Signal Processing-Driven Graph Learning: Some Studies on Coherence, Structure, and Unrolling

In this thesis, we focus on this signal processing perspective of graph learning: we try to reconstruct the underlying graph with some desirable structure and rate of change or frequency properties. We study three distinct problems arising in Graph learning, motivated towards target applications. In the first study, we explore the importance of robustness and coherence in graph-learning algorithms. Our algorithms are similar in spirit to robust versions of well-known algorithms like PCA; however, due to the specific framework we operate in, we obtain different and much simpler solutions. We apply our robust graph learning techniques for the classification of neuroimaging data and show better performance than existing graph learning techniques.

In the second study, we investigate the possibility of learning graphs with a priori known structure. Specifically, we design a module that can be incorporated into existing structure-unaware algorithms, enabling them to learn bipartite and regular graphs.

Most graph learning algorithms are evaluated by employing the learned graph to perform certain signal-processing tasks. In our final study, we delve into the role of feedback from these tasks in fine-tuning the graph learning algorithm. We introduce a parameterized graph learning model, with parameters adjusted based on feedback from the signal processing task. This adjustment is achieved by interpreting the resulting computational diagram as a neural network, a concept akin to the tech-niques used in. Our findings indicate that incorporating feedback into graph learning in this manner enhances performance in tasks such as data inpainting.