# Filtration-Domination in Bifiltered Graphs

arXiv: https://arxiv.org/abs/2211.05574 · HTML: https://mlsanity.com/paper/2211.05574/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures](https://mlsanity.com/paper/2306.03801/) (2023)

## Abstract (arXiv)

Bifiltered graphs are a versatile tool for modelling relations between data points across multiple grades of a two-dimensional scale. They are especially popular in topological data analysis, where the homological properties of the induced clique complexes are studied. To reduce the large size of these clique complexes, we identify filtration-dominated edges of the graph, whose removal preserves the relevant topological properties. We give two algorithms to detect filtration-dominated edges in a bifiltered graph and analyze their complexity. These two algorithms work directly on the bifiltered graph, without first extracting the clique complexes, which are generally much bigger. We present extensive experimental evaluation which shows that in most cases, more than 90% of the edges can be removed. In turn, we demonstrate that this often leads to a substantial speedup, and reduction in the memory usage, of the computational pipeline of multiparameter topological data analysis.