标题： 非迭代联合和个体变异解释 显示英文标题

标题： Non-iterative Joint and Individual Variation Explained

摘要： 对在共同实验样本上测量的异构数据块进行综合分析是现代数据分析中的一个主要挑战。 这种数据结构自然地促使同时探索每个数据块中的联合和个体变化，从而产生新的见解。 例如，人们迫切希望整合《癌症基因组图谱》（TCGA）中的多个基因组数据集，以描述每个来源的癌症遗传学和细胞生物学的共性和独特方面。 在本文中，我们引入了非迭代联合和个体变异解释（Non-iterative JIVE），能够捕捉每个数据块中的联合和个体变异。 这在概念理解、对数据异质性的更好适应以及快速的线性代数计算方面是对这一挑战早期方法的重大改进。 重要的数学贡献是使用得分子空间作为变化结构的主要描述符，以及使用扰动理论作为变化分割的指导。 这导致了一种方法，在不需要归一化的情况下，对数据块之间的异质性具有鲁棒性。 对TCGA数据的应用揭示了每种信号在表征肿瘤亚型中的不同行为。 对死亡率数据集的应用揭示了有趣的的历史教训。 显示英文摘要

摘要： Integrative analysis of disparate data blocks measured on a common set of experimental subjects is one major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there is a strong desire to integrate the multiple genomic data sets in The Cancer Genome Atlas (TCGA) to characterize the common and also the unique aspects of cancer genetics and cell biology for each source. In this paper we introduce Non-iterative Joint and Individual Variation Explained (Non-iterative JIVE), capturing both joint and individual variation within each data block. This is a major improvement over earlier approaches to this challenge in terms of a new conceptual understanding, much better adaption to data heterogeneity and a fast linear algebra computation. Important mathematical contributions are the use of score subspaces as the principal descriptors of variation structure and the use of perturbation theory as the guide for variation segmentation. This leads to a method which is robust against the heterogeneity among data blocks without a need for normalization. An application to TCGA data reveals different behaviors of each type of signal in characterizing tumor subtypes. An application to a mortality data set reveals interesting historical lessons.