A validity index for outlier detection

Defining a boundary between inliers and outliers is a major challenge in unsupervised outlier detection. In the absence of labeled data, the true outliers set cannot be evaluated. This lays the burden on both the choice of an efficient outlier detection criterion, and parameter selection. While numerous unsupervised outlier detection criteria, with different parameters, have been proposed, an unsupervised evaluation of outliers is still missing. This work introduces a theoretical basis, and proposes a validity index, to evaluate the quality of outliers. This is not a trivial problem when nothing is known about the structure and density of the data. The proposed index considers the outlierness quality, the deviation between characteristics of outliers and inliers, and the data distortion. Low and high dimensional data sets are used to evaluate the proposed index.