Non Linear SVM and Kernal function

 Non-Linear SVM and Kernal function

Non Linear Data: If a data set or given sample can not be separated by a single line then it is non linear data.

Non Linear SVM: To separate non linear data, non linear SVM is used.

Trick Kernel Function: To separate non linear data Trick Kernals are used. Both non linear data and Trick Kernals are related to each other.

Non Linear Data: Figure 2 shows non linear data. Single line or straight line can not separate these data. Straight line gives less than 50% accuracy.

        Figure1: Non Linear Data

Solution to this problem is use of Trick Kernel.

Trick Kernel takes input low dimensional feature space and convert into high dimensional feature space so that non separable data get separated

 Two dimensional data converted into three dimensional data using kernel as shown in figure 1 and it become seperable.

·         Following are the different kernel used in SVM:

Ø  Liner Kernel

·     A linear kernel is a dot product of any two given observations.The product between two vectors is the sum of the multiplication of each pair of input values.

Ø  Polynomial Kernel

·     A more generalized form of linear kernel is Polynomial Kernel.The Polynomial Kernel  can differentiate between curved or nonlinear input space

Ø  Radial basis Function Kernel

·    The Input space can be mapped in infinite dimensional space by RBF kernel It is a local kernel and can create complex regions within the feature space like e.g. closed polygons in 2D space.

Ø  Sigmoid Kernel

·     The Sigmoid kernel has its origin form Neural Networks.Neural Networks approach as we used for classification of input data.  

Imp:Trick Kernel takes input low dimensional feature space and convert into high dimensional feature space so that non separable data get separated