Kernel regression on manifold valued data

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    9 Citations (Scopus)

    Abstract

    We consider an unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is an unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given a training dataset with 'input-output' pairs, Regression with Manifold Valued Inputs problem is to estimate the unknown function and its Jacobian matrix. Previously proposed solutions are very computationally expensive. The paper presents a new geometrically motivated kernel regression method for solving the considered problem with a much lower computational complexity while preserving accuracy.

    Original languageEnglish
    Title of host publicationProceedings - 2018 IEEE 5th International Conference on Data Science and Advanced Analytics, DSAA 2018
    EditorsTina Eliassi-Rad, Wei Wang, Ciro Cattuto, Foster Provost, Rayid Ghani, Francesco Bonchi
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages120-129
    Number of pages10
    ISBN (Electronic)9781538650905
    DOIs
    Publication statusPublished - 31 Jan 2019
    Event5th IEEE International Conference on Data Science and Advanced Analytics, DSAA 2018 - Turin, Italy
    Duration: 1 Oct 20184 Oct 2018

    Publication series

    NameProceedings - 2018 IEEE 5th International Conference on Data Science and Advanced Analytics, DSAA 2018

    Conference

    Conference5th IEEE International Conference on Data Science and Advanced Analytics, DSAA 2018
    Country/TerritoryItaly
    CityTurin
    Period1/10/184/10/18

    Keywords

    • Manifold learning
    • Regression with manifold valued inputs
    • Tangent bundle manifold learning

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