Adaptive Local Clustering over Attributed Graphs

TL;DR

This work addresses local graph clustering on attributed graphs by introducing Bidirectional Diffusion Distribution (BDD), an attribute-aware affinity that blends topology and node attributes. The authors propose LACA, a scalable pipeline with TNAM preprocessing and an adaptive RWR-based diffusion engine that provably achieves locality with complexity $O\left(\frac{k}{(1-\alpha)\epsilon}\right)$. The three-step framework constructs an approximate BDD vector and extracts the local cluster around a seed, achieving state-of-the-art precision across 8 real datasets while offering substantial speedups over embedding- and flow-based baselines. This attribute-aware diffusion approach enables efficient, high-quality, seed-centric clustering suitable for large-scale attributed graphs and real-world applications.

Abstract

Given a graph $G$ and a seed node $v_s$, the objective of local graph clustering (LGC) is to identify a subgraph $C_s \in G$ (a.k.a. local cluster) surrounding $v_s$ in time roughly linear with the size of $C_s$. This approach yields personalized clusters without needing to access the entire graph, which makes it highly suitable for numerous applications involving large graphs. However, most existing solutions merely rely on the topological connectivity between nodes in $G$, rendering them vulnerable to missing or noisy links that are commonly present in real-world graphs. To address this issue, this paper resorts to leveraging the complementary nature of graph topology and node attributes to enhance local clustering quality. To effectively exploit the attribute information, we first formulate the LGC as an estimation of the bidirectional diffusion distribution (BDD), which is specialized for capturing the multi-hop affinity between nodes in the presence of attributes. Furthermore, we propose LACA, an efficient and effective approach for LGC that achieves superb empirical performance on multiple real datasets while maintaining strong locality. The core components of LACA include (i) a fast and theoretically-grounded preprocessing technique for node attributes, (ii) an adaptive algorithm for diffusing any vectors over $G$ with rigorous theoretical guarantees and expedited convergence, and (iii) an effective three-step scheme for BDD approximation. Extensive experiments, comparing 17 competitors on 8 real datasets, show that LACA outperforms all competitors in terms of result quality measured against ground truth local clusters, while also being up to orders of magnitude faster. The code is available at https://github.com/HaoranZ99/alac.

Figures (10)

• Figure 1: Figurative Illustration of BDD.
• Figure 2: Basic Idea of LACA.
• Figure 3: Overview of LACA.
• Figure 4: GreedyDiffuse with $\alpha=0.8$ and $\epsilon=0.1$.
• Figure 5: Greedy v.s. Non-greedy.

Theorems & Definitions (19)

• Theorem 4.1
• proof
• Theorem 4.2
• Lemma 4.3
• Lemma 5.1
• Theorem 5.2
• Lemma 5.3
• Theorem 5.4
• Definition 5.5: Graph Signal Denoising ma2021unified
• Lemma 5.6