Given two data samples (vectors) x1 ∈ ℝn and x2 ∈ ℝn , and a non-zero parameter σ, radial basis function kernelK ( x1, x2) , or RBF kernel or Gaussian RBF kernel, is defined as: K (x1, x2) = exp ( - ‖x1 - x2‖22σ2 ) , where ‖x1 - x2‖ is the Euclidean distance between x1 and x2 . Alternatively, if we use parameter γ = 12σ2 , we can define: K (x1, x2) = e - γ‖x1-x2‖2 If we are given data samples xi , i=1,m, as rows of a ℝm×n matrix X, then we can calculate m×m matrix K of RBF distances (differences) K (xi, xj) between the ith and the jth row of a matrix X. Given that K (xi, xj) = K (xj, xi) and K (xi, xi) = 1 , we are returning only the upper triangle of K as a result.
Please Note:
All values are calculated with the precision of 10-15, but are displayed with the precision of 10-9.
Empty cell will be defaulted to value 0
If uploading values for x1 and x2 from a file, file must be an ASCII file. Values for x1 must be in the first row of the file, and the values for the x2 must be in the second row of the file. The individual numbers in the row must be separated by either comma ( , ), semicolon ( ; ) or pipe ( | ) character.
