  We introduce the anti-profile Support Vector Machine (apSVM) as a novel
algorithm to address the anomaly classification problem, an extension of
anomaly detection where the goal is to distinguish data samples from a number
of anomalous and heterogeneous classes based on their pattern of deviation from
a normal stable class. We show that under heterogeneity assumptions defined
here that the apSVM can be solved as the dual of a standard SVM with an
indirect kernel that measures similarity of anomalous samples through
similarity to the stable normal class. We characterize this indirect kernel as
the inner product in a Reproducing Kernel Hilbert Space between representers
that are projected to the subspace spanned by the representers of the normal
samples. We show by simulation and application to cancer genomics datasets that
the anti-profile SVM produces classifiers that are more accurate and stable
than the standard SVM in the anomaly classification setting.
