# Learning Simplicial Complexes from Persistence Diagrams

arXiv: https://arxiv.org/abs/1805.10716 · HTML: https://mlsanity.com/paper/1805.10716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2018.

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

- [Convolutional Persistence Transforms](https://mlsanity.com/paper/2208.02107/) (2022)

## Abstract (arXiv)

Topological Data Analysis (TDA) studies the shape of data. A common topological descriptor is the persistence diagram, which encodes topological features in a topological space at different scales. Turner, Mukeherjee, and Boyer showed that one can reconstruct a simplicial complex embedded in R^3 using persistence diagrams generated from all possible height filtrations (an uncountably infinite number of directions). In this paper, we present an algorithm for reconstructing plane graphs K=(V,E) in R^2 , i.e., a planar graph with vertices in general position and a straight-line embedding, from a quadratic number height filtrations and their respective persistence diagrams.