A Mathematical Introduction to SVMs with Self-Concordant Kernel

EasyChair Preprint 15341

Abstract

A derivation of so-called ``soft-margin
support vector machines with kernel'' is presented
along with elementary proofs that do not rely
on concepts from functional analysis such as Mercer's theorem
or reproducing kernel Hilbert spaces which are 
frequently cited in this context.
The analysis leads to new 
continuity properties of the kernel functions,
in particular a self-concordance condition for the kernel.
Practical aspects concerning the implementation
and the choice of the kernel are addressed and illustrated with
some numerical examples.
The derivations are intended for a general audience, requiring 
basic knowledge of calculus and linear algebra, while
some more advanced results
from optimization theory are being introduced in a
self-contained form.

Keyphrases: Support Vector Machine, continuity, kernel

@booklet{EasyChair:15341,
  author    = {Florian Jarre},
  title     = {A Mathematical Introduction to SVMs with Self-Concordant Kernel},
  howpublished = {EasyChair Preprint 15341},
  year      = {EasyChair, 2024}}