Abstract
Robust Principal Component Analysis (RPCA) offers a powerful tool for recovering a low-rank matrix from highly corrupted data, with growing applications in computational biology. Biological processes commonly form intrinsic hierarchical structures, such as tree structures of cell development trajectories and tumor evolutionary history. The rapid development of single-cell sequencing (SCS) technology calls for the recovery of embedded tree structures from noisy and heterogeneous SCS data. In this study, we propose RobustTree, a unified framework to reconstruct the inherent topological structure underlying high-dimensional data with noise. By extending RPCA to handle tree structure optimization, RobustTree leverages data denoising, clustering, and tree structure reconstruction. It solves the tree optimization problem with an adaptive parameter selection scheme that we proposed. In addition to recovering real datasets, RobustTree can reconstruct continuous topological structure and discrete-state topological structure of underlying SCS data. We apply RobustTree on multiple synthetic and real datasets and demonstrate its high accuracy and robustness when analyzing high-noise SCS data with embedded complex structures. The code is available at https://github.com/ucasdp/RobustTree.