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Graph Learning from Incomplete Graph Signals

Noori, Alireza | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58487 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Massoud
  7. Abstract:
  8. Graph learning problem aims to infer a meaningful graph structure from a dataset that can effectively represent the relationships among its data points. With the emergence of graph signal processing, efficient methods for graph learning have been introduced, which leverage the smoothness assumption of signals to learn the underlying graph. However, these methods typically require access to all data points, while in practical applications this is not always feasible. In this Master's Thesis, an optimization problem is proposed that simultaneously learns the underlying graph and estimates the missing data points from a dataset of graph signals. To solve the proposed optimization problem, a block coordinate descent algorithm is employed that alternates between the two subproblems of graph learning and signal recovery. Moreover, for the signal recovery subproblem, a closed-form solution is derived and a rigorous convergence analysis is provided for the overall algorithm. Finally, through experiments on both synthetic and real datasets, the superiority of the proposed algorithm over existing methods is demonstrated. The problem of outlier detection and recovery aims to identify anomalous patterns in a dataset and estimate their true values. Existing methods typically assume that outliers are sparse, and to exploit this assumption, they often rely on sparsity norms. In this thesis, an alternative algorithm is also proposed that, given a graph and without relying on the sparsity assumption, identifies and then recovers outliers in a dataset of smooth graph signals. The algorithm addresses outlier detection and recovery in two separate steps: first, the locations of the outliers are determined, and then their true values are estimated. Finally, through experiments on both synthetic and real datasets, it is shown that the proposed method is able to maintain its detection and recovery performance even in the presence of a large number of outliers in the dataset
  9. Keywords:
  10. Graph Signal Processing ; Graph Learning ; Incomplete Data ; Outliers Detection ; Block Coordinate Descent (BCD)

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