Where and How: Mining Convertible Outlying Aspect for Outlier Interpretation

Outlier interpretation methods, based on outlying aspect mining, have been extensively utilized in diverse applications due to their effectiveness and interpretability. The primary objective of these methods is to identify an outlying feature subspace where a detected outlier deviates most significantly from the inliers. However, this subspace is typically not personalized and incomplete. In this article, we propose a novel convertible outlying aspect mining method named Mining convErtible ouTlying Aspect (META) to interpret the detected outlier. META not only identifies a personalized outlying feature subspace (i.e., where) that differentiates the detected outlier from inliers, but also quantifies the outlying direction and degree within this subspace (i.e., how), thereby offering actionable interpretative insights, rather than corrective actions, for understanding the outlier. Specifically, META defines a convertible outlying aspect with a convertible cost to convert the detected outlier into a converted instance, and employs a pretrained adversary to evaluate whether the instance is an inlier or not. Subsequently, we formulate an objective function that minimizes the convertible cost, ensures the successful conversion of the instance into an inlier, and minimizes the size of the outlying feature subspace. META leverages this objective function to learn an optimal convertible outlying aspect for the detected outlier. The optimal convertible outlying aspect provides the outlying feature subspace, outlying direction, outlying degree, and converted instance. Empirical results from experiments conducted on both real-world and synthetic datasets demonstrate that META outperforms state-of-the-art (SOTA) baselines.