Modern biomedical studies often collect multi-view data, that is, multiple types of data measured on the same set of objects. A popular model in high-dimensional multi-view data analysis is to decompose each view's data matrix into a low-rank common-source matrix generated by latent factors common across all data views, a low-rank distinctive-source matrix corresponding to each view, and an additive noise matrix. We propose a novel decomposition method for this model, called decomposition-based generalized canonical correlation analysis (D-GCCA). The D-GCCA rigorously defines the decomposition on the L2 space of random variables in contrast to the Euclidean dot product space used by most existing methods, thereby being able to provide the estimation consistency for the low-rank matrix recovery. Moreover, to well calibrate common latent factors, we impose a desirable orthogonality constraint on distinctive latent factors. Existing methods, however, inadequately consider such orthogonality and may thus suffer from substantial loss of undetected common-source variation. Our D-GCCA takes one step further than generalized canonical correlation analysis by separating common and distinctive components among canonical variables, while enjoying an appealing interpretation from the perspective of principal component analysis. Furthermore, we propose to use the variable-level proportion of signal variance explained by common or distinctive latent factors for selecting the variables most influenced. Consistent estimators of our D-GCCA method are established with good finite-sample numerical performance, and have closed-form expressions leading to efficient computation especially for large-scale data. The superiority of D-GCCA over state-of-the-art methods is also corroborated in simulations and real-world data examples.
Computer Science Research Institute, Sandia National Laboratories（桑迪亚国家实验室计算机科学研究所）；Department of Statistics & Data Science, University of California, Los Angeles（加州大学洛杉矶分校统计与数据科学系）
DEMAND: Deep Matrix Approximately Nonlinear Decomposition to Identify Meta, Canonical, and Sub-Spatial Pattern of functional Magnetic Resonance Imaging in the Human Brain
University of California San Francisco（加州大学旧金山分校）；James Madison University（詹姆斯麦迪逊大学）
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；CentraleSupélec（中央理工-高等电力学院）；Laboratoire des signaux et systèmes（信号与系统实验室）；Sorbonne Université（索邦大学）；Institut du Cerveau - Paris Brain Institute - ICM（巴黎大脑研究所）；Inserm（法国国家健康与医学研究院）；APHP（巴黎公立医院集团）；Hôpital Pitié Salpétrière Univ. Hosp.（皮提耶-萨尔佩特里埃大学医院）；Centre National de Recherche en Génomique Humaine（国家人类基因组研究中心）；Institut François Jacob（弗朗索瓦·雅各布研究所）；CEA（法国原子能委员会）
Binarized Canonical Polyadic Decomposition for Knowledge Graph Completion
Osaka University（大阪大学）；The University of Tokyo（东京大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
