Yu Na, Zhang Yusen, Gao Rui
IEEE J Biomed Health Inform. 2023 Mar;27(3):1225-1236. doi: 10.1109/JBHI.2022.3231908. Epub 2023 Mar 7.
As a powerful data representation technique, tensor robust principal component analysis (TRPCA) has been widely used for clustering and feature selection tasks. However, it ignores the significant difference in singular values of tensor data and the manifold information contained in different views, thereby causing serious degradation of conventional TRPCA performance. In this paper, a novel tensor method based on enhanced tensor nuclear norm and hypergraph Laplacian regularization (ETHLR) is developed to address the above problem. ETHLR can jointly learn the prior knowledge of singular values and high-order manifold structures in the unified tensor space and the view-specific feature spaces, respectively. Specifically, the enhanced tensor nuclear norm, namely, the weighted tensor Schatten p-norm, is used to shrink the singular values by fully considering the salient difference information of singular values and the complementary information embedded in the tensor space; the hypergraph Laplacian constraint helps encode high-order geometric structures among multiple samples in the nonlinear view-specific feature space. Furthermore, we employ inexact augmented Lagrange multipliers (ALM) to optimize the ETHLR method. Numerous experiments on pan-cancer omics data show that the superiority of ETHLR over several state-of-the-art competitors.
作为一种强大的数据表示技术，张量鲁棒主成分分析（TRPCA）已广泛应用于聚类和特征选择任务。然而，它忽略了张量数据奇异值的显著差异以及不同视图中包含的流形信息，从而导致传统TRPCA性能严重下降。本文提出了一种基于增强张量核范数和超图拉普拉斯正则化（ETHLR）的新型张量方法来解决上述问题。ETHLR可以分别在统一的张量空间和特定视图的特征空间中联合学习奇异值的先验知识和高阶流形结构。具体来说，增强张量核范数，即加权张量Schatten p-范数，通过充分考虑奇异值的显著差异信息和张量空间中嵌入的互补信息来收缩奇异值；超图拉普拉斯约束有助于在非线性特定视图特征空间中对多个样本之间的高阶几何结构进行编码。此外，我们采用不精确增广拉格朗日乘子（ALM）来优化ETHLR方法。在泛癌组学数据上的大量实验表明，ETHLR优于几种现有最先进的竞争对手。
