Delta-Convex Skins for Constructing Training and Testing sets in Supervised Learning

The paper presents heuristics and several algorithms for constructing training/testing sets for supervised machine learning based on layered geometric structures <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\delta$</tex>-convex decompositions) extracted from input space data. Experiments with well-known datasets from public repositories showed that models derived from training/testing sets constructed via the proposed heuristics closely match or improve upon those using sets coming solely from random sampling. The insights coming from the exploitation of structural information represent a promising way of better using the available data for unsupervised and supervised modeling. Despite the advantages, the presented approaches have limitations and challenges associated with data complexities and geometric degeneracies usually related to the increased dimensionality of input feature spaces. The study discusses these issues and includes explorations of mitigation strategies based on working with lower dimensional manifold data representations with promising results. This is a preliminary study and future work exploring these concepts and approaches is necessary.