A Density-Based Backward Approach to Isolate Rare Events in Large-Scale Applications

While significant work in data mining has been dedicated to the detection of single outliers in the data, less research has approached the problem of isolating a group of outliers, i.e. rare events representing micro-clusters of less – or significantly less – than 1% of the whole dataset. This research issue is critical for example in medical applications. The problem is difficult to handle as it lies at the frontier between outlier detection and clustering and distinguishes by a clear challenge to avoid missing true positives. We address this challenge and propose a novel two-stage framework, based on a backward approach, to isolate abnormal groups of events in large datasets. The key of our backward approach is to first identify the core of the dense regions and then gradually augments them based on a density-driven condition. The framework outputs a small subset of the dataset containing both rare events and outliers. We tested our framework on a biomedical application to find micro-clusters of pathological cells. The comparison against two common clustering (DBSCAN) and outlier detection (LOF) algorithms show that our approach is a very efficient alternative to the detection of rare events – generally a recall of 100% and a higher precision, positively correlated wih the size of the rare event – while also providing a

$\mathcal{O}(N)$

solution to the existing algorithms dominated by a

$\mathcal{O}(N^2)$

complexity.