Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. A principal curve acts as a nonlinear generalization of PCA, and the present paper proposes a novel algorithm to automatically and sequentially learn principal curves from data streams. We show that our procedure is supported by regret bounds with optimal sublinear remainder terms. A greedy local search implementation (called slpc, for sequential learning principal curves) that incorporates both sleeping experts and multi-armed bandit ingredients is presented, along with its regret computation and performance on synthetic and real-life data.

scShaper: ensemble method for fast and accurate linear trajectory inference from single-cell RNA-seq data

Computational models are needed to infer a representation of the cells, i.e. a trajectory, from single-cell RNA-sequencing data that model cell differentiation during a dynamic process. Although many trajectory inference methods exist, their performance varies greatly depending on the dataset and hence there is a need to establish more accurate, better generalizable methods. We introduce scShaper, a new trajectory inference method that enables accurate linear trajectory inference. The ensemble approach of scShaper generates a continuous smooth pseudotime based on a set of discrete pseudotimes. We demonstrate that scShaper is able to infer accurate trajectories for a variety of nonlinear mathematical trajectories, including many for which the commonly used principal curves method fails. A comprehensive benchmarking with state-of-the-art methods revealed that scShaper achieved superior accuracy of the cell ordering and, in particular, the differentially expressed genes. Moreover, scShaper is a fast method with few hyperparameters, making it a promising alternative to the principal curves method for linear pseudotemporal ordering. scShaper is available as an R package (https://github.com/elolab/scshaper).