Learning Sparse Graph Laplacian with K Eigenvector Prior via Iterative GLASSO and Projection

Learning a suitable graph is an important precursor to many graph signal processing (GSP) tasks, such as graph signal compression and denoising. Previous graph learning algorithms either make assumptions on graph connectivity (e.g., graph sparsity), or make individual edge weight assumptions such as positive edges only. In this thesis, given an empirical covariance matrix computed from data as input, an eigen-structural assumption on the graph Laplacian matrix is considered: the first K eigenvectors of the graph Laplacian are pre-selected, e.g., based on domain-specific criteria, and the remaining eigenvectors are then learned from data.
One example use case is image coding, where the first eigenvector is pre-chosen to be constant, regardless of available observed data. Experimental results show that given the first K eigenvectors as a prior, the algorithm in this thesis outperforms competing graph learning schemes using a variety of graph comparison metrics.