Many machine learning systems rely on data collected in the
wild from untrusted sources, exposing the learning algorithms to data
poisoning. Attackers can inject malicious data in the training dataset
to subvert the learning process, compromising the performance of the
algorithm producing errors in a targeted or an indiscriminate way. Label
flipping attacks are a special case of data poisoning, where the attacker
can control the labels assigned to a fraction of the training points. Even
if the capabilities of the attacker are constrained, these attacks have
been shown to be effective to significantly degrade the performance of
the system. In this paper we propose an efficient algorithm to perform
optimal label flipping poisoning attacks and a mechanism to detect and
relabel suspicious data points, mitigating the effect of such poisoning
attacks.