PreprintCC BY 4.0arXiv
Diagonal Multi-omics Integration of Heterogeneous Datasets
Abstract
In this paper, we consider methods for the diagonal multi-omics integration of heterogeneous datasets. Several approaches to the nature of biological heterogeneity are analyzed and developed to comprehend more clearly the generated differences. Specifically, the extremal trace problems for the coupled Laplacian on sets homeomorphic to the Stiefel manifold embedded in the complex Euclidean space are investigated. The gradient ascent method for the maximization problem is elaborated in the classical terms of functional analysis, which is of significant interest in itself. On this basis, we introduce a novel characteristic of dataset heterogeneity by employing the norm of the difference between the maximum and minimum points.
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BibTeX
@misc{kukushkin2026diagonal,
title = {{Diagonal Multi-omics Integration of Heterogeneous Datasets}},
author = {Maksim V. Kukushkin and Mikhail S. Arbatskiy and Dmitriy E. Balandin and Alexey V. Churov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.16968},
eprint = {2608.16968},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.16968},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diagonal Multi-omics Integration of Heterogeneous Datasets
AU - Maksim V. Kukushkin
AU - Mikhail S. Arbatskiy
AU - Dmitriy E. Balandin
AU - Alexey V. Churov
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2608.16968
UR - https://arxiv.org/abs/2608.16968
AB - In this paper, we consider methods for the diagonal multi-omics integration of heterogeneous datasets. Several approaches to the nature of biological heterogeneity are analyzed and developed to comprehend more clearly the generated differences. Specifically, the extremal trace problems for the coupled Laplacian on sets homeomorphic to the Stiefel manifold embedded in the complex Euclidean space are investigated. The gradient ascent method for the maximization problem is elaborated in the classical terms of functional analysis, which is of significant interest in itself. On this basis, we introduce a novel characteristic of dataset heterogeneity by employing the norm of the difference between the maximum and minimum points.
ER -