# Lattice Paths for Persistent Diagrams

arXiv: https://arxiv.org/abs/2105.00351 · HTML: https://mlsanity.com/paper/2105.00351/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 30 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 4 of 4)

- [On the Bootstrap for Persistence Diagrams and Landscapes](https://mlsanity.com/paper/1311.0376/) (2013)
- [Smile-GANs: Semi-supervised clustering via GANs for dissecting brain disease heterogeneity from medical images](https://mlsanity.com/paper/2006.15255/) (2020)
- [Persistent Homology in Sparse Regression and its Application to Brain Morphometry](https://mlsanity.com/paper/1409.0177/) (2014)
- [Exact Combinatorial Inference for Brain Images](https://mlsanity.com/paper/1807.02885/) (2018)

## Abstract (arXiv)

Persistent homology has undergone significant development in recent years. However, one outstanding challenge is to build a coherent statistical inference procedure on persistent diagrams. In this paper, we first present a new lattice path representation for persistent diagrams. We then develop a new exact statistical inference procedure for lattice paths via combinatorial enumerations. The lattice path method is applied to the topological characterization of the protein structures of the COVID-19 virus. We demonstrate that there are topological changes during the conformational change of spike proteins.