Unsupervised Deep Spectral Basis Learning for Generalized Eigendecomposition and Spectral Embedding

Spectral embedding has been widely used in statistical learning and geometric processing. Existing deep neural networks (DNNs) construct nonlinear mappings from node descriptors to embedding coordinates, relieving the scalability and generalization problems in traditional eigendecomposition-based graph embedding. However, additional QR-based orthogonalization or affine transformation is required for training deep spectral embedding models. In this work, we introduce an unsupervised spectral basis learning (SBL) framework for generalized eigendecomposition of graph matrices, benefiting from linear graph convolutions (LGCs) for spectral embedding. We design a novel spectral embedding criterion to learn the spectral basis in an analogous way to iterative power deflation, avoiding additional QR-based orthogonalization or transformations for spectral bases estimation. However, the proposed approach enables the lining up of spectral bases between graphs, which relieves eigenvector switching and facilitates graph matching. We showcase the efficacy of the proposed SBL for generalized graph eigendecomposition with performance gains over state-of-the-art deep spectral embedding methods. The source code is available at https://github.com/DYS2108/SBL.