  Learning on high-order correlation has shown superiority in data
representation learning, where hypergraph has been widely used in recent
decades. The performance of hypergraph-based representation learning methods,
such as hypergraph neural networks, highly depends on the quality of the
hypergraph structure. How to generate the hypergraph structure among data is
still a challenging task. Missing and noisy data may lead to "bad connections"
in the hypergraph structure and destroy the hypergraph-based representation
learning process. Therefore, revealing the high-order structure, i.e., the
hypergraph behind the observed data, becomes an urgent but important task. To
address this issue, we design a general paradigm of deep hypergraph structure
learning, namely DeepHGSL, to optimize the hypergraph structure for
hypergraph-based representation learning. Concretely, inspired by the
information bottleneck principle for the robustness issue, we first extend it
to the hypergraph case, named by the hypergraph information bottleneck (HIB)
principle. Then, we apply this principle to guide the hypergraph structure
learning, where the HIB is introduced to construct the loss function to
minimize the noisy information in the hypergraph structure. The hypergraph
structure can be optimized and this process can be regarded as enhancing the
correct connections and weakening the wrong connections in the training phase.
Therefore, the proposed method benefits to extract more robust representations
even on a heavily noisy structure. Finally, we evaluate the model on four
benchmark datasets for representation learning. The experimental results on
both graph- and hypergraph-structured data demonstrate the effectiveness and
robustness of our method compared with other state-of-the-art methods.
