Title: Robust And Scalable Learning Of Complex Dataset Topologies Via Elpigraph,
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.