Using Laplacian Spectrum as Graph Feature Representation
This provides a simple baseline for graph representation, but it is incremental as it builds on known spectral properties.
The paper tackles the problem of representing graphs for analysis by proposing the graph Laplacian spectrum (GLS) as a feature, showing it preserves structural information and performs well in classification tasks.
Graphs possess exotic features like variable size and absence of natural ordering of the nodes that make them difficult to analyze and compare. To circumvent this problem and learn on graphs, graph feature representation is required. A good graph representation must satisfy the preservation of structural information, with two particular key attributes: consistency under deformation and invariance under isomorphism. While state-of-the-art methods seek such properties with powerful graph neural-networks, we propose to leverage a simple graph feature: the graph Laplacian spectrum (GLS). We first remind and show that GLS satisfies the aforementioned key attributes, using a graph perturbation approach. In particular, we derive bounds for the distance between two GLS that are related to the \textit{divergence to isomorphism}, a standard computationally expensive graph divergence. We finally experiment GLS as graph representation through consistency tests and classification tasks, and show that it is a strong graph feature representation baseline.