  Multivariate association analysis is of primary interest in many
applications. Despite the prevalence of high-dimensional and non-Gaussian data
(such as count-valued or binary), most existing methods only apply to
low-dimensional data with continuous measurements. Motivated by the Computer
Audition Lab 500-song (CAL500) music annotation study, we develop a new
framework for the association analysis of two sets of high-dimensional and
heterogeneous (continuous/binary/count) data. We model heterogeneous random
variables using exponential family distributions, and exploit a structured
decomposition of the underlying natural parameter matrices to identify shared
and individual patterns for two data sets. We also introduce a new measure of
the strength of association, and a permutation-based procedure to test its
significance. An alternating iteratively reweighted least squares algorithm is
devised for model fitting, and several variants are developed to expedite
computation and achieve variable selection. The application to the CAL500 data
sheds light on the relationship between acoustic features and semantic
annotations, and provides effective means for automatic music annotation and
retrieval.
