The field of graph signal processing and hypergraph learning is moving towards the development of more efficient and effective algorithms for processing and analyzing data on non-Euclidean domains. Researchers are exploring new techniques for interpolating low-pass graph filters, which are essential for signal processing on graphs, and developing new methods for learning on hypergraphs, which can model higher-order interactions. These advancements have the potential to improve the performance of various applications, such as node classification and graph-based measures. Notable papers in this area include:

• Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications, which proposes a novel algorithm for low-pass graph filter interpolation based on Riemannian interpolation in normal coordinates on the Grassmann manifold.
• Analysis of Semi-Supervised Learning on Hypergraphs, which provides an asymptotic consistency analysis of variational learning on random geometric hypergraphs and proposes a new method for higher-order hypergraph learning.
• Generalized Sobolev IPM for Graph-Based Measures, which generalizes Sobolev IPM through the lens of Orlicz geometric structure and proposes a novel regularization for the generalized Sobolev IPM.
• Higher-Order Regularization Learning on Hypergraphs, which extends the theoretical foundation of Higher-Order Hypergraph Learning and demonstrates its strong empirical performance in active learning and datasets lacking an underlying geometric structure.