Graph Learning from Incomplete and Noisy Graph Signals

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Daghestani, Amir Hossein | 2021

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 54105 (05)
University: Sharif University of Technology
Department: Electrical Engineering
Advisor(s): Babaiezadeh, Masoud
Abstract:
The problem of inferring a graph from a set of graph signals over it plays a crucial role in the field of Graph Signal Processing (GSP). When provided with a graph that best models the structure of data, the GSP algorithms can offer high data processing capability. However, a meaningful graph of data is not always available, hence in some applications, the graph needs to be learned from the data itself. When the data is corrupted and missing, this task becomes even more challenging. In this paper, we present a graph learning algorithm that is capable of learning the underlying structure of data from an incomplete and noisy dataset of graph signals. We propose an algorithm that jointly derives the underlying structure of data and imputes the missing part of the graph signals within the dataset. Numerical experiments demonstrate the close performance of this algorithm compared to the complete data case.
Keywords:
Graph Signal Processing ; Graph Learning ; Optimization ; Alternating Direction Method of Multipliers (ADMM)Algorithm ; Data Incomplete ; Missing Sample Imputation

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