  Finding appropriate low dimensional representations of high-dimensional
multi-modal data can be challenging, since each modality embodies unique
deformations and interferences. In this paper, we address the problem using
manifold learning, where the data from each modality is assumed to lie on some
manifold. In this context, the goal is to characterize the relations between
the different modalities by studying their underlying manifolds. We propose two
new diffusion operators that allow to isolate, enhance and attenuate the hidden
components of multi-modal data in a data-driven manner. Based on these new
operators, efficient low-dimensional representations can be constructed for
such data, which characterize the common structures and the differences between
the manifolds underlying the different modalities. The capabilities of the
proposed operators are demonstrated on 3D shapes and on a fetal heart rate
monitoring application.
