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Adversarial machine learning has attracted a great amount of attention inrecent years. In a poisoning attack, the adversary can inject a small number ofspecially crafted samples into the training data which make the decisionboundary severely deviate and cause unexpected misclassification. Due to thegreat importance and popular use of support vector machines (SVM), we considerdefending SVM against poisoning attacks in this paper. We study two commonlyused strategies for defending: designing robust SVM algorithms and datasanitization. Though several robust SVM algorithms have been proposed before,most of them either are in lack of adversarial-resilience, or rely on strongassumptions about the data distribution or the attacker's behavior. Moreover,the research on their complexities is still quite limited. We are the first, tothe best of our knowledge, to prove that even the simplest hard-marginone-class SVM with outliers problem is NP-complete, and has no fully PTASunless P$=$NP (that means it is hard to achieve an even approximate algorithm).For the data sanitization defense, we link it to the intrinsic dimensionalityof data; in particular, we provide a sampling theorem in doubling metrics forexplaining the effectiveness of DBSCAN (as a density-based outlier removalmethod) for defending against poisoning attacks. In our empirical experiments,we compare several defenses including the DBSCAN and robust SVM methods, andinvestigate the influences from the intrinsic dimensionality and data densityto their performances.

Defending SVMs against Poisoning Attacks: the Hardness and DBSCAN Approach