Graph Embedding in the Graph Fractional Fourier Transform Domain

Spectral graph embedding plays a critical role in graph representation learning by generating low-dimensional vector representations from graph spectral information. However, the embedding space of traditional spectral embedding methods often exhibit limited expressiveness, failing to exhaustively capture latent structural features across alternative transform domains. To address this issue, we use the graph fractional Fourier transform to extend the existing state-of-the-art generalized frequency filtering embedding (GEFFE) into fractional domains, giving birth to the generalized fractional filtering embedding (GEFRFE), which enhances embedding informativeness via the graph fractional domain.The GEFRFE leverages graph fractional domain filtering and a nonlinear composition of eigenvector components derived from a fractionalized graph Laplacian. To dynamically determine the fractional order, two parallel strategies are introduced: search-based optimization and a ResNet18-based adaptive learning. Extensive experiments on five benchmark datasets demonstrate that the GEFRFE captures richer structural features and significantly enhance classification performance. The GEFRFE provides a new paradigm for the development of graph embedding from the "fixed domain" to the "generalized domain". The results indicate that introducing the GFRFT into the graph embedding domain is a correct and effective research path. Notably, the proposed method retains computational complexity comparable to GEFFE approaches.