Graph Scattering beyond Wavelet Shackles
This work addresses the problem of improving graph-based learning for tasks like social network analysis and quantum chemistry, offering a more flexible framework than existing methods, though it appears incremental in extending scattering transforms.
The paper tackles the design of flexible graph scattering networks with variable branching ratios and generic filters, deriving stability guarantees and introducing new feature aggregation methods; it shows that these networks outperform traditional graph-wavelet scattering in social network classification and significantly exceed other methods in quantum-chemical energy regression on QM7.
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for node- and graph-level perturbations are derived; the vertex-set non-preserving case is treated by utilizing recently developed mathematical-physics based tools. Energy propagation through the network layers is investigated and related to truncation stability. New methods of graph-level feature aggregation are introduced and stability of the resulting composite scattering architectures is established. Finally, scattering transforms are extended to edge- and higher order tensorial input. Theoretical results are complemented by numerical investigations: Suitably chosen cattering networks conforming to the developed theory perform better than traditional graph-wavelet based scattering approaches in social network graph classification tasks and significantly outperform other graph-based learning approaches to regression of quantum-chemical energies on QM7.