# Robust And Scalable Learning Of Complex Dataset Topologies Via Elpigraph

arXiv: https://arxiv.org/abs/1804.07580 · HTML: https://mlsanity.com/paper/1804.07580/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2018.

## Built on by (most cited first, 5 of 5)

- [Scikit-dimension: a Python package for intrinsic dimension estimation](https://mlsanity.com/paper/2109.02596/) (2021)
- [High-dimensional separability for one- and few-shot learning](https://mlsanity.com/paper/2106.15416/) (2021)
- [Rosenblatt's first theorem and frugality of deep learning](https://mlsanity.com/paper/2208.13778/) (2022)
- [Domain Adaptation Principal Component Analysis: base linear method for learning with out-of-distribution data](https://mlsanity.com/paper/2208.13290/) (2022)
- [Skeletal Prototypes on Iterative Nerve Expansions](https://mlsanity.com/paper/2609.16170/) (2026)

## Abstract (arXiv)

Large datasets represented by multidimensional data point clouds often possess non-trivial distributions with branching trajectories and excluded regions, with the recent single-cell transcriptomic studies of developing embryo being notable examples. Reducing the complexity and producing compact and interpretable representations of such data remains a challenging task. Most of the existing computational methods are based on exploring the local data point neighbourhood relations, a step that can perform poorly in the case of multidimensional and noisy data. Here we present ElPiGraph, a scalable and robust method for approximation of datasets with complex structures which does not require computing the complete data distance matrix or the data point neighbourhood graph. This method is able to withstand high levels of noise and is capable of approximating complex topologies via principal graph ensembles that can be combined into a consensus principal graph. ElPiGraph deals efficiently with large and complex datasets in various fields from biology, where it can be used to infer gene dynamics from single-cell RNA-Seq, to astronomy, where it can be used to explore complex structures in the distribution of galaxies.