Dictionary Learning techniques aim to find sparse signal representations that capture prominent characteristics in the given data. For signals residing on non-Euclidean topologies, represented by weighted graphs, an additional challenge is incorporating the underlying geometric structure of the data domain into the learning process. We introduce an approach that aims to infer and preserve the local intrinsic geometry in both dimensions of the data. Combining ideas from spectral graph theory, manifold learning and sparse representations, our proposed algorithm simultaneously takes into account the underlying graph topology as well as the data manifold structure. The efficiency of this approach is demonstrated on a variety of applications, including sensor network data completion and enhancement, image structure inference, and challenging multi-label classification problems.
Yael is a PhD student in the Computer Science Department at the Technion, working under the supervision of prof. Michael Elad. Her research interests include signal and image processing, machine learning, sparse representations, inverse problems and graphical models.