We currently put a special focus on the problem of domain adaptation. More specifically, we study the problem of domain adaptation on manifolds (learned and analytic) and develop methods based on geometric considerations.
We study the manifold of diffusion operators, on which we can define geometric, differential, and probabilistic structures. This research direction entails a fresh approach to multi-manifold learning, departing from the traditional use of spectral decomposition of diffusion operators for embedding.
Diffusion operators are positive (semi-)definite and have a particular Riemannian geometry. While each diffusion operator extracts the manifold of a single data set, transportation of diffusion operators on the associated Riemannian manifold enables us to merge and compare multiple data sets.
One of the long-standing challenges in signal processing and data analysis is the fusion of information acquired by multiple, multimodal sensors.
Of particular interest in the context of our research are the massive data sets of medical recordings and healthcare-related information, acquired routinely in operation rooms, intensive care units, and clinics. Such distinct and complementary information calls for the development of new theories and methods, leveraging it toward achieving concrete objectives such as analysis, filtering, and prediction, in a broad range of fields.