Table 6.

Guidelines for which implementation is best-suited for which data set, based on our benchmarking

Data type	Complex	Suggested software
networks	WRCF	jHoles
image data	cubical	Gudhi or DIPHA (st)
distance matrix	VR	Ripser
distance matrix	W	javaPlex
points in Euclidean space	VR	Gudhi
points in Euclidean space	Č	Dionysus
points in Euclidean space	α (only in dim 2 and 3)	Dionysus ((st) in dim 2, (d) in dim 3) or Gudhi

Recall that we indicate the implementation of the dual algorithm using the abbreviation ‘d’ following the name of a package, and similarly we indicate the implementation of the standard algorithm by ‘st’. Note that for smaller data sets one can also use javaPlex to compute PH with VR complexes from points in Euclidean space, and Perseus to compute PH with cubical complexes for image data, and with VR complexes for distance matrices. The library jHoles can only handle networks with density much less than 1.