Editing Support vector machine (section)

=== Regularization and stability ===
In order for the minimization problem to have a well-defined solution, we have to place constraints on the set <math>\mathcal{H}</math> of hypotheses being considered. If <math>\mathcal{H}</math> is a [[Normed vector space|normed space]] (as is the case for SVM), a particularly effective technique is to consider only those hypotheses <math> f</math> for which <math>\lVert f \rVert_{\mathcal H} < k</math> . This is equivalent to imposing a ''regularization penalty'' <math>\mathcal R(f) = \lambda_k\lVert f \rVert_{\mathcal H}</math>, and solving the new optimization problem

<math display="block">\hat f = \mathrm{arg}\min_{f \in \mathcal{H}} \hat \varepsilon(f) + \mathcal{R}(f).</math>

This approach is called ''[[Tikhonov regularization]].''

More generally, <math>\mathcal{R}(f)</math> can be some measure of the complexity of the hypothesis <math>f</math>, so that simpler hypotheses are preferred.