Unsupervised Deep Spectral Basis Learning for Generalized Eigendecomposition and Spectral Embedding.

Area of Science:

• Graph theory
• Machine learning
• Geometric processing

Background:

• Spectral embedding is crucial for statistical learning and geometric processing.
• Deep neural networks (DNNs) offer scalable graph embedding but require orthogonalization.
• Existing methods face challenges with generalization and scalability.

Purpose of the Study:

• Introduce an unsupervised spectral basis learning (SBL) framework.
• Enable generalized eigendecomposition of graph matrices.
• Improve spectral embedding by avoiding complex transformations.

Main Methods:

• Developed a novel spectral embedding criterion for spectral basis estimation.
• Utilized linear graph convolutions (LGCs) for spectral embedding.
• Employed an iterative power deflation-like approach to learn spectral bases.

Main Results:

• The SBL framework avoids QR-based orthogonalization or affine transformations.
• Achieved aligned spectral bases across graphs, mitigating eigenvector switching.
• Demonstrated performance gains over state-of-the-art deep spectral embedding methods.

Conclusions:

• SBL provides an effective unsupervised framework for generalized graph eigendecomposition.
• The method simplifies spectral embedding training and enhances graph matching.
• SBL offers a promising alternative to existing deep spectral embedding techniques.