Structure-Aware Manifold Learning Methods for Modern Biomedical Data Analysis

Abstract: In this talk, I will present recent advances in developing manifold learning algorithms for biomedical data analysis that explicitly account for underlying structural information.

In the first example, motivated by applications in RNA velocity analysis—where both gene expression levels and their temporal velocities are simultaneously observed—we develop a tangent-lift embedding method based on a tangent bundle model in Riemannian geometry. We demonstrate both theoretically and empirically that the proposed approach can effectively recover RNA velocity, while remaining robust to noise and high dimensionality. This work is joint with Rong Ma (Harvard).

In the second example, motivated by neuroimaging analysis in brain–computer interface applications, we propose a projection-design-based scaled manifold learning algorithm to extract latent structures while accounting for sparsity in the data. We show, both empirically and theoretically, that the proposed method achieves high clustering and classification accuracy in brain–computer interface tasks using neuroimaging data. This work is joint with Yichen Hu (UC Davis) and Jian Kang (University of Michigan).