Double-Matched Matrix Decomposition for Multi-View Data

• Published in: Journal of computational and graphical statistics Vol. 31; no. 4; pp. 1114 - 1126
• Main Authors: Yuan, Dongbang, Gaynanova, Irina
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.10.2022; Taylor & Francis Ltd
• Subjects: Data integration; Decomposition; Dimension reduction; Iterative algorithms; Iterative methods; Matching; Matrices (mathematics); Matrix factorization; MicroRNAs; Multi-block data; Optimization; Principal component analysis; Professional soccer; Soccer
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2022.2067860

We consider the problem of extracting joint and individual signals from multi-view data, that is, data collected from different sources on matched samples. While existing methods for multi-view data decomposition explore single matching of data by samples, we focus on double-matched multi-view data (matched by both samples and source features). Our motivating example is the miRNA data collected from both primary tumor and normal tissues of the same subjects; the measurements from two tissues are thus matched both by subjects and by miRNAs. Our proposed double-matched matrix decomposition allows us to simultaneously extract joint and individual signals across subjects, as well as joint and individual signals across miRNAs. Our estimation approach takes advantage of double-matching by formulating a new type of optimization problem with explicit row space and column space constraints, for which we develop an efficient iterative algorithm. Numerical studies indicate that taking advantage of double-matching leads to superior signal estimation performance compared to existing multi-view data decomposition based on single-matching. We apply our method to miRNA data as well as data from the English Premier League soccer matches and find joint and individual multi-view signals that align with domain-specific knowledge. Supplementary materials for this article are available online.