[2603.19439] Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphs

Statistics > Machine Learning arXiv:2603.19439 (stat) [Submitted on 19 Mar 2026] Title:Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphs Authors:Mohammad Eini, Abdullah Karaaslanli, Vassilis Kalantzis, Panagiotis A. Traganitis View a PDF of the paper titled Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphs, by Mohammad Eini and 3 other authors View PDF Abstract:Several graph data mining, signal processing, and machine learning downstream tasks rely on information related to the eigenvectors of the associated adjacency or Laplacian matrix. Classical eigendecomposition methods are powerful when the matrix remains static but cannot be applied to problems where the matrix entries are updated or the number of rows and columns increases frequently. Such scenarios occur routinely in graph analytics when the graph is changing dynamically and either edges and/or nodes are being added and removed. This paper puts forth a new algorithmic framework to update the eigenvectors associated with the leading eigenvalues of an initial adjacency or Laplacian matrix as the graph evolves dynamically. The proposed algorithm is based on Rayleigh-Ritz projections, in which the original eigenvalue problem is projected onto a restricted subspace which ideally encapsulates the invariant subspace associated with the sought eigenvectors. Following ideas from eigenvector perturbation analysis, we present a new methodology to build the projection subspa...