How to decide the range for the hyperparameter space in SVM tuning? (MATLAB)

Question

I am tuning an SVM using a for loop to search in the range of hyperparameter's space. The svm model learned contains the following fields

   SVMModel: [1×1 ClassificationSVM]
          C: 2
FeaturesIdx: [4 6 8]
      Score: 0.0142

Question1) What is the meaning of the field 'score' and its utility?

Question2) I am tuning the BoxConstraint, C value. Let, the number of features be denoted by the variable featsize. The variable gridC will contain the search space which can start from any value say 2^-5, 2^-3, to 2^15 etc. So, gridC = 2.^(-5:2:15). I cannot understand if there is a way to select the range?

Answer 1

1. score had been documented in here, which says:

Classification Score The SVM classification score for classifying observation x is the signed distance from x to the decision boundary ranging from -∞ to +∞. A positive score for a class indicates that x is predicted to be in that class. A negative score indicates otherwise.

In two class cases, if there are six observations, and the predict function gave us some score value called TestScore, then we could determine which class does the specific observation ascribed by:

TestScore=[-0.4497    0.4497
           -0.2602    0.2602;
           -0.0746    0.0746;
            0.1070   -0.1070;
            0.2841   -0.2841;
            0.4566   -0.4566;];
[~,Classes] = max(TestScore,[],2);

In the two-class classification, we can also use find(TestScore > 0) instead, and it is clear that the first three observations are belonging to the second class, and the 4th to 6th observations are belonging to the first class.

In multiclass cases, there could be several scores > 0, but the code max(scores,[],2) is still validate. For example, we could use the code (from here, an example called Find Multiple Class Boundaries Using Binary SVM) following to determine the classes of the predict Samples.

for j = 1:numel(classes);
    [~,score] = predict(SVMModels{j},Samples);
    Scores(:,j) = score(:,2); % Second column contains positive-class scores
end
[~,maxScore] = max(Scores,[],2);

Then the maxScore will denote the predicted classes of each sample.

2. The BoxConstraint denotes C in the SVM model, so we can train SVMs in different hyperparameters and select the best one by something like:

gridC = 2.^(-5:2:15);
for ii=1:length(gridC)
SVModel = fitcsvm(data3,theclass,'KernelFunction','rbf',...
    'BoxConstraint',gridC(ii),'ClassNames',[-1,1]);
%if (%some constraints were meet) 
%  %save the current SVModel
%end
end

Note: Another way to implement this is using libsvm, a fast and easy-to-use SVM toolbox, which has the interface of MATLAB.