K Minimum Enclosing Balls for Outlier Detection

Outlier detection means to characterize the distribution of inliers exactly enough such that outliers stand out. A natural and interpretable model is an enclosing ball that includes non-outliers but excludes outliers. However, a single enclosing ball is insufficient for data with multiple, distinct clusters or modes. Therefore, we propose a model with K enclosing balls, each of which can cover a separate cluster of data. We investigate two optimization schemes, one based on stochastic gradient descent and one based on alternating optimization and quadratic programming. On synthetic and real-world data we compare our proposed K minimum enclosing ball (K-MEB) approach to baselines from the literature.