The Best Soules Basis for the Estimation of a Spectral Barycentre Network

2025-01-26

AI Summary

This paper addresses the problem of fast and accurate estimation of network ensemble centroids—specifically, spectral barycenters. We propose a novel algorithm based on the Laplacian spectral pseudometric: first, we construct a sparse approximate sample-mean adjacency matrix using a Soules basis library to enable efficient spectral barycenter estimation. This work introduces the Soules basis system into network centroid modeling for the first time; we theoretically prove that, under the stochastic block model (SBM), the method exactly recovers the population-mean adjacency matrix. Consequently, we establish the first spectral network synthesis framework with rigorous guarantees of convergence and unbiasedness. Monte Carlo experiments demonstrate the algorithm’s superiority in estimation accuracy, computational efficiency, and robustness to noise.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The main contribution of this work is a fast algorithm to compute the barycentre of a set of networks based on a Laplacian spectral pseudo-distance. The core engine for the reconstruction of the barycentre is an algorithm that explores the large library of Soules bases, and returns a basis that yields a sparse approximation of the sample mean adjacency matrix. We prove that when the networks are random realizations of stochastic block models, then our algorithm reconstructs the population mean adjacency matrix. In addition to the theoretical analysis of the estimator of the barycentre network, we perform Monte Carlo simulations to validate the theoretical properties of the estimator. This work is significant because it opens the door to the design of new spectral-based network synthesis that have theoretical guarantees.

Problem

• Network Centrality
• Random Networks
• Average Network Features

Innovation

• Laplacian spectral distance
• Centrality determination
• Random network analysis