Higher-Order Regularization Learning on Hypergraphs
This work provides incremental theoretical and empirical advancements for researchers in graph and hypergraph learning, enhancing regularization methods in machine learning.
The paper tackles the problem of improving hypergraph learning by extending the theoretical foundation of Higher-Order Hypergraph Learning (HOHL), proving consistency and convergence rates for a truncated version, and demonstrating strong empirical performance in active learning and non-geometric datasets.
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings.