Spectral Integration of Noisy High-Dimensional Datasets

Music City Center 

Joint analysis of heterogeneous high-dimensional data is central to modern applications such as single-cell genomics and medical informatics. We introduce a novel kernel spectral method for jointly embedding independently observed noisy datasets. Our approach captures shared nonlinear manifold structures, handles noise and high dimensionality, and adapts to signal and sample size imbalance. The method is supported by sharp theoretical guarantees under a joint manifold model, including signal recovery consistency and convergence to meaningful limiting operators associated with the manifold. Empirical results on synthetic and real single-cell omics data show clear improvements in embedding, clustering, and denoising over existing methods.