Optimization-Free Graph Embedding via Distributional Kernel for Community Detection

TL;DR

This paper introduces an optimization-free graph embedding method that uses a distributional kernel to enhance community detection, effectively mitigating over-smoothing issues in neighborhood aggregation strategies.

Contribution

It is the first to explicitly incorporate node and degree distributional characteristics into a kernel for graph embedding without requiring optimization.

Findings

Achieves superior community detection performance on benchmarks.

Effectively mitigates over-smoothing in graph embeddings.

Outperforms existing methods, including deep learning approaches.

Abstract

Neighborhood Aggregation Strategy (NAS) is a widely used approach in graph embedding, underpinning both Graph Neural Networks (GNNs) and Weisfeiler-Lehman (WL) methods. However, NAS-based methods are identified to be prone to over-smoothing-the loss of node distinguishability with increased iterations-thereby limiting their effectiveness. This paper identifies two characteristics in a network, i.e., the distributions of nodes and node degrees that are critical for expressive representation but have been overlooked in existing methods. We show that these overlooked characteristics contribute significantly to over-smoothing of NAS-methods. To address this, we propose a novel weighted distribution-aware kernel that embeds nodes while taking their distributional characteristics into consideration. Our method has three distinguishing features: (1) it is the first method to explicitly incorporate both distributional characteristics; (2) it requires no optimization; and (3) it effectively mitigates the adverse effects of over-smoothing, allowing WL to preserve node distinguishability and expressiveness even after many iterations of embedding. Experiments demonstrate that our method achieves superior community detection performance via spectral clustering, outperforming existing graph embedding methods, including deep learning methods, on standard benchmarks.