  Previous matching component analysis (MCA) techniques map two data domains to
a common domain for further processing in data fusion and transfer learning
contexts. In this paper, we extend these techniques to the star-graph
multimodal (SGM) case in which one particular data domain is connected to $m$
others via an objective function. We provide a particular feasible point for
the resulting trace maximization problem in closed form and algorithms for its
computation and iterative improvement, leading to our main result, the SGM
maps. We also provide numerical examples demonstrating that SGM is capable of
encoding into its maps more information than MCA when few training points are
available. In addition, we develop a further generalization of the MCA
covariance constraint, eliminating a previous feasibility condition and
allowing larger values of the rank of the prescribed covariance matrix.
