Abstract: Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative repre- sentations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

Bio: Ya-Wei Eileen Lin is a 3rd year ECE PhD student at Technion - Israel Institute of Technology, advised by Professor Ronen Talmon. Her research interests are Riemannian geometry in machine learning and optimal transport. Ms. Lin is the recipient of Faculty Excellence Scholarship for 2022, VATAT Prize for Students of the Data Sciences Research for 2021, Freud Award for 2021, Fine Fellowship for 2020-2021, and The Lady Davis Fellowship for 2017-2018.