2013/05/28 by Cerri, Andrea, Landi, Claudia
#Computational Geometry (cs.CG) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Primary 68U05 #Secondary 55N05
paper · doi:10.48550/arxiv.1305.6425
Multidimensional persistence modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. The main result is its stability under function perturbations: any change in vector-valued functions implies a not greater change in the Hausdorff distance between their persistence spaces.