# Computing multiparameter persistent homology through a discrete Morse-based approach

arXiv: https://arxiv.org/abs/1811.05396 · HTML: https://mlsanity.com/paper/1811.05396/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2018.

## Built on by (most cited first, 3 of 3)

- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [Stability for Inference with Persistent Homology Rank Functions](https://mlsanity.com/paper/2307.02904/) (2023)
- [Prototype Selection Using Topological Data Analysis](https://mlsanity.com/paper/2511.04873/) (2025)

## Abstract (arXiv)

Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by multiple functions is becoming an important task in several applications, including physics, chemistry, medicine, geography, etc. Multiparameter Persistent Homology (MPH) generalizes persistent homology opening to the exploration and analysis of shapes endowed with multiple filtering functions. Still, computational constraints prevent MPH to be feasible over real-sized data. In this paper, we consider discrete Morse Theory as a tool to simplify the computation of MPH on a multiparameter dataset. We propose a new algorithm, well suited for parallel and distributed implementations and we provide the first evaluation of the impact on MPH computations of a preprocessing approach.