[Paper Review] Robust And Scalable Learning Of Complex Dataset Topologies Via Elpigraph

Luca Albergante, Evgeny M. Mirkes+7 more|arXiv (Cornell University)|Apr 20, 2018

Single-cell and spatial transcriptomics42 references4 citations

TL;DR

ElPiGraph is a robust, scalable method for learning complex dataset topologies without requiring full distance matrices or neighborhood graphs. It constructs principal graph ensembles that form consensus representations, effectively handling high-dimensional, noisy data—demonstrated in single-cell genomics and galaxy distribution analysis—enabling accurate inference of branching structures and gene dynamics.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of learning complex, non-linear dataset topologies in high-dimensional, noisy data.
• To overcome limitations of neighborhood-based methods that fail under high noise and complex structures.
• To develop a scalable method that avoids computing full distance matrices or neighborhood graphs.
• To enable interpretable, compact representations of complex data, such as branching trajectories in single-cell RNA-Seq.
• To support inference of gene dynamics and large-scale spatial structures in diverse scientific domains.

Proposed method

• ElPiGraph constructs a principal graph ensemble by iteratively building spanning trees on data points using a greedy, local optimization strategy.
• It employs a graph-based approximation of the data manifold that avoids explicit computation of the full distance matrix.
• The method uses a robust distance metric and local density estimation to guide edge selection, enhancing noise resilience.
• Principal graphs are generated through a sequence of graph refinement steps that preserve topological features.
• Consensus principal graphs are formed by aggregating multiple graph realizations, improving stability and accuracy.
• The algorithm scales efficiently to large datasets by focusing on local connectivity and incremental graph construction.

Experimental results

Research questions

• RQ1 Can a scalable method learn complex, branching data topologies without relying on full distance matrices or neighborhood graphs?
• RQ2 How well can ElPiGraph recover true underlying topologies in high-dimensional, noisy datasets?
• RQ3 To what extent does ElPiGraph outperform traditional neighborhood-based methods in preserving complex structures under noise?
• RQ4 Can ElPiGraph effectively model gene expression dynamics in single-cell transcriptomics data?
• RQ5 How does ElPiGraph perform in capturing large-scale spatial structures, such as galaxy distributions?

Key findings

• ElPiGraph successfully reconstructs complex, branching topologies in single-cell RNA-Seq data, revealing biologically meaningful gene dynamics.
• The method demonstrates robustness to high levels of noise, maintaining topological accuracy where traditional methods fail.
• ElPiGraph achieves scalable performance on large datasets, with computational efficiency superior to methods requiring full distance matrices.
• Consensus principal graphs produced by ElPiGraph show improved stability and reduced sensitivity to initialization.
• The approach enables accurate inference of developmental trajectories in embryonic development from single-cell data.
• ElPiGraph was validated on real-world datasets in biology and astronomy, showing strong performance in capturing non-linear, high-dimensional structures.