Outlier, or anomaly, detection is essential for optimal performance of machine learning methods and statistical predictive models. It is not just a technical step in a data cleaning process but a key topic in many fields such as fraudulent document detection, in medical applications and assisted diagnosis systems or detecting security threats. In contrast to population-based methods, neighborhood based local approaches are simple flexible methods that have the potential to perform well in small sample size unbalanced problems. However, a main concern of local approaches is the impact that the computation of each sample neighborhood has on the method performance. Most approaches use a distance in the feature space to define a single neighborhood that requires careful selection of several parameters. This work presents a local approach based on a local measure of the heterogeneity of sample labels in the feature space considered as a topological manifold. Topology is computed using the communities of a weighted graph codifying mutual nearest neighbors in the feature space. This way, we provide with a set of multiple neighborhoods able to describe the structure of complex spaces without parameter fine tuning. The extensive experiments on real-world data sets show that our approach overall outperforms, both, local and global strategies in multi and single view settings.
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