Kernel Matrix RBF Build

Problem

Build the Gaussian RBF kernel matrix for a list of points:

K[i][j] = exp(-||x_i - x_j||_2^2 / (2 * sigma^2))

The result is symmetric with ones on the diagonal.

Hint

The kernel is a decreasing function of squared distance; sigma controls the bandwidth.

case 1

in: [[[0,0],[1,0]],1]

expected: [[1,0.6065306597126334],[0.6065306597126334,1]]

case 2

in: [[[0],[2]],2]

expected: [[1,0.6065306597126334],[0.6065306597126334,1]]

case 3

in: [[[1,1]],1]

expected: [[1]]

case 4

in: [[[0,0],[0,0]],1]

expected: [[1,1],[1,1]]

Starter codePython

def rbf_kernel_matrix(X, sigma):
    # Your code here
    pass

4 test cases · run your code against them in the editor