  Data integration is the problem of combining multiple data groups (studies,
cohorts) and/or multiple data views (variables, features). This task is
becoming increasingly important in many disciplines due to the prevalence of
large and heterogeneous data sets. Data integration commonly aims to identify
structure that is consistent across multiple cohorts and feature sets. While
such joint analyses can boost information from single data sets, it is also
possible that a globally restrictive integration of heterogeneous data may
obscure signal of interest.
  Here, we therefore propose a data adaptive integration method, allowing for
structure in data to be shared across an a priori unknown \emph{subset of
cohorts and views}. The method, Multi-group Multi-view Principal Component
Analysis (MM-PCA), identifies partially shared, sparse low-rank components.
This also results in an integrative bi-clustering across cohorts and views. The
strengths of MM-PCA are illustrated on simulated data and on 'omics data from
The Cancer Genome Atlas. MM-PCA is available as an R-package.
  Key words: Data integration, Multi-view, Multi-group, Bi-clustering
