  Multimodal datasets contain observations generated by multiple types of
sensors. Most works to date focus on uncovering latent structures in the data
that appear in all modalities. However, important aspects of the data may
appear in only one modality due to the differences between the sensors.
Uncovering modality-specific attributes may provide insights into the sources
of the variability of the data. For example, certain clusters may appear in the
analysis of genetics but not in epigenetic markers. Another example is
hyper-spectral satellite imaging, where various atmospheric and ground
phenomena are detectable using different parts of the spectrum. In this paper,
we address the problem of uncovering latent structures that are unique to a
single modality. Our approach is based on computing a graph representation of
datasets from two modalities and analyzing the differences between their
connectivity patterns. We provide an asymptotic analysis of the convergence of
our approach based on a product manifold model. To evaluate the performance of
our method, we test its ability to uncover latent structures in multiple types
of artificial and real datasets.
