How to customize a kernel function in ksvm of kernlab package?

Question

I have latitudes and longitudes, so I need to redefine the RBF kernel into exp(-1/2||sophere distrance||^2), which means I need to rewrite a kernel function myself. I write my kernel as follows:

round.kernel <- function(x,y){
  sigma <- 1
  #R <- 6371
  R <- 1
  a <- (sin( (x[1]-y[1])/2 ))^2+cos(x[1])*cos(y[1])*(sin((x[2]-y[2])/2))^2
  c <- 2*atan2(sqrt(a),sqrt(1-a))
  d <- R*c
  res <- exp(-d^2/(2*sigma))
  return (res)
}
class(round.kernel) <- "kernel"

I tested the function, the kernel should be correct. But with the following training command I am getting the error:

fit <- ksvm(y=train[,2],x=train[,3:4],kernel=round.kernel,type='eps-svr')

Error in .local(x, ...) : 
  List interface supports only the stringdot kernel.

The more trickly thing is, I tried the sample code in ksvm document:

k <- function(x,y) {(sum(x*y) +1)*exp(-0.001*sum((x-y)^2))}
class(k) <- "kernel"

But I am getting the same error.

Anyone knows how to correctly define a kernel function?

This is really helpful. Can you explain how you derived the kernel function? I don't see the connection between exp(-1/2||sphere distnace||^2) and how you complete `res`. — momeara, Aug 24 '13 at 13:29
@momeara, I think it is basically based on triangle functions, so there can be multiple ways to do it using arctan, arcsin, or here like atan2. Check this link: http://www.movable-type.co.uk/scripts/latlong.html — Yitong Zhou, Aug 25 '13 at 10:59

score 7 · Accepted Answer · answered Jun 12 '13 at 22:17

My problem is solved as follows: the kernel codes are correct, I should directly define a function(x,y), and declare its class as "kernel". The problem is even in the doc the ksvm does support x,y styles, they actually do not work. Changing it to formula-data style can finally get things running:

fit <- ksvm(Freq~lat+lon,data=train[,2:4],kernel=roundrbf,type='eps-svr')

Moreover, I also read the source code of rbfdot, and other kernels defined in the kernlab itself. Notice their codes style is like this:

function(params){
  val <- function(x,y){
  # True kernel defined here
  }
  return (new ("kernel_name",.Data=val,kpar=list(params)))
}

But seriously, I tried, and making the kernel functions in this style won't work. The working way is like this style directly:

k <- function(x,y){
  #calculate the result
}
class(k) <- "kernel"

How to customize a kernel function in ksvm of kernlab package?

1 Answers1