# sf.apps.points.rbf_kernel¶

rbf_kernel(R, sigma)[source]

Calculate the RBF kernel matrix from a set of input points.

The kernel parameter $$\sigma$$ is used to define the kernel scale. Points that are much further than $$\sigma$$ from each other lead to small entries of the kernel matrix, whereas points much closer than $$\sigma$$ generate large entries.

The Euclidean norm is used to measure distance in this function, resulting in a positive-semidefinite kernel.

Example usage:

>>> R = np.array([[0, 1], [1, 0], [0, 0], [1, 1]])
>>> rbf_kernel (R, 1.0)
array([[1., 0.36787944, 0.60653066, 0.60653066],
[0.36787944, 1., 0.60653066, 0.60653066],
[0.60653066, 0.60653066, 1., 0.36787944],
[0.60653066, 0.60653066, 0.36787944, 1.,]])

Parameters
• R (array) – Coordinate matrix. Rows of this array are the coordinates of the points.

• sigma (float) – kernel parameter

Returns

the RBF kernel matrix

Return type

K (array)