The persistent homology of a sampled map: from a viewpoint of quiver representations

Abstract This paper is intended to introduce a filtration analysis of sampled maps based on persistent homology, providing new method for reconstructing the underlying maps. The key idea extend definition homology induced correspondences using framework quiver representations. Our given by most direct summands uniquely determine homology. We provide stability theorems this process and show that output map same as if sample sufficiently dense. Compared existing methods eigenspace functors, our represents an important advantage no prior information related eigenvalues required. Some numerical examples are demonstrate effectiveness method.