BIDIMENSIONAL LINKED MATRIX FACTORIZATION FOR PAN-OMICS PAN-CANCER ANALYSIS.
BIDIMENSIONAL LINKED MATRIX FACTORIZATION FOR PAN-OMICS PAN-CANCER ANALYSIS.
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DOI：
10.1214/21-aoas1495
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发表时间：
2022-03
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一些现代应用程序需要集成具有共享行和/或列的多个大型数据矩阵。例如，整合多种癌症类型的多个组学平台的癌症研究，泛组学泛癌症分析，扩展了我们对分子异质性的认识，超出了在单一肿瘤和单一平台研究中观察到的范围。然而，这些研究受到现有统计方法的限制。我们提出了一种灵活的方法来同时分解和分解这种二维链接矩阵的变化，BIDIFAC+。BIDIFAC+将变异分解为一系列低秩成分，这些成分可以在任意数量的行集（如组学平台）或列集（如癌症类型）中共享。这建立在一个不断增长的文献中，关于链接矩阵的分解和分解，主要集中在一维（行或列）中链接的多个矩阵。我们的目标函数扩展了核范数惩罚，由随机矩阵理论驱动，在相对温和的条件下给出了唯一的分解，并且可以证明给出了贝叶斯后验分布的模式。我们将BIDIFAC+应用于来自TCGA的泛组学泛癌症数据，确定了四种不同组学平台和29种不同癌症类型的共享和特定变异性模式。
Several modern applications require the integration of multiple large data matrices that have shared rows and/or columns. For example, cancer studies that integrate multiple omics platforms across multiple types of cancer, pan-omics pan-cancer analysis, have extended our knowledge of molecular heterogeneity beyond what was observed in single tumor and single platform studies. However, these studies have been limited by available statistical methodology. We propose a flexible approach to the simultaneous factorization and decomposition of variation across such bidimensionally linked matrices, BIDIFAC+. BIDIFAC+ decomposes variation into a series of low-rank components that may be shared across any number of row sets (e.g., omics platforms) or column sets (e.g., cancer types). This builds on a growing literature for the factorization and decomposition of linked matrices which has primarily focused on multiple matrices that are linked in one dimension (rows or columns) only. Our objective function extends nuclear norm penalization, is motivated by random matrix theory, gives a unique decomposition under relatively mild conditions, and can be shown to give the mode of a Bayesian posterior distribution. We apply BIDIFAC+ to pan-omics pan-cancer data from TCGA, identifying shared and specific modes of variability across four different omics platforms and 29 different cancer types.