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Learning Topology: Bridging Computational Topology and Machine Learning

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Pattern Recognition. ICPR International Workshops and Challenges (ICPR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12665))

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Abstract

Topology is a classical branch of mathematics, born essentially from Euler’s studies in the XVII century, which deals with the abstract notion of shape and geometry. Last decades were characterised by a renewed interest in topology and topology-based tools, due to the birth of computational topology and Topological Data Analysis (TDA). A large and novel family of methods and algorithms computing topological features and descriptors (e.g. persistent homology) have proved to be effective tools for the analysis of graphs, 3d objects, 2D images, and even heterogeneous datasets. This survey is intended to be a concise but complete compendium that, offering the essential basic references, allows you to orient yourself among the recent advances in TDA and its applications, with an eye to those related to machine learning and deep learning.

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Authors and Affiliations

  1. Institute of Information Science and Technologies, National Research Council of Italy, Via Moruzzi, 1, 56124, Pisa, Italy

    Davide Moroni & Maria Antonietta Pascali

Authors
  1. Davide Moroni
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  2. Maria Antonietta Pascali
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Correspondence to Maria Antonietta Pascali .

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Editors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, University of Firenze, Firenze, Italy

    Alberto Del Bimbo

  2. Dipartimento di Ingegneria “Enzo Ferrari”, Università di Modena e Reggio Emilia, Modena, Italy

    Rita Cucchiara

  3. Department of Computer Science, Boston University, Boston, MA, USA

    Stan Sclaroff

  4. Dipartimento di Matematica e Informatica, University of Catania, Catania, Italy

    Giovanni Maria Farinella

  5. Cloud & AI, JD.COM, Beijing, China

    Tao Mei

  6. Dipartimento di Ingegneria dell’Informazione, University of Firenze, Firenze, Italy

    Marco Bertini

  7. Computational Sciences Department, National Institute of Astrophysics, Optics and Electronics (INAOE), Tonantzintla, Puebla, Mexico

    Hugo Jair Escalante

  8. Dipartimento di Ingegneria “Enzo Ferrari”, Università di Modena e Reggio Emilia, Modena, Italy

    Roberto Vezzani

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Moroni, D., Pascali, M.A. (2021). Learning Topology: Bridging Computational Topology and Machine Learning. In: Del Bimbo, A., et al. Pattern Recognition. ICPR International Workshops and Challenges. ICPR 2021. Lecture Notes in Computer Science(), vol 12665. Springer, Cham. https://doi.org/10.1007/978-3-030-68821-9_20

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  • DOI: https://doi.org/10.1007/978-3-030-68821-9_20

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