Re:An Introduction to Support Vector Machines
by Longwelwind on Friday June 23, 2017 @02:47AM
(#14617415)
During the learning phase of the SVM, you try to find an hyperplane that maximizes the margin.
The decision function of an SVM can be written as:
f(x) = sign(sum alpha_sv y_sv k(x, sv))
Where sum represents the sum over all support vectors "sv", "y_sv" represents the class of the sample (red=1, blue=-1, for example), "alpha_sv" is the result of the optimization in the learning phase during the learning phase (it is equal to zero for a point that is not a support vector, and is positive otherwise).
The decision function is a sum over all support vectors balanced by the "k" function (that can thus be seen a similarity function between 2 points in your kernel), the y_i will make the term positive or negative depending on the class of the support vector. You take the sign of this sum (1 -> red, -1 -> blue, in our example), and it gives you the predicted class of your sample.
The decision function of an SVM can be written as:
Where sum represents the sum over all support vectors "sv", "y_sv" represents the class of the sample (red=1, blue=-1, for example), "alpha_sv" is the result of the optimization in the learning phase during the learning phase (it is equal to zero for a point that is not a support vector, and is positive otherwise).The decision function is a sum over all support vectors balanced by the "k" function (that can thus be seen a similarity function between 2 points in your kernel), the y_i will make the term positive or negative depending on the class of the support vector. You take the sign of this sum (1 -> red, -1 -> blue, in our example), and it gives you the predicted class of your sample.