.rst .pdf

Kernel Functions

A kernel function takes input vectors from the original (\(p\)-dimensional) space and returns the dot product of the vectors in the \(s\)-dimensional feature space. Thus, having \(x,y \in \mathbb{R}^p\) and \(\phi \in \mathbb{R}^p \leftarrow \mathbb{R}^s\), the kernel function is

\[K(x, y) \equiv <\phi (x), \phi (y)>\]

Where \(\phi(x)\) is a vector-valued function: \(\phi(x) = \phi_1(x), \phi_2(x), \ldots, \phi_s(x)\).

If \(\phi (x) = x\), the kernel is linear. Kernels are used in the SVM model, but for some tasks they could be used separately to transform vectors from one space to another.

The following table describes current device support:

Kernel type	CPU	GPU
Linear	Yes	Yes
Polynomial	Yes	No
RBF	Yes	Yes
Sigmoid	Yes	No

• Linear kernel
• Polynomial kernel
• Radial Basis Function (RBF) kernel
• Sigmoid kernel

Examples: Linear Kernel

oneAPI DPC++oneAPI C++

Batch Processing:

• linear_kernel_dense_batch.cpp

Examples: Polynomial Kernel

oneAPI C++

Batch Processing:

• polynomial_kernel_dense_batch.cpp

Examples: RBF Kernel

oneAPI DPC++oneAPI C++

Batch Processing:

• rbf_kernel_dense_batch.cpp

Examples: Sigmoid Kernel

oneAPI C++

Batch Processing:

• sigmoid_kernel_dense_batch.cpp

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