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The theory of homology induced maps of correspondences proposed by Shaun Harker et al. in 2016 is a powerful tool which allows the retrieval of underlying homological information from sampled maps with noise or defects. In this paper, we redefine induced maps of correspondences within the framework of quiver representations, and provide more concise proofs of the main theorems in the original paper. With this point of view, we extend these ideas to filtration analysis based on persistent homology, which provides new methods for analyzing sampled maps, especially sampled dynamical systems, and moreover 2-D persistent homology.

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