Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets

Speaker: 马嵘（哈佛大学）

Title: Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets

Language: Chinese 

Time & Venue: 2026 年6月16日16:00–17:00 南楼620

Abstract: Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A primary approach for learning such a shared structure is to jointly embed different datasets into a common low-dimensional space. In this talk, I will present two recent and closely related methods for nonlinear joint embedding of high-dimensional datasets. The first method builds on ideas from entropic optimal transport, while the second is based on duo-landmark integral operators. Both are principled approaches for aligning and jointly embedding multiple datasets, supported by rigorous theoretical guarantees. We show that for a pair of noisy, high-dimensional datasets, these methods consistently recover the shared underlying manifold structure while mitigating dataset-specific nuisance structures. I will provide an intuitive geometric explanation of each methodology, along with the theoretical results justifying their performance. I will demonstrate their effectiveness in analyzing a single-cell multiomic dataset for human brain cells, which uncovers interesting cell-type-specific interactions between transcription and epigenomic regulation. This talk is based on recent work in collaboration with Xiucai Ding, Boris Landa, and Yuval Kluger.