Delaunay Component Analysis for Evaluation of Data Representations

TL;DR

This paper introduces Delaunay Component Analysis (DCA), a novel evaluation method for data representations that reliably estimates data manifolds using Delaunay graphs, outperforming existing methods especially in complex geometric scenarios.

Contribution

The paper presents DCA, a new manifold approximation technique based on Delaunay graphs, and a framework for assessing individual data representations, addressing limitations of prior geometric analysis methods.

Findings

DCA provides reliable manifold estimation in complex geometric arrangements.

The framework effectively evaluates the quality of individual data representations.

Experimental validation shows DCA's advantages over existing methods across various neural network models.

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.