Orateurs
Description
Representing large and complex scientific data as graphs requires methods that capture their structure across different scales while remaining computationally tractable. In this context, the FoSFor (Forest Screening for Multiscales Network Processing) toolbox, a CNRS Innovation Open project, provides a forest-based coarse-graining framework for constructing compact and multiscale graph representations.
The coarse-graining is driven by the stochastic dynamics associated with the graph rather than by purely geometric or topological criteria. At each step, a subset of representative states is selected through a random forest construction, and the dynamics is projected onto this reduced set while retaining a link with the original state space through an intertwining kernel.
Repeating this procedure produces a hierarchy of graphs and associated transition kernels across scales. The resulting representation is therefore not only a compact encoding of the graph, but also a dynamics-aware description in which coarse states retain information about the "microscopic" configurations they represent.
This provides a natural framework for studying graph signals at multiple scales and for constructing bases adapted to the underlying graph dynamics.
At each scale, the intertwining operator links the coarse representation to the original graph.
This construction naturally leads to a multiscale wavelet basis for graph signals, with approximation and detail functions associated with different resolutions. The resulting basis enables the analysis and reconstruction of signals at successive resolutions while retaining the link with the underlying graph dynamics.
This compact and structured representation can provide an efficient input for Graph ML and representation learning, while its multiscale structure supports graph signal processing and reconstruction tasks, including signal inpainting. For example, this approach achieves a recovery score of 0.8 when reconstructing a signal from 50% of the available signal information.
These methods are made available through the FoSFor toolbox, providing open-source implementations, pre-built binaries, and a user-friendly API to facilitate their adoption and integration into scientific workflows.