Estimating data complexity and drift through a multiscale generalized impurity approach

The quality of machine learning solutions, and of classifier models in general, depend largely on the performance of the chosen algorithm, and on the intrinsic characteristics of the input data. Although work has been extensive on the former of these aspects, the latter has received comparably less attention. In this paper, we introduce the Multiscale Impurity Complexity Analysis (MICA) algorithm for the quantification of class separability and decision-boundary complexity of datasets. MICA is both model and dimensionality-independent and can provide a measure of separability based on regional impurity values. This makes it so that MICA is sensible to both global and local data conditions. We show MICA to be capable of properly describing class separability in a comprehensive set of both synthetic and real datasets and comparing it against other state-of-the-art methods. After establishing the robustness of the proposed method, alternative applications are discussed, including a streaming-data variant of MICA (MICA-S), that can be repurposed into a model-independent method for concept drift detection.