3
$\begingroup$

I have read here that an easy way to turn a distance function $d$ into a similarity function $s$ is to compute: $s = e^{-\gamma * d}$. I believe that this is also what is done with the RBF kernel. There the distance function is the squared eucledian distance $||x - y||^2$ and the corresponding kernel function is: $e^{-\gamma * ||x - y||^2}$. However I'm unable to find a name for this kind of method and I can't find any scientific papers where this method is introduced or applied. Can you point me to some papers with more information ?

(Notice that the distance function I want to turn into a similarity function (kernel function) is not a distance metric. I'm also aware that the resulting kernel function might not be a valid psd kernel.)

$\endgroup$
2
$\begingroup$

Seminal NIPS paper:

  • Schölkopf, B. (2000). The kernel trick for distances. In Neural Information Processing Systems, pages 301-307.

There are many kernel design papers and books:

  • Schölkopf, B. and Smola, A. J. (2002). Learning with kernels : support vector machines, regularization, optimization, and beyond. Adaptive computation and machine learning. MIT Press.
  • Pekalska, E., Paclik, P., and Duin, R. P. W. (2002). A generalized kernel approach to dissimilarity-based classification. J. Mach. Learn. Res., 2:175-211.
  • Pekalska, E. and Duin, R. P. W. (2005). The Dissimilarity Representation for Pattern Recognition. World Scientific Publishing Co., Inc., River Edge, NJ, USA.
  • Haasdonk, B. and Bahlmann, C. (2004). Learning with distance substitution kernels. Pattern Recognition, volume 3175 of Lecture Notes in Computer Science, pages 220-227-227.
$\endgroup$
  • $\begingroup$ yes the last paper you listed is exactly what I was looking for thanks :) $\endgroup$ – nico1510 Apr 14 '15 at 15:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.