论文标题

用于评估数据表示的Delaunay组件分析

Delaunay Component Analysis for Evaluation of Data Representations

论文作者

Poklukar, Petra, Polianskii, Vladislav, Varava, Anastasia, Pokorny, Florian, Kragic, Danica

论文摘要

高级表示学习技术需要可靠的一般评估方法。最近,已经提出了几种算法基于从学习的数据表示近似的流形的几何和拓扑分析的共同思想。在这项工作中,我们介绍了Delaunay组件分析(DCA) - 一种评估算法,该算法使用称为Delaunay图的更合适的邻域图近似数据歧管。即使对于具有不同形状和密度和异常值的群集等表征的几何布置,这也提供了可靠的多种估计,这是现有方法经常失败的地方。此外,我们利用Delaunay图的性质,并引入了一个评估单个新型数据表示质量的框架。我们在实验中验证了提出的DCA方法,以从具有对比目标,监督和生成模型训练的神经网络获得的表示,并演示了我们扩展的单点评估框架的各种用例。

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.

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