Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation

TL;DR

This paper introduces a scalable tensor decomposition method for large-scale multi-dimensional networks modeled as random Kronecker graphs, improving inference efficiency and accuracy.

Contribution

It extends Kronecker graph analysis to tensors, combining tensor decomposition with Einstein summation for scalable network inference.

Findings

Reduces computational complexity in large-scale network analysis

Effective separation of signal and noise in tensor representations

Demonstrates strong performance in network inference tasks

Abstract

In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of such networks into two components: a low-rank signal tensor that captures the essential network structure and a zero-mean noise tensor that accounts for random variations. Building on recent advancements in tensor decomposition and random tensor theory, we introduce a generalized denoise-and-solve framework that leverages the Einstein summation convention for efficient tensor operations. This approach significantly reduces computational complexity while demonstrating strong performance in network inference tasks, providing a scalable and efficient solution for analyzing large-scale, multi-dimensional networks.