Tight basis cycle representatives for persistent homology of large biological data sets
Table 1
Our algorithms process large data sets within a minute.
n is the number of points, τ = τu + ϵ is the threshold for PH computation, #H1 is the number of nontrivial H1 features, #cycles is the number of cycles born at a spatial scale less than or equal to τu, Ttot is the time taken in seconds to compute the PD, birth-cycles, and shorten and smooth birth-cycles, while Mtot is the peak memory usage in GB.