libsvm with precomputed kernel: How do I compute the classification scores?

Question

I am working with libsvm in MATLAB and am training and testing a 1-vs-all SVM with a precomputed non-linear kernel. I'm a bit new to SVMs and I am trying to calculate the decision function. I know that for a linear SVM, we can obtain w by (according to libsvm documentation):

w = model.sv_coef'*model.SVs;

We can then calculate the decision values according to:

w'*x

and subsequently, predict the label accoding to sign(w'*x+b)where b is some threshold.

I am interested specifically in obtaining the classification score from my non-linear kernel. How do I go about this?

Answer 1

I'm trying to understand what do you mean by classification score. Actually you can compare the probability of each model, and select the largest one, as what I did in your previous post.

It is also fine if you are using decision functions. Suppose you are using RBF kernel, and model.Label(1) = 1, then you have (if model.Label(1) = -1, then w = -w; b = -b;)

[m,n] = size(model.SVs); % m is the number of support vectors,...
                           and n is the number of features
w = model.sv_coef; % m*1 weight vector
b = -model.rho; % scalar

Now you are given v under test. And you also have [1,n] = size(v); Then for each row i in support vectors, compute the Euclidean distance (you can vectorize the code below):

for i = 1:m
    d(i) = norm(model.SVs(i,:) - v);
    t(i) = exp(-gamma* d(i) .^2); % RBF model, t is 1*m vector
end

And the decision function (or score from the decision function) is:

s = t * w + b;

You can obtain the decision function similarly with other non-linear kernels.

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EDIT

With a self-written precomputed kernel, let's take the RBF kernel as example:

% RBF kernel: exp(-gamma*|u-v|^2)

rbf = @(X,Y) exp(-gamma .* pdist2(X,Y,'euclidean').^2);

% Kernel matrices with sample serial number as first column as required 

K_train =  [(1:numTrain)' , rbf(trainData,trainData)];
K_test =   [(1:numTest)'  , rbf(testData,trainData)];

%# train and test
model             = svmtrain(trainLabel, K_train, '-t 4');
[predLabel, ~, ~] = svmpredict(testLabel, K_test, model);

%# confusion matrix
C = confusionmat(testLabel,predLabel);