2017/05/24 by Geert Leus, Santiago Segarra, Leus, Geert +5
Computer Science · Engineering · #Advanced Graph Neural Networks #FOS: Computer and information sciences #Information Theory (cs.IT) #Power Systems and Technologies
paper · pdf · doi:10.48550/arxiv.1705.08987
openalex publication_date 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Contemporary data is often supported by an irregular structure, which can be\nconveniently captured by a graph. Accounting for this graph support is crucial\nto analyze the data, leading to an area known as graph signal processing (GSP).\nThe two most important tools in GSP are the graph shift operator (GSO), which\nis a sparse matrix accounting for the topology of the graph, and the graph\nFourier transform (GFT), which maps graph signals into a frequency domain\nspanned by a number of graph-related Fourier-like basis vectors. This\nalternative representation of a graph signal is denominated the graph frequency\nsignal. Several attempts have been undertaken in order to interpret the support\nof this graph frequency signal, but they all resulted in a one-dimensional\ninterpretation. However, if the support of the original signal is captured by a\ngraph, why would the graph frequency signal have a simple one-dimensional\nsupport? That is why, for the first time, we propose an irregular support for\nthe graph frequency signal, which we coin the dual graph. The dual GSO leads to\na better interpretation of the graph frequency signal and its domain, helps to\nunderstand how the different graph frequencies are related and clustered,\nenables the development of better graph filters and filter banks, and\nfacilitates the generalization of classical SP results to the graph domain.\n