提出三种可处理多视角高维数据的非线性稀疏CCA方法,提升变量选择效果。
Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data
- 基于核方法和稀疏正则化,扩展传统CCA至多视角非线性建模
- 在TCGA-BRCA数据中,HSIC-SGCCA在多视角变量选择上表现最优
- 适用于多组学等高维生物数据整合分析,适合研究人员快速定位关键变量
生物医学研究日益产生多视角高维数据(如多组学),亟需整合分析方法。现有典型相关分析(CCA)与广义CCA方法最多同时满足以下三方面中的两点:(i) 非线性依赖关系建模,(ii) 变量选择的稀疏性,(iii) 扩展至两个以上数据视角。本研究提出三种非线性、稀疏、广义CCA方法:HSIC-SGCCA、SA-KGCCA 和 TS-KGCCA,用于多视角高维数据的变量选择。这些方法将 SCCA-HSIC、SA-KCCA、TS-KCCA 从双视角推广至多视角设置。其中,SA-KGCCA 与 TS-KGCCA 通过块坐标下降求解多凸优化问题;而 HSIC-SGCCA 引入此前被忽略的单位方差约束,形成非凸且非多凸问题,我们通过结合块近端线性化方法与线性化交替方向乘子法高效求解。模拟实验与 TCGA-BRCA 数据分析表明,HSIC-SGCCA 在多视角变量选择上优于对比方法。
原文摘要 · Abstract (English)
Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of the following three key aspects simultaneously: (i) nonlinear dependence, (ii) sparsity for variable selection, and (iii) generalization to more than two data views. There is a pressing need for CCA methods that integrate all three aspects to effectively analyze multi-view high-dimensional data. Results: We propose three nonlinear, sparse, generalized CCA methods, HSIC-SGCCA, SA-KGCCA, and TS-KGCCA, for variable selection in multi-view high-dimensional data. These methods extend existing SCCA-HSIC, SA-KCCA, and TS-KCCA from two-view to multi-view settings. While SA-KGCCA and TS-KGCCA yield multi-convex optimization problems solved via block coordinate descent, HSIC-SGCCA introduces a necessary unit-variance constraint previously ignored in SCCA-HSIC, resulting in a nonconvex, non-multiconvex problem. We efficiently address this challenge by integrating the block prox-linear method with the linearized alternating direction method of multipliers. Simulations and TCGA-BRCA data analysis demonstrate that HSIC-SGCCA outperforms competing methods in multi-view variable selection.
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