  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 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.
