HeNCler: Node Clustering in Heterophilous Graphs via Learned Asymmetric Similarity
Sonny Achten, Zander Op de Beeck, Francesco Tonin, Volkan Cevher, Johan A. K. Suykens
TL;DR
HeNCler introduces a novel method for clustering nodes in heterophilous graphs by learning an asymmetric similarity graph, enabling effective spectral clustering and outperforming traditional approaches.
Contribution
It proposes a new approach that learns an asymmetric similarity graph for heterophilous node clustering, overcoming computational challenges of previous methods.
Findings
Significantly improves clustering performance in heterophilous graphs.
Enables spectral clustering on directed and undirected graphs.
Overcomes computational difficulties of adjacency partitioning.
Abstract
Clustering nodes in heterophilous graphs is challenging as traditional methods assume that effective clustering is characterized by high intra-cluster and low inter-cluster connectivity. To address this, we introduce HeNCler-a novel approach for Heterophilous Node Clustering. HeNCler learns a similarity graph by optimizing a clustering-specific objective based on weighted kernel singular value decomposition. Our approach enables spectral clustering on an asymmetric similarity graph, providing flexibility for both directed and undirected graphs. By solving the primal problem directly, our method overcomes the computational difficulties of traditional adjacency partitioning-based approaches. Experimental results show that HeNCler significantly improves node clustering performance in heterophilous graph settings, highlighting the advantage of its asymmetric graph-learning framework.
Peer Reviews
Decision·Submitted to ICLR 2025
1. The proposed method is easy to understand. 2. It addresses an important problem.
1. The innovation seems limited, as graph rewiring is already a common approach to tackle heterophilous graphs, as seen in [1] and [2]. However, it would be beneficial for the authors to clarify how their kernel spectral biclustering approach meaningfully differs from existing graph rewiring techniques. Specifically, a comparison of how these methods address heterophily and clustering effectiveness would strengthen the argument for the novelty of their approach. By expanding on the specific adva
1. Novelty: Although the overall idea of learning a similarity matrix for heterophilous graph learning is not new, this paper proposed an interesting framework by observing the advantage of RMK framework. 2. The theoretical support brings interpretability to this framework. 3. The discussion could empirically interpret how the method works.
1. One weakness is the lack of literature on heterophyllous graph learning. The authors only list three works for heterophilous node clustering. Other methods for heterophyllous graph representation learning are suggested to be included on top of node clustering (such as heterophilous node classification, multi-view heterophilous node clustering, etc). 2. Analysis about the experimental results are somehow insufficient. The experimental results on undirected graphs seems not as good as directed
1. The paper addresses a significant and under-explored problem in the field of node clustering for heterophilous graphs. This is a practical and relevant issue, as many real-world graphs exhibit heterophily. 2. Leveraging weighted kernel singular value decomposition to learn a similarity graph for deep node clustering appears to be novel. 3. The whole objective combines the proposed wKSVD loss with a graph autoencoder. Ablation studies suggest that both components contribute to the overall perf
1. The relationship between the proposed wKSVD loss and the characteristics of heterophilous graphs is unclear, which limits the soundness of the method. To my understanding, the most important part of wKSVD is its asymmetric similarity measure, which applies different projections to the pairs. However, it is a pretty trivial operation and this paper does not provide a in-depth explanation of how it helps in the context of heterophilous graphs. 2. While the paper claims significant performance i
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Taxonomy
TopicsAdvanced Graph Neural Networks · Complex Network Analysis Techniques