Statistical learning via manifold learning

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    4 Citations (Scopus)

    Abstract

    A new geometrically motivated method is proposed for solving the non-linear regression task consisting in constructing a predictive function which estimates an unknown smooth mapping f from q-dimensional inputs to m-dimensional outputs based on a given 'input-output' training pairs. The unknown mapping f determines q-dimensional Regression manifold M(f) consisting of all the (q+m)-dimensional 'input-output' vectors. The manifold is covered by a single chart, the training data set determines a manifold-valued sample from this manifold. Modern Manifold Learning technique is used for constructing the certain estimator M∗ of the Regression manifold from the sample which accurately approximates the Regression manifold. The proposed method called Manifold Learning Regression (MLR) finds the predictive function fMLR to ensure an equality M(fMLR) = M∗. The MLR estimates also the m×q Jacobian matrix of the mapping f.

    Original languageEnglish
    Title of host publicationProceedings - 2015 IEEE 14th International Conference on Machine Learning and Applications, ICMLA 2015
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages64-69
    Number of pages6
    ISBN (Electronic)9781509002870
    DOIs
    Publication statusPublished - 2015
    EventIEEE 14th International Conference on Machine Learning and Applications, ICMLA 2015 - Miami, United States
    Duration: 9 Dec 201511 Dec 2015

    Publication series

    NameProceedings - 2015 IEEE 14th International Conference on Machine Learning and Applications, ICMLA 2015

    Conference

    ConferenceIEEE 14th International Conference on Machine Learning and Applications, ICMLA 2015
    Country/TerritoryUnited States
    CityMiami
    Period9/12/1511/12/15

    Keywords

    • Manifold learning
    • Manifold learning regression
    • Statistical learning
    • Tangent bundle manifold learning

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