|
Abstract
|
A directed acyclic graph (DAG) is a specialized form
of directed graph used extensively for analyzing relationships and
dependencies across various domains. However, spectral analysis—a core technique in signal processing on graphs—has been
challenging to apply directly to DAGs due to their inherent acyclic
structure. In this paper, we introduce a spectral filtering approach
for DAGs using graph zero-padding. By adding extra nodes to the
DAG, we create a modified graph structure that enables spectral
analysis. This new structure supports the application of the
graph Fourier transform (GFT) and spectral filtering techniques,
enabling spectral filtering while maintaining key aspects of the
DAG’s topology and dynamics.
|