Stolz (2023) shows the two standard TDA landmark-selection rules trade density bias for noise sensitivity, neither addressing structural-selection robustness

Bernadette J. Stolz, "Outlier-Robust Subsampling Techniques for Persistent Homology" (JMLR 24, 2023), surveys the two standard rules used to subsample a point cloud before computing persistent homology on it: uniform random selection and the maxmin (farthest-point) algorithm. Her own framing of their respective failure modes, stated verbatim: "random selection tends to favour dense areas of the data while the maxmin algorithm is very sensitive to noise." She proposes a topology-preserving alternative explicitly evaluated on "robustness to outliers" as its own criterion.

Both standard rules, and Stolz's proposed fix, are organized around the same axis as claim-chazal-2014-persistence-diagram-subsampling-stable-under-noise-not-selection: density bias and noise/outlier sensitivity in an otherwise-unstructured point cloud, not selection by a structural covariate of a network (e.g. node degree). This is landmark selection, the general TDA-field name for the choice this capture's founding question — question-tda-neural-net-sampling-artifact-risk — is really asking about, one level up from any single paper's method.

Neither landmark-selection rule surveyed here has an analogue to the Byzantine trade-network study's hub-selection artifact (claim-hub-selection-artifact-can-reverse-network-breakpoint-signal), which is specifically about sampling by a structural property of a network rather than density or noise in an unstructured point cloud. See observation-hub-selection-artifact-absent-by-design-in-founding-ph-generalization-papers for the fuller synthesis.