    accuracy=cp.CorrectRate*100
    sensitivity=cp.Sensitivity*100
    specificity=cp.Specificity*100
    PPV=cp.PositivePredictiveValue*100
    NPV=cp.NegativePredictiveValue*100
    %# get confusion matrix
    %# columns:actual, rows:predicted, last-row: unclassified instances
    cp.CountingMatrix
    recallP = sensitivity;
    recallN = specificity;
    precisionP = PPV;
    precisionN = NPV;
    f1P = 2*((precisionP*recallP)/(precisionP + recallP));
    f1N = 2*((precisionN*recallN)/(precisionN + recallN));
    fscore = ((f1P+f1N)/2);

    end

Answer 1

所以基本上你想采用你的这条线：

svmModel = svmtrain(input(trIdx,:), target(trIdx), ...
       'Autoscale',true, 'Showplot',false, 'Method','ls', ...
      'BoxConstraint',0.1, 'Kernel_Function','rbf', 'RBF_Sigma',0.1);

将它放在一个循环中，改变您的 'BoxConstraint' 和 'RBF_Sigma' 参数，然后使用 crossval 输出该迭代参数组合的 f1 分数。

您可以像在 libsvm 代码示例中一样使用单个 for 循环（即使用 meshgrid 和 1:numel()，这可能更快）或嵌套 for 循环。我将使用嵌套循环，以便您拥有两种方法：

C = [0.001, 0.003, 0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100, 300] %// you must choose your own set of values for the parameters that you want to test. You can either do it this way by explicitly typing out a list
S = 0:0.1:1 %// or you can do it this way using the : operator
fscores = zeros(numel(C), numel(S)); %// Pre-allocation
for c = 1:numel(C)   
    for s = 1:numel(S)
        vals = crossval(@(XTRAIN, YTRAIN, XVAL, YVAL)(fun(XTRAIN, YTRAIN, XVAL, YVAL, C(c), S(c)),input(trIdx,:),target(trIdx));
        fscores(c,s) = mean(vals);
    end
end

%// Then establish the C and S that gave you the bet f-score. Don't forget that c and s are just indexes though!
[cbest, sbest] = find(fscores == max(fscores(:)));
C_final = C(cbest);
S_final = S(sbest);

现在我们只需要定义函数fun。文档对fun 有这样的说法：

fun 是具有两个输入的函数的函数句柄，训练 X 的子集 XTRAIN 和 X 的测试子集 XTEST，如下：

testval = fun(XTRAIN,XTEST) 每次调用时，fun 应该使用 XTRAIN 拟合一个模型，然后返回一些计算的标准 testval 使用该拟合模型进行 XTEST。

所以fun 需要：

• 输出单个 f 分数
• 将 X 和 Y 的训练和测试集作为输入。请注意，这些都是实际训练集的子集！把它们想象成你的训练集的训练和验证子集。另请注意，crossval 会为您拆分这些设置！
• 在训练子集上训练分类器（使用循环中当前的 C 和 S 参数）
• 在测试（或验证）子集上运行您的新分类器
• 计算并输出性能指标（在您的情况下，您需要 f1 分数）

你会注意到 fun 不能接受任何额外的参数，这就是为什么我将它包装在一个匿名函数中以便我们可以传递当前的 C 和 S 值。（即所有@(...)(fun(...)) 上面的东西。这只是将我们的六个参数fun“转换”为crossval 所需的第四个参数的技巧。

function fscore = fun(XTRAIN, YTRAIN, XVAL, YVAL, C, S)

   svmModel = svmtrain(XTRAIN, YTRAIN, ...
       'Autoscale',true, 'Showplot',false, 'Method','ls', ...
      'BoxConstraint', C, 'Kernel_Function','rbf', 'RBF_Sigma', S);

   pred = svmclassify(svmModel, XVAL, 'Showplot',false);

   CP = classperf(YVAL, pred)

   fscore = ... %// You can do this bit the same way you did earlier
end

Answer 2

我发现target(trainIdx) 的唯一问题。这是一个行向量，所以我将target(trainIdx) 替换为target(trainIdx)，它是一个列向量。