MATLAB: Score calculation in ClassificationSVM using linear kernel function

Question

I have binary ClassificationSVM classifier: svmModel. It's trained using linear kernel. I know the score of test data can be obtained through predict(svmModel, testdata). I want to imitate the actual score calculation in the function predict, so I followed the documentation of ClassificationSVM which says:

The linear SVM score function is f(x)=(x/s)′β+b where: x is an observation (corresponding to a row of X). s is the kernel scale and β is the vector of fitted linear coefficients. b is the bias term (corresponding to SVMModel.Bias).

However, when I calculate the score using f(x)=(x/s)′β+b, the score is different from what is returned by the function predict.

My svmModel:

Beta is [-0.9608 0.4401 -1.8665 -0.0358 -1.2389 0.9508 -1.9353 -2.9381 2.2893 1.4051 1.4547] svmModel.KernelParameters.Scale is 1.8839

My test data (1 observation) is [8.939 8.497 7.899 6.755 5.674 7.433 8.600 10.355 5.017 7.442 9.668]. Score from the function predict is 3.2217 -3.2217. Score from f(x)=(x/s)′β+b is -10.9064.

Is there any other steps required besides f(x)=(x/s)′β+b or I am using some parameters wrong ?

Thanks.

Answer 1

In 14a and 14b, the Beta coefficients of an SVM model need to be divided by KernelParameters.Scale to get correct predictions. In 15a, dividing by the scale is no longer necessary.