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Lei Yang, Mengxue Xu and Yunan He
Convolutional Neural Networks (CNNs) have become essential in deep learning applications, especially in computer vision, yet their complex internal mechanisms pose significant challenges to interpretability, crucial for ethical applications. Addressing t...
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Steve de Rose, Philippe Meyer and Frédéric Bertrand
Accurate sizing systems of a population permit the minimization of the production costs of the textile apparel industry and allow firms to satisfy their customers. Hence, information about human body shapes needs to be extracted in order to examine, comp...
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Mattia G. Bergomi and Massimo Ferri
Among the various generalizations of persistent topology, that based on rank functions and leading to indexing-aware functions appears to be particularly suited to catching graph-theoretical properties without the need for a simplicial construction and a...
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Ran Deng and Fedor Duzhin
Topological data analysis has recently found applications in various areas of science, such as computer vision and understanding of protein folding. However, applications of topological data analysis to natural language processing remain under-researched...
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Douglas Lenseth and Boris Goldfarb
We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field V is generated using a fixed algorithm...
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Paul Samuel Ignacio, Jay-Anne Bulauan and David Uminsky
Stability of persistence diagrams under slight perturbations is a key characteristic behind the validity and growing popularity of topological data analysis in exploring real-world data. Central to this stability is the use of Bottleneck distance which e...
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Sarah Tymochko, Elizabeth Munch and Firas A. Khasawneh
Bifurcations in dynamical systems characterize qualitative changes in the system behavior. Therefore, their detection is important because they can signal the transition from normal system operation to imminent failure. In an experimental setting, this t...
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Daniel Lütgehetmann, Dejan Govc, Jason P. Smith and Ran Levi
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology compu...
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Kevin P. Knudson
We define the notion of an approximate triangulation for a manifold M embedded in Euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in M and use persistent homology to find a complex in the family whos...
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Shafie Gholizadeh, Armin Seyeditabari and Wlodek Zadrozny
Topological Data Analysis (TDA) refers to a collection of methods that find the structure of shapes in data. Although recently, TDA methods have been used in many areas of data mining, it has not been widely applied to text mining tasks. In most text pro...
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