A derivation of so-called ``soft-margin Support Vector Machines with kernel'' is presented which does not rely on concepts from functional analysis such as Mercer's theorem that is frequently cited in this context, and that leads to a new analysis of the continuity properties of the kernel functions such as a new self-concordance condition for the kernel. The derivations are intended for a general audience, requiring some knowledge of calculus and linear algebra, while more advanced results used from optimization theory are being introduced in a self-contained form.

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View A mathematical introduction to SVMs with self-concordant kernel