persim

persim starts where every engine in this corpus stops. A persistence diagram is a multiset of birth–death points with no fixed cardinality, and almost nothing downstream can consume that directly: a distance matrix wants a metric, a neural network wants a fixed-length vector, a statistical test wants a number. persim supplies both answers, and they are genuinely different answers rather than two spellings of one.

Two different things in one library

Distances put a metric on diagram space without leaving it. bottleneck and wasserstein compute optimal matchings between two diagrams; sliced_wasserstein and heat are cheaper kernel-flavoured surrogates that trade exactness for the ability to run on more than a handful of pairs. This route keeps the stability guarantee that made persistence worth using — perturb the input a little and the distance moves a little — and it is the honest choice when the question is how similar are these two structures.

Vectorizations leave diagram space for ℝⁿ. PersistenceImager rasterizes a diagram into a grid; PersLandscapeExact / PersLandscapeApprox / PersistenceLandscaper build landscape functions and sample them. This is what makes persistence usable as features in an ordinary model, and it is where the choices come back. Resolution, kernel bandwidth, and the weighting applied along the persistence axis are all parameters, and they all change the feature. Persistent homology declined to pick a scale; vectorizing it picks several other things instead, and the note that matters is that those picks are yours to defend rather than the method’s to justify.

The stability results carry over, but only with the qualifiers attached — landscapes are well-behaved against bottleneck distance, and persistence images are stable against 1-Wasserstein for weighting functions that vanish appropriately at the diagonal. A weighting chosen for downstream accuracy is not automatically one of those.

The outlier

gromov_hausdorff estimates a modified Gromov–Hausdorff distance between graphs, not between diagrams. It is the one function here that does not take a diagram, and it is worth knowing about because a library organized around one input type quietly containing a second is exactly the kind of thing that gets missed when reading an API list quickly.

In this corpus

persim-environment resolves entirely from conda-forge, so it needs no recipe and grades L3 — one of the least troublesome fixtures here. gudhi also ships a representations layer covering much of the same ground, and this corpus routes the question here anyway, on the argument that computing persistence and representing it are separate decisions with separate failure modes and should be separately swappable. scikit-tda bundles it. The technique is persistent-homology.