Further reading

The categorical database foundation is functorial data migration [ Spivak , 2012 ] . For manifold learning, UMAP [ McInnes et al. , 2018 ] , PaCMAP [ Wang et al. , 2021 ] , and densMAP [ Narayan et al. , 2021 ] illustrate different choices about neighborhood, global, and density preservation. These methods begin after data have been presented as points or a proximity structure; RADAR asks what typed relational information is lost in that presentation.

Relational graph convolution [ Schlichtkrull et al. , 2018 ] , simplicial neural networks [ Ebli et al. , 2020 ] , cellular networks [ Bodnar et al. , 2021 ] , and generalized simplicial attention [ Battiloro et al. , 2024 ] show how typed edges and higher cells can enter a learned representation. Statistical Hodge theory [ Jiang et al. , 2011 ] provides a complementary spectral decomposition. RADAR should be compared with these methods under matched information access and output dimension; its distinctive claim is exact, apex-directed compatibility auditing rather than universal superiority of relational geometry.