When Dictionary Learning Meets Graph Signal Processing

Yael Yankelevsky, Ph.D. Thesis Seminar
Tuesday, 12.6.2018, 11:30
Taub 337
Prof. Michael Elad

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. In this talk, we introduce an approach that aims to infer and preserve the local intrinsic geometry 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. Furthermore, we show that in cases where the underlying graph is unknown, we can infer it from the given data as an integral part of the dictionary learning process. We then present a recent extension to this algorithm, relying on a novel graph-wavelet construction tailored to the particular given data structure, which is able to cope with graph signals of much higher dimensions. The efficiency of this approach is demonstrated on a variety of applications in both supervised and unsupervised settings, including sensor network data completion and enhancement, inference of correlation patterns in image patches, and challenging multi-label classification problems.

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