Statistical Depth Measures in Density-Based Clustering with Automatic Adjustment for Skewed Data

Statistical data depth measures have been applied to density-based clustering techniques in an effort to achieve robustness in parameter selection via the affine invariant property of the depth measure. Specifically, the Mahalanobis depth measure is used in the application of DBSCAN. In this paper, we examine properties of the Mahalanobis depth measure that lead to instances where it fails to detect clusters in DBSCAN, whereas Euclidean distance is able to differentiate the clusters. We propose two solutions to the problems induced by these properties. The first re-examines clusters to determine if data shape is causing multiple clusters to be grouped into a single cluster. The second examines the use of a different measure as an alternate depth function. Experiments are provided.