Which of the following is not a kernel?(1 Point)Polynomial KernelGaussian KernelSigmoid KernelNone of these

To determine which of the given options is not a kernel, we need to analyze each of the suggested kernels to verify their validity under the mathematical framework of kernel functions.

1. Polynomial Kernel: This kernel is defined as $K(x, y) = (x \cdot y + c)^d$, where $c$ is a constant and $d$ is the degree of the polynomial. It is a valid kernel since it satisfies Mercer's theorem.

2. Gaussian Kernel: Also known as the Radial Basis Function (RBF) kernel, it is defined as $K(x, y) = e^{-\frac{\|x - y\|^2}{2\sigma^2}}$, where $\sigma$ is a parameter. This kernel is proven to be valid as it meets the requirements of a kernel function.

3. Sigmoid Kernel: This kernel is defined as $K(x, y) = \tanh(\alpha (x \cdot y) + c)$, where $\alpha$ and $c$ are constants. However, this kernel does not always satisfy the conditions of Mercer's theorem for certain parameters, which means it is not a general valid kernel.

4. None of these: This option suggests that all the listed kernels are valid.

Final Answer

The option that is not a kernel is the Sigmoid Kernel.