Topological Signal

Topological signal processing (TSP) aims to analyze and process data residing on complex, higher-order structures like simplicial complexes, moving beyond traditional graph-based methods. Current research focuses on developing novel neural network architectures, such as simplicial and generalized simplicial attention networks, and algorithms leveraging concepts like the Dirac operator and Euler characteristic profiles to effectively handle these signals. This field is significant because it enables the analysis of data with intricate relationships beyond pairwise interactions, finding applications in diverse areas including network compression, time series analysis, and data imputation.