NSF Award
2406896
Graph-structured data appear in many applications such as social networks, functional brain networks, and protein-protein interaction networks. Graph convolutional networks have demonstrated significant performance improvements over traditional methods for performing large scale graph tasks due to their learnable parameters that can capture more and task-adaptive information. Despite the success of graph convolutional networks, accurate and efficient algorithm development is still in its early stages. This proposal focuses on addressing the challenges for handling large-scale graph tasks using graph convolutional networks. New models will be built to produce task-desired solutions and to exploit feature information in challenging large-scale graph tasks. Novel numerical approaches will be designed to solve existing and new-built models in an efficient and reliable way. This project aims at achieving good practical performance on real graph tasks, provably fast convergence for the designed algorithms, and low overall complexity in computing numerical solutions. The project will involve graduate and undergraduate students, in particular underrepresented students in STEM, by involving them in research activities. The research findings will be integrated into curricula, thus impacting both undergraduate and graduate education.<br/><br/>Novel mathematical models and algorithms for deep graph learning will be designed and analyzed. First, variance-reduced neighbor sampling approaches and a new constrained optimization model aimed at enabling more efficient algorithms will be designed for deep graph representation learning. Asynchronous parallel versions of these new methods will also be developed to increase efficiency. Second, new deep graph representation learning -assisted models will be built for graph matching, by using sparsity-promoting regularizers or penalty terms that can lead to task-desired solutions. On solving the new models, accelerated low-order methods will be designed by using the proposed variance-reduced neighbor sampling and momentum acceleration techniques, under the framework of the augmented Lagrangian method or the alternating minimization. Third, new models with finite-sum structured nonconvex constraints will be built for graph clustering by using deep graph representation learning to exploit feature information. Variance-reduced stochastic methods will be designed to solve the models by exploiting the finite-sum structure. These investigations are expected to lead to novel models and efficient algorithms for large-scale graph tasks that currently cannot be completed in an accurate and/or efficient way.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
