Triangular Alignment (TAME): A Tensor-based Approach for Higher-order Network Alignment

TL;DR

This paper introduces TAME, a tensor-based algorithm for higher-order network alignment that maximizes conserved substructures like triangles, improving alignment quality over existing methods.

Contribution

It formulates a novel higher-order network alignment problem using tensor eigenvectors and proposes the TAME algorithm for triangle-based network alignment.

Findings

TAME outperforms state-of-the-art methods in conserved triangle detection.

Aligned triangles correlate more strongly with node correctness and co-expression.

The approach can be extended to arbitrary motifs.

Abstract

Network alignment has extensive applications in comparative interactomics. Traditional approaches aim to simultaneously maximize the number of conserved edges and the underlying similarity of aligned entities. We propose a novel formulation of the network alignment problem that extends topological similarity to higher-order structures and provides a new objective function that maximizes the number of aligned substructures. This objective function corresponds to an integer programming problem, which is NP-hard. Consequently, we identify a closely related surrogate function whose maximization results in a tensor eigenvector problem. Based on this formulation, we present an algorithm called Triangular AlignMEnt (TAME), which attempts to maximize the number of aligned triangles across networks. Using a case study on the NAPAbench dataset, we show that triangular alignment is capable of producing mappings with high node correctness. We further evaluate our method by aligning yeast and human interactomes. Our results indicate that TAME outperforms the state-of-art alignment methods in terms of conserved triangles. In addition, we show that the number of conserved triangles is more significantly correlated, compared to the conserved edge, with node correctness and co-expression of edges. Our formulation and resulting algorithms can be easily extended to arbitrary motifs.