Finding Kernel function for the data set

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For a set of data points how to find an appropriate kernel function to map it to higher dimension so that it will be linearly seperable

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RBF kernels are the most popular one. Preferably, you'd like a kernel that satisfies Mercer's condition, but neural networks normally use sigmoid functions which do not satisfy this condition and it can still work. If your only goal is to make the data linearly separable just use radial basis functions and worry more about the parameters than the type of kernel.