[2405.12317] Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators

Statistics > Machine Learning arXiv:2405.12317 (stat) [Submitted on 20 May 2024 (v1), last revised 27 Feb 2026 (this version, v3)] Title:Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators Authors:Xiucai Ding, Rong Ma View a PDF of the paper titled Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators, by Xiucai Ding and Rong Ma View PDF HTML (experimental) Abstract:Integrative analysis of multiple heterogeneous datasets has become standard practice in many research fields, especially in single-cell genomics and medical informatics. Existing approaches oftentimes suffer from limited power in capturing nonlinear structures, insufficient account of noisiness and effects of high-dimensionality, lack of adaptivity to signals and sample sizes imbalance, and their results are sometimes difficult to interpret. To address these limitations, we propose a novel kernel spectral method that achieves joint embeddings of two independently observed high-dimensional noisy datasets. The proposed method automatically captures and leverages possibly shared low-dimensional structures across datasets to enhance embedding quality. The obtained low-dimensional embeddings can be utilized for many downstream tasks such as simultaneous clustering, data visualization, and denoising. The proposed method is justified by rigorous theoretical analysis. Specifically, we show the consistency of our ...