  Research in several fields now requires the analysis of data sets in which
multiple high-dimensional types of data are available for a common set of
objects. In particular, The Cancer Genome Atlas (TCGA) includes data from
several diverse genomic technologies on the same cancerous tumor samples. In
this paper we introduce Joint and Individual Variation Explained (JIVE), a
general decomposition of variation for the integrated analysis of such data
sets. The decomposition consists of three terms: a low-rank approximation
capturing joint variation across data types, low-rank approximations for
structured variation individual to each data type, and residual noise. JIVE
quantifies the amount of joint variation between data types, reduces the
dimensionality of the data and provides new directions for the visual
exploration of joint and individual structures. The proposed method represents
an extension of Principal Component Analysis and has clear advantages over
popular two-block methods such as Canonical Correlation Analysis and Partial
Least Squares. A JIVE analysis of gene expression and miRNA data on
Glioblastoma Multiforme tumor samples reveals gene-miRNA associations and
provides better characterization of tumor types. Data and software are
available at https://genome.unc.edu/jive/
