  Detecting the components common or correlated across multiple data sets is
challenging due to a large number of possible correlation structures among the
components. Even more challenging is to determine the precise structure of
these correlations. Traditional work has focused on determining only the model
order, i.e., the dimension of the correlated subspace, a number that depends on
how the model-order problem is defined. Moreover, identifying the model order
is often not enough to understand the relationship among the components in
different data sets. We aim at solving the complete modelselection problem,
i.e., determining which components are correlated across which data sets. We
prove that the eigenvalues and eigenvectors of the normalized covariance matrix
of the composite data vector, under certain conditions, completely characterize
the underlying correlation structure. We use these results to solve the
model-selection problem by employing bootstrap-based hypothesis testing.
