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Scale Vector Classifier

 Gaussian Radial Basis Function Kernel in SVC. 

    Gaussian Radial Basis (RBF) kernel used to classify non linearly separable data. It is a most powerful function to gain high accuracy. Non linearly separable data is shown as below as first image.

    In this type of data the data points are spread irregularly that's why it is hard to separate them in two dimensional plot, so we use RBF kernel. It is a transform function create landmark(y) in imaginary 3D space. See second image. Assume a data point x on the plane, kernel measures the distance from x to landmark(y) and create a circumference σ. if the data point x is closer to the landmark, the distance will be small and hence the point will be in the circumference. That way we can separate the data points using a circle having σ circumference by getting a projection a 2D plane.

    

    Equation of Gaussian Radial Basis Function: 

    

    k(x,y) = - exp( r||x-y||^2 / 2σ^2 )     

    

    where, r = 1/2d^2 > 0

           d = distance

           x = data point (which had to find out)

           y = landmark

           σ = circumference 





    

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