Anomaly Classification with the Anti-Profile Support Vector Machine

TL;DR

This paper presents the anti-profile SVM, a new algorithm for anomaly classification that improves accuracy and stability over standard SVMs by using an indirect kernel based on similarity to normal samples, demonstrated through simulations and cancer genomics data.

Contribution

The paper introduces the anti-profile SVM, extending anomaly detection to classify heterogeneous anomalies using an indirect kernel approach, which is a novel contribution.

Findings

Anti-profile SVM outperforms standard SVM in accuracy.

The method is stable across different datasets.

Effective in cancer genomics anomaly classification.

Abstract

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.