Quiver Signal Processing (QSP)
This foundational work addresses the problem of processing complex network data for researchers in machine learning and signal processing, though it is incremental as it builds on existing representation theory.
The authors introduced a signal processing framework based on quiver representations to handle heterogeneous multidimensional information in networks, providing examples that reveal hidden structures and laying groundwork for alternative graph neural network designs.
In this paper we state the basics for a signal processing framework on quiver representations. A quiver is a directed graph and a quiver representation is an assignment of vector spaces to the nodes of the graph and of linear maps between the vector spaces associated to the nodes. Leveraging the tools from representation theory, we propose a signal processing framework that allows us to handle heterogeneous multidimensional information in networks. We provide a set of examples where this framework provides a natural set of tools to understand apparently hidden structure in information. We remark that the proposed framework states the basis for building graph neural networks where information can be processed and handled in alternative ways.