  Multiple sets of measurements on the same objects obtained from different
platforms may reflect partially complementary information of the studied
system. The integrative analysis of such data sets not only provides us with
the opportunity of a deeper understanding of the studied system, but also
introduces some new statistical challenges. First, the separation of
information that is common across all or some of the data sets, and the
information that is specific to each data set is problematic. Furthermore,
these data sets are often a mix of quantitative and discrete (binary or
categorical) data types, while commonly used data fusion methods require all
data sets to be quantitative. In this paper, we propose an exponential family
simultaneous component analysis (ESCA) model to tackle the potential mixed data
types problem of multiple data sets. In addition, a structured sparse pattern
of the loading matrix is induced through a nearly unbiased group concave
penalty to disentangle the global, local common and distinct information of the
multiple data sets. A Majorization-Minimization based algorithm is derived to
fit the proposed model. Analytic solutions are derived for updating all the
parameters of the model in each iteration, and the algorithm will decrease the
objective function in each iteration monotonically. For model selection, a
missing value based cross validation procedure is implemented. The advantages
of the proposed method in comparison with other approaches are assessed using
comprehensive simulations as well as the analysis of real data from a chronic
lymphocytic leukaemia (CLL) study.
  Availability: the codes to reproduce the results in this article are
available at https://gitlab.com/uvabda.
