Investigating All Uncertainties in Hypergraph Representation Learning and Inference

Hypergraph representation learning (HGRL) has attracted widespread attention for its ability to capture high-order relationships (simultaneous interactions among multiple entities) in hypergraphs. However, most existing HGRL methods struggle with uncertainties throughout HGRL processes, including input signals, message passing, and inference. These uncertainties, such as redundant or noisy attributes, distorted structures, noisy node/hyperedge representations, and parameter estimation biases, undermine model robustness and reliability. To address this issue, we introduce fuzzy logic into HGRL for the first time, and propose a new HGRL framework called fuzzy hypergraph representation learning and inference (FHRLI). It effectively manages uncertainties from both data and model perspectives, resulting in more expressive representations. In addition, it allows for more precise and robust inference based on uncertain evidence. Contemplating the influence of label scarcity and uncertainties (annotation errors), we further develop an unsupervised HGRL algorithm, named fuzzy hypergraph contrastive representation learning (FHCRL), by combining the proposed FHRLI framework with hypergraph contrastive learning. Extensive experiments across various tasks verify the effectiveness and competitiveness of the proposed FHRLI framework and FHCRL compared to the state-of-the-art baselines. Furthermore, we experimentally demonstrate that the proposed FHRLI framework can achieve superior robustness and wide universality, along with providing a certain explanatory analysis.