Delaunay Component Analysis for Evaluation of Data Representations

Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data representations have been proposed. In this work, we introduce Delaunay Component Analysis (DCA) -an evaluation algorithm which approximates the data manifold using a more suitable neighbourhood graph called Delaunay graph. This provides a reliable manifold estimation even for challenging geometric arrangements of representations such as clusters with varying shape and density as well as outliers, which is where existing methods often fail. Furthermore, we exploit the nature of Delaunay graphs and introduce a framework for assessing the quality of individual novel data representations. We experimentally validate the proposed DCA method on representations obtained from neural networks trained with contrastive objective, supervised and generative models, and demonstrate various use cases of our extended single point evaluation framework. Recently, more general evaluation methods such as Geometry Score (GS) (Khrulkov & Oseledets, 2018) , Improved Precision and Recall (IPR) (Kynkäänniemi et al., 2019) and Geometric Component Analysis (GeomCA) (Poklukar et al., 2021) have been proposed.