On Generalized Signature Graphs

Abstract

Graph signal processing (GSP) has provided a wide range of powerful methodologies for diverse learning tasks. While the data domain in GSP is fundamentally non-Euclidean, the relation between graph signal samples has mostly been studied using Euclidean similarity metrics. In our recent work on signature graphs we have explored GSP models specifically suited for data featuring symmetries that can be characterized by the sign-flip involution. In this paper, we introduce a generalized GSP framework with models and tools that build on generalized similarity/dissimilarity metrics and on different involutions to capture domain-specific data symmetries. We illustrate the usefulness of our generalized signature graph framework in graph learning and clustering problems.