[Paper Review] Multi-Scale Link Prediction

Donghyuk Shin, Si Si+1 more|arXiv (Cornell University)|Jun 8, 2012

Complex Network Analysis Techniques21 references4 citations

TL;DR

This paper proposes Multi-Scale Link Prediction (MSLP), a scalable and accurate framework for link prediction in massive social networks. By constructing low-rank approximations of the network at multiple hierarchical levels using a tree-structured subspace approximation, MSLP combines predictions across scales to improve robustness and performance, achieving state-of-the-art results on real-world datasets with over a million nodes.

ABSTRACT

The automated analysis of social networks has become an important problem due to the proliferation of social networks, such as LiveJournal, Flickr and Facebook. The scale of these social networks is massive and continues to grow rapidly. An important problem in social network analysis is proximity estimation that infers the closeness of different users. Link prediction, in turn, is an important application of proximity estimation. However, many methods for computing proximity measures have high computational complexity and are thus prohibitive for large-scale link prediction problems. One way to address this problem is to estimate proximity measures via low-rank approximation. However, a single low-rank approximation may not be sufficient to represent the behavior of the entire network. In this paper, we propose Multi-Scale Link Prediction (MSLP), a framework for link prediction, which can handle massive networks. The basis idea of MSLP is to construct low rank approximations of the network at multiple scales in an efficient manner. Based on this approach, MSLP combines predictions at multiple scales to make robust and accurate predictions. Experimental results on real-life datasets with more than a million nodes show the superior performance and scalability of our method.

Motivation & Objective

• To address the high computational complexity of proximity-based link prediction in large-scale social networks.
• To overcome the limitations of single-scale low-rank approximations, which may fail to capture global or local network structures effectively.
• To develop a flexible, scalable framework that integrates multiple granular views of the network for improved prediction accuracy.
• To enable the use of advanced proximity measures like Katz and common neighbors in networks with millions of nodes.

Proposed method

• MSLP uses hierarchical clustering to generate a multi-scale view of the network, where each level represents a different granularity of approximation.
• It applies a tree-structured subspace approximation method to compute low-rank approximations efficiently at each level of the hierarchy.
• The framework combines proximity scores from all levels using a weighted fusion strategy, enhancing both local and global prediction accuracy.
• It leverages memory reuse across levels to ensure computational efficiency and low memory footprint.
• The method is compatible with any proximity measure (e.g., Katz, common neighbors) and any clustering algorithm, ensuring flexibility.
• It supports parallelization within each level, enabling high scalability on large networks.

Experimental results

Research questions

• RQ1 Can multi-scale low-rank approximation improve link prediction accuracy compared to single-scale methods in large networks?
• RQ2 How does MSLP perform relative to state-of-the-art link prediction methods on real-world networks with over a million nodes?
• RQ3 Does combining predictions across multiple hierarchical levels lead to more robust and accurate results than relying on a single approximation?
• RQ4 How sensitive is MSLP to the quality of the underlying clustering structure?
• RQ5 Can MSLP maintain high performance even when the network lacks well-defined clusters?

Key findings

• MSLP-Katz achieved a 15% relative improvement in precision at top-100 results compared to the next best method on the MySpace dataset.
• MSLP-Katz improved AUC by up to 4% relative to the best baseline across all three datasets (Flickr, LiveJournal, MySpace).
• In the low FPR region, MSLP reduced false positive rate by 10% on average and up to 20% compared to other methods, especially excelling in high-confidence predictions.
• MSLP-CN performed comparably to CN but outperformed EIG and CLRA, indicating consistent improvement over dimensionality reduction baselines.
• The method achieved significant performance gains even when using poor-quality clustering structures, demonstrating robustness.
• MSLP showed strong scalability, with low-rank approximations at upper levels computed efficiently after the deepest level, enabling parallelization and memory reuse.