Detecting and ranking outliers in high-dimensional data

Detecting outliers in high-dimensional data is a challenging problem. In high-dimensional data, outlying behaviour of data points can only be detected in the locally relevant subsets of data dimensions. The subsets of dimensions are called subspaces and the number of these subspaces grows exponentially with increase in data dimensionality. A data point which is an outlier in one subspace can appear normal in another subspace. In order to characterise an outlier, it is important to measure its outlying behaviour according to the number of subspaces in which it shows up as an outlier. These additional details can aid a data analyst to make important decisions about what to do with an outlier in terms of removing, fixing or keeping it unchanged in the dataset. In this paper, we propose an effective outlier detection algorithm for high-dimensional data which is based on a recent density-based clustering algorithm called SUBSCALE. We also provide ranking of outliers in terms of strength of their outlying behaviour. Our outlier detection and ranking algorithm does not make any assumptions about the underlying data distribution and can adapt according to different density parameter settings. We experimented with different datasets, and the top-ranked outliers were predicted with more than 82% precision as well as recall.