Papers › Box Filtration
Box Filtration
Enrique Alvarado, Prashant Gupta, Bala Krishnamoorthy
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We define a new framework that unifies the filtration and mapper approaches from TDA, and present efficient algorithms to compute it. Termed the box filtration of a PCD, we grow boxes (hyperrectangles) that are not necessarily centered at each point (in place of balls centered at points). We grow the boxes non-uniformly and asymmetrically in different dimensions based on the distribution of points. We present two approaches to handle the boxes: a point cover where each point is assigned its own box at start, and a pixel cover that works with a pixelization of the space of the PCD. Any box cover in either setting automatically gives a mapper of the PCD. We show that the persistence diagrams generated by the box filtration using both point and pixel covers satisfy the classical stability based on the Gromov-Hausdorff distance. Using boxes also implies that the box filtration is identical for pairwise or higher order intersections whereas the VR and Cech filtration are not the same. Growth in each dimension is computed by solving a linear program (LP) that optimizes a cost functional balancing the cost of expansion and benefit of including more points in the box. The box filtration algorithm runs in O(m|U(0)|log(mnπ)L(q)) time, where m is number of steps of increments considered for box growth, |U(0)| is the number of boxes in the initial cover (≤ number of points), π is the step length for increasing each box dimension, each LP is solved in O(L(q)) time, n is the PCD dimension, and q = n ×|X|. We demonstrate through multiple examples that the box filtration can produce more accurate results to summarize the topology of the PCD than VR and distance-to-measure (DTM) filtrations. Software for our implementation is available at https://github.com/pragup/Box-Filteration.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections