TL;DR
This paper introduces AdE, an adaptive hypergraph expansion method that preserves higher-order structures by dynamically adjusting edge weights, improving upon classical fixed-weight expansions in hypergraph learning.
Contribution
The paper proposes a novel adaptive expansion technique for hypergraphs, utilizing a global simulation network and distance-aware kernel to better retain structural information.
Findings
AdE outperforms classic expansion models on seven benchmark datasets.
The method effectively preserves higher-order relationships in hypergraph representations.
Theoretical analysis supports the rationality and generalization of AdE.
Abstract
Hypergraph, with its powerful ability to capture higher-order relationships, has gained significant attention recently. Consequently, many hypergraph representation learning methods have emerged to model the complex relationships among hypergraphs. In general, these methods leverage classic expansion methods to convert hypergraphs into weighted or bipartite graphs, and further employ message passing mechanisms to model the complex structures within hypergraphs. However, classical expansion methods are designed in straightforward manners with fixed edge weights, resulting in information loss or redundancy. In light of this, we design a novel clique expansion-based Adaptive Expansion method called AdE to adaptively expand hypergraphs into weighted graphs that preserve the higher-order structure information. Specifically, we introduce a novel Global Simulation Network to select two…
Peer Reviews
Decision·Submitted to ICLR 2024
1. The authors have made a good observation that hypergraph expansion has grown to be an important area of study in hypergraph-related learning and analysis. Therefore, I think the subject of study is very meaningful. 2. The experiments are well designed to support the main claims in the methodology. They are also quite extensive in coverage of various expansion methods (Table 1) as well as hypergraph learning methods (Table 2)
1. I am not fully convinced about the design choice that, regardless of the size of the hyperedge, always two nodes are chosen as representative nodes. Why is it not three or an adaptive number of representative nodes? Also, in expansion, this essentially always approximate any internal connectivity within a hypergraph by a "bar-bell" shaped graph, which does not look very intuitive to me. Can the authors explain more on this matter? 2. I remains very unclear to me why we should use S, the sum
1. The idea of adaptively learning a weighted graph from the hypergraph is useful. Most existing works merely expand the hypergraph into a graph roughly and feed the converted graph into neural networks for representation learning, which results in information loss or information redundancy. 2. From my perspective, the model design of AdT including GSi-Net and the distance-aware kernel function is novel and rational, with theoretical proof and extensive experiments over five benchmark datasets.
1. This work discusses three existing expansion methods, i.e., clique expansion, line expansion, and star expansion. As this work introduces these three methods briefly in related Works, I do not get the difference between AdE, CE, LE, and SE. I am curious about the advantages and disadvantages of each method. 2. This work claims that AdE is equivalent to the weighted clique expansion in 3-uniform hypergraphs in Proposition 4. I am a bit confused about that as AdE is designed to dynamically lea
1. The problem space is very interesting. There is very little attention paid to finding innovative ways to convert hypergraphs to graphs by preserving the desired properties. 2. The proposed method outperforms the existing baselines. The ablation study provides an understanding of the contribution of different components.
1. Existing works like node-degree preserving hypergraph projection [1] are not considered. Clique/star-based expansions are not the right representative of SOTA methods. 2. The idea of using node features to compute edge weights assumes that there is an underlying homophily, which was not well captured by hyperedges (hence, the existence of a hyperedge does not mean the constituent nodes share the same strengthened bond), but the projected graph will capture it better. It requires more justifi
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