Before revision: We present ElPiGraph, a method for approximating data distributions having non-trivial topological features such as the existence of excluded regionsor branching structures. Unlike many existing methods, ElPiGraph is not based on the construction of a k-nearest neighbour graph, a procedure that can perform poorly in the case of multidimensional and noisy data.
After revision: We present ElPiGraph, a method for approximating data distributions having 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.