A processor may generate initial subspaces by reducing data of a plurality of domains to a same dimensionality, cluster data within each initial subspace into clusters, create an input data matrix by projecting data from each cluster to an associated one of a plurality of generative subspaces associated with the plurality of clusters, perform a parallel transport between first and second sets of generative subspaces to identify a set of directions between pairs of subspaces of the first and second sets, sample points comprising a plurality of intermediate representations along the directions via an exponential mapping, create an expanded set of prior information by projecting the data from the first and second sets to the plurality of intermediate representations, perform a sparse coding with the input data matrix and the expanded set of prior information, and perform a cross domain inference using the output of the sparse coding.