[Paper Review] SPECTRE: Seedless Network Alignment via Spectral Centralities

Mikhail Hayhoe, Francisco Barreras+2 more|arXiv (Cornell University)|Nov 2, 2018

Complex Network Analysis Techniques53 references4 citations

TL;DR

SPECTRE is a scalable, seedless network alignment algorithm that uses spectral centrality to generate a noisy initial seed set and bootstrap percolation to iteratively refine alignments, achieving high accuracy even on moderately correlated networks without prior knowledge of correct node pairs. It outperforms state-of-the-art methods in edge correctness and ICS score on real-world and synthetic networks.

ABSTRACT

Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of proteins in computational biology, to the de-anonymization of social networks, as well as recognition tasks in computer vision. In this work we introduce SPECTRE, a scalable algorithm that uses spectral centrality measures and percolation techniques. Unlike most network alignment algorithms, SPECTRE requires no seeds (i.e., pairs of nodes identified beforehand), which in many cases are expensive, or impossible, to obtain. Instead, SPECTRE generates an initial noisy seed set via spectral centrality measures which is then used to robustly grow a network alignment via bootstrap percolation techniques. We show that, while this seed set may contain a majority of incorrect pairs, SPECTRE is still able to obtain a high-quality alignment. Through extensive numerical simulations, we show that SPECTRE allows for fast run times and high accuracy on large synthetic and real-world networks, even those which do not exhibit a high correlation.

Motivation & Objective

• To address the critical limitation of existing network alignment algorithms that require high edge correlation or seed pairs, which are often unavailable in real-world applications.
• To develop a scalable, robust algorithm that achieves high alignment quality without relying on prior information or correct seed pairs.
• To demonstrate that a noisy initial seed set derived from spectral centrality can still yield high-quality alignments through iterative refinement via bootstrap percolation.
• To evaluate performance on diverse real-world networks, including PPI, social, and infrastructure networks, under varying correlation levels.
• To establish SPECTRE as the first scalable algorithm that maintains high precision and accuracy without seeds or strong correlation assumptions.

Proposed method

• SPECTRE uses eigenvector centrality to generate an initial noisy seed set by ranking nodes based on spectral properties of the network adjacency matrix.
• It applies a bootstrap percolation framework with two expansion modes: SafeExpand and LooseExpand, which iteratively grow the alignment based on local consistency.
• A backtracking strategy is employed to correct misaligned nodes during expansion, improving alignment quality over iterations.
• The algorithm uses a parameter sweep over k (number of initial seed pairs) and w (percolation threshold) to optimize alignment performance.
• It leverages low-rank approximations and spectral decomposition to ensure computational scalability on large networks.
• The method is designed to be robust to noise in the initial seed set, allowing it to succeed even when most initial pairs are incorrect.

Experimental results

Research questions

• RQ1 Can a network alignment algorithm achieve high accuracy without requiring any seed pairs or prior knowledge of node correspondences?
• RQ2 How effective is spectral centrality in generating a useful, albeit noisy, initial seed set for network alignment?
• RQ3 To what extent can bootstrap percolation with backtracking correct errors in a noisy initial alignment?
• RQ4 How does SPECTRE perform on real-world networks with low to moderate edge correlation, where existing methods fail?
• RQ5 What is the trade-off between alignment quality, runtime, and parameter choices (e.g., k and w) in the absence of seeds?

Key findings

• SPECTRE achieves 32% edge correctness and 35% ICS score on C. jejuni and E. coli PPI networks, significantly outperforming GHOST and MI-GRAAL.
• The best alignment quality is achieved with w=1 and k=90, indicating robustness to parameter variation and high tolerance for initial noise.
• Runtime scales efficiently with network size, with SPECTRE completing in under 100 seconds on networks with over 50,000 nodes.
• SPECTRE maintains high performance even on networks with low edge correlation, where most existing algorithms fail.
• The algorithm is robust to a majority of incorrect initial seed pairs, as the bootstrap percolation process effectively corrects errors through iterative refinement.
• SPECTRE demonstrates superior scalability and accuracy compared to state-of-the-art methods, especially in seedless settings.