Estimation of partially observed multiple graph signals by learning spectrally concentrated graph kernels

Turhan, Gülce
Graph models provide flexible tools for the representation and analysis of signals defined over domains such as social or sensor networks. However, in real applications data observations are often not available over the whole graph, due to practical problems such as broken sensors, connection loss, or storage problems. In this thesis, we study the problem of estimating partially observed graph signals on multiple graphs. We consider possibly multiple graph domains over which a set of signals is available with missing observations. We study the problem of learning a graph signal model that allows an accurate estimation of the missing observations. The proposed method is based on learning a sparse representation of the graph signals over spectrally characterized graph dictionaries. The dictionary on each graph consists of a set of spectrally concentrated, narrowband graph atoms localized at different graph nodes. We formulate the dictionary learning problem in the spectral domain, as opposed to the vertex domain, which provides the flexibility of incorporating signals from more than one graph in the learning. The learnt dictionaries consist of several sub-dictionaries, where each sub-dictionary consists of atoms with a spectrum concentrated at a certain graph frequency, so that each sub-dictionary captures a different spectral component of the graph signals at hand. We approximate the narrowband graph spectra with Gaussian kernels, the parameters of which are learnt jointly with the sparse coefficients of the graph signals. The resulting optimization problem is solved with an alternating optimization approach. Finally, the incomplete entries of the given graph signals are estimated using the learnt dictionaries and sparse coefficients. Experimental results on synthetic graph data sets suggest that the proposed method has promising performance in comparison to baseline solutions.


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Citation Formats
G. Turhan, “Estimation of partially observed multiple graph signals by learning spectrally concentrated graph kernels,” M.S. - Master of Science, Middle East Technical University, 2021.