Discrete signal processing on graphs: Graph filters

We propose a novel discrete signal processing framework for structured datasets that arise from social, economic, biological, and physical networks. Our framework extends traditional discrete signal processing theory to datasets with complex structure that can be represented by graphs, so that data elements are indexed by graph nodes and relations between elements are represented by weighted graph edges. We interpret such datasets as signals on graphs, introduce the concept of graph filters for processing such signals, and discuss important properties of graph filters, including linearity, shift-invariance, and invertibility. We then demonstrate the application of graph filters to data classification by demonstrating that a classifier can be interpreted as an adaptive graph filter. Our experiments demonstrate that the proposed approach achieves high classification accuracy.