Delaunay Component Analysis for Evaluation of Data Representations

Petra Poklukar, Vladislav Polianskii, Anastasiia Varava, Florian T. Pokorny, Danica Kragic Jensfelt

Keywords: Interpretation and Evaluation of Learned Representations, Generative Models, Contrastive Learning

Abstract: 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.

One-sentence Summary: We present Delaunay Component Analysis (DCA) framework for evaluation of learned data representations which anayzes geometric and topological properties of representation spaces using Delaunay graphs.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2202.06866/code)