Resistant learning on the envelope bulk for identifying anomalous patterns

Anomalous patterns are observations that lie far away from the fitting function deduced from the bulk of the given observations. This work addresses the research issue to effectively identify anomalous patterns in both contexts of resistant learning, where there is no assumption about the fitting function form, and of changing environments. The resistant learning means that the learning procedure is not impacted significantly by the outlying observations. In literature, there is the resistant learning with searching a near-perfect fitting function for identifying the bulk of the majority of observations. However, the learning algorithm with searching a near-perfect fitting function suffers from time inefficiency. To effectively identify anomalous patterns in both contexts of resistant learning and changing environments, this study proposes a new resistant learning algorithm with envelope module that learns to evolve a nonlinear fitting function wrapped with a constant-width envelope for containing the majority of observations and thus identifying anomalous patterns. An illustrative experiment is set up to justify the effectiveness of the envelope module and the experimental result shows the positive promise.