Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph

Luca Albergante (1, 2, 3, 4) , Evgeny Mirkes (5, 6) , Jonathan Bac (1, 7, 2, 3) , Huidong Chen (8, 9) , Alexis Martin (1, 10, 2, 3) , Louis Faure (1, 11, 2, 3) , Emmanuel Barillot (1, 2, 3) , Luca Pinello (8, 9) , Alexander Gorban (5, 6) , Andrei Zinovyev (1, 2, 3)

1 Institut Curie [Paris]
2 Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe
3 CBIO - Centre de Bioinformatique
4 Sensyne Health [Oxford]
5 University of Leicester
6 Lobachevsky State University [Nizhni Novgorod]
7 CRI - Centre de Recherches Interdisciplinaires [Paris]
8 HMS - Harvard Medical School [Boston]
9 BROAD INSTITUTE - Broad Institute of MIT and Harvard
10 ECE Paris – Ecole d'ingénieurs
11 Medizinische Universität Wien = Medical University of Vienna

Multidimensional datapoint clouds representing large datasets are frequently characterized by non-trivial low-dimensional geometry and topology which can be recovered by unsupervised machine learning approaches, in particular, by principal graphs. Principal graphs approximate the multivariate data by a graph injected into the data space with some constraints imposed on the node mapping. Here we present ElPiGraph, a scalable and robust method for constructing principal graphs. ElPiGraph exploits and further develops the concept of elastic energy, the topological graph grammar approach, and a gradient descent-like optimization of the graph topology. The method is able to withstand high levels of noise and is capable of approximating data point clouds via principal graph ensembles. This strategy can be used to estimate the statistical significance of complex data features and to summarize them into a single consensus principal graph. ElPiGraph deals efficiently with large datasets in various fields such as biology, where it can be used for example with single-cell transcriptomic or epigenomic datasets to infer gene expression dynamics and recover differentiation landscapes.

Mots clés: data approximation; principal graphs; principal trees; topological grammars; software

Domaines: Bio-Informatique, Biologie Systémique [q-bio.QM]

Luca Albergante, Evgeny Mirkes, Jonathan Bac, Huidong Chen, Alexis Martin, et al.. Robust and Scalable Learning of Complex Intrinsic Dataset Geometry via ElPiGraph. Entropy, 2020, 22 (3), pp.296. ⟨10.3390/e22030296⟩. ⟨hal-02971955⟩