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 subspace. The proposed framework features lower computational and memory complexity with respect to competitive alternatives while empirical results show strong qualitative performance, both in terms of eigenvector approximation and accuracy of downstream learning tasks of central node identification and node clustering.

Out-of-distribution (OOD) generalization issue is a well-known challenge within deep learning tasks. In dynamic graphs, the change of temporal environments is regarded as the main cause of data distribution shift. While numerous OOD studies focusing on environment factors have achieved remarkable performance, they still fail to systematically solve the two issue of environment inference and utilization. In this work, we propose a novel dynamic graph learning model named EpoD based on prompt learning and structural causal model to comprehensively enhance both environment inference and utilization. Inspired by the superior performance of prompt learning in understanding underlying semantic and causal associations, we first design a self-prompted learning mechanism to infer unseen environment factors. We then rethink the role of environment variable within spatio-temporal causal structure model, and introduce a novel causal pathway where dynamic sub-graphs serve as mediating variables. The extracted dynamic subgraph can effectively capture the data distribution shift by incorporating the inferred environment variables into the node-wise dependencies.

Our experiments with multiple real-world dynamic graph datasets demonstrate thatSI-VGRNN andVGRNN consistently outperform the existing baseline and state-of-the-art methods by a significant marginindynamiclinkprediction.

Despite the prevalence ofrecent success inlearning from static graphs, learning from time-evolving graphs remains an open challenge.