Local Graph Clustering with Noisy Labels

TL;DR

Empirically, it is shown that reliable node labels can be obtained with just a few samples from an attributed graph, and utilizing these labels via diffusion in the weighted graph leads to significantly better local clustering performance across several real-world datasets.

Abstract

The growing interest in machine learning problems over graphs with additional node information such as texts, images, or labels has popularized methods that require the costly operation of processing the entire graph. Yet, little effort has been made to the development of fast local methods (i.e. without accessing the entire graph) that extract useful information from such data. To that end, we propose a study of local graph clustering using noisy node labels as a proxy for additional node information. In this setting, nodes receive initial binary labels based on cluster affiliation: 1 if they belong to the target cluster and 0 otherwise. Subsequently, a fraction of these labels is flipped. We investigate the benefits of incorporating noisy labels for local graph clustering. By constructing a weighted graph with such labels, we study the performance of graph diffusion-based local clustering method on both the original and the weighted graphs. From a theoretical perspective, we consider recovering an unknown target cluster with a single seed node in a random graph with independent noisy node labels. We provide sufficient conditions on the label noise under which, with high probability, using diffusion in the weighted graph yields a more accurate recovery of the target cluster. This approach proves more effective than using the given labels alone or using diffusion in the label-free original graph. Empirically, we show that reliable node labels can be obtained with just a few samples from an attributed graph. Moreover, utilizing these labels via diffusion in the weighted graph leads to significantly better local clustering performance across several real-world datasets, improving F1 scores by up to 13%.

Figures (5)

• Figure 1: Label-based edge weights avoid mass leakage by attenuating more boundary edges than internal edges. This helps local diffusion more accurately recover the target cluster.
• Figure 2: F1 scores obtained by employing flow diffusion over the original graph (FD) and the label-weighted graph (LFD). For comparison, we also plot the F1 obtained by the noisy labels (Labels). The solid line and error bar show mean and standard deviation over 100 trials, respectively. As discussed in Section \ref{['sec:results']}, even fairly noisy labels can already help boost local clustering performance.
• Figure 3: F1 scores for local clustering using Flow Diffusion (FD), Weighted Flow Diffusion (WFD), Label-based Flow Diffusion (LFD), and Logistic Regression (Classifier) with an increasing number of positive and negative ground-truth samples.
• Figure 4: F1 scores obtained by employing $\ell_1$-regularized PageRank (FKSCM2017) over the original graph (PR) and the label-weighted graph (LPR). For comparison, we also plot the F1 obtained by the noisy labels (Labels). The solid line and error bar show mean and standard deviation over 100 trials, respectively.
• Figure 5: F1 scores across datasets for $\ell_1$-regularized PageRank, Label-based PageRank (LPR), and Logistic Regression (Classifier) with an increasing number of positive and negative ground truth samples

Theorems & Definitions (14)

• Definition 3.2
• Remark 3.3: Locality
• Theorem 3.4: Simplified version
• Theorem A.1: Formal version of Theorem \ref{['thm:main']}
• Proposition A.2
• proof
• Proposition A.3
• proof
• Lemma A.4: External degree in $G$
• proof