  In the current era of systems biological research there is a need for the
integrative analysis of binary and quantitative genomics data sets measured on
the same objects. One standard tool of exploring the underlying dependence
structure present in multiple quantitative data sets is simultaneous component
analysis (SCA) model. However, it does not have any provisions when a part of
the data are binary. To this end, we propose the generalized SCA (GSCA) model,
which takes into account the distinct mathematical properties of binary and
quantitative measurements in the maximum likelihood framework. Like in the SCA
model, a common low dimensional subspace is assumed to represent the shared
information between these two distinct types of measurements. However, the GSCA
model can easily be overfitted when a rank larger than one is used, leading to
some of the estimated parameters to become very large. To achieve a low rank
solution and combat overfitting, we propose to use a concave variant of the
nuclear norm penalty. An efficient majorization algorithm is developed to fit
this model with different concave penalties. Realistic simulations (low
signal-to-noise ratio and highly imbalanced binary data) are used to evaluate
the performance of the proposed model in recovering the underlying structure.
Also, a missing value based cross validation procedure is implemented for model
selection. We illustrate the usefulness of the GSCA model for exploratory data
analysis of quantitative gene expression and binary copy number aberration
(CNA) measurements obtained from the GDSC1000 data sets.
