提出新方法整合不同组学数据，揭示数据异质性本质。
Diagonal Multi-omics Integration of Heterogenous Datasets
- 基于斯特费尔流形上的耦合拉普拉斯矩阵，研究极值迹问题。
- 通过梯度上升法求解最大化问题，提升多组学数据融合效果。
- 引入最大最小点差的范数作为异质性新指标，适合生物信息研究者。
本文研究异质性多组学数据的对角整合方法。分析并发展了多种生物异质性的表征方式，以更清晰地理解数据生成差异。具体而言，研究了嵌入复欧几里得空间的斯特费尔流形上耦合拉普拉斯矩阵的极值迹问题。在经典泛函分析框架下，详述了最大化问题的梯度上升方法，其本身具有重要理论价值。在此基础上，提出一种新的数据异质性度量：利用最大点与最小点之间差值的范数，量化数据间的差异程度。
原文摘要 · Abstract (English)
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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