Augmenting these graph models with topological features via persistent homology (PH) has gained prominence, but identifying the class of attributed graphs that PH can recognize remains open. We introduce a novel concept of color-separating sets to provide a complete resolution to this important problem.

This state of the art was recently critiqued by O'Bray et al.

PsHD compared to sample representation and pair-wise similarity distillation methods theoretically and experimentally.

Neural Information Processing Systems http://nips.cc/

However, PDs are point multi-sets which can not be used in machine learning algorithms for vector data.

Graphcodes handle datasets that are filtered along two real-valued scale parameters.

A multiset is a set where each element appears with some non-zero multiplicity.

Because of the generality of Definition 1.1, it may be that