  Kernel-based regularized risk minimizers, also called support vector machines
(SVMs), are known to possess many desirable properties but suffer from their
super-linear computational requirements when dealing with large data sets. This
problem can be tackled by using localized SVMs instead, which also offer the
additional advantage of being able to apply different hyperparameters to
different regions of the input space. In this paper, localized SVMs are
analyzed with regards to their consistency. It is proven that they inherit
$L_p$- as well as risk consistency from global SVMs under very weak conditions
and even if the regions underlying the localized SVMs are allowed to change as
the size of the training data set increases.
