Inferring Graph Signal Translations as Invariant Transformations for Classification Tasks
This addresses a fundamental limitation in GSP for researchers and practitioners by providing a data-driven approach to infer translations, though it is incremental as it builds on existing translation concepts.
The paper tackles the ill-posed problem of defining translations in Graph Signal Processing by inferring them as edge-constrained operations that make supervised classification invariant, using a deep learning framework that combines graph structure and labeled signals, and demonstrates effectiveness on regular 2D images and hyperlink networks.
The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to define translations using solely the graph structure (i.e. edges). Such a problem is ill-posed in general as a graph conveys information about neighborhood but not about directions. In this paper, we propose to infer translations as edge-constrained operations that make a supervised classification problem invariant using a deep learning framework. As such, our methodology uses both the graph structure and labeled signals to infer translations. We perform experiments with regular 2D images and abstract hyperlink networks to show the effectiveness of the proposed methodology in inferring meaningful translations for signals supported on graphs.