Geometrically motivated nonstationary kernel density estimation on manifold

    Research output: Contribution to conferencePaperpeer-review

    Abstract

    Consider a problem of estimating an unknown high dimensional density whose support lies on unknown low-dimensional data manifold. This problem arises in many data mining tasks, and the paper proposes a new geometrically motivated solution for the problem in manifold learning framework, including an estimation of an unknown support of the density. Firstly, tangent bundle manifold learning problem is solved resulting in transforming high dimensional data into their low-dimensional features and estimating the Riemannian tensor on the Data manifold. After that, an unknown density of the constructed features is estimated with the use of appropriate kernel approach. Finally, with the use of estimated Riemannian tensor, the final estimator of the initial density is constructed.

    Original languageEnglish
    Publication statusPublished - 2018
    Event2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018 - Fort Lauderdale, United States
    Duration: 3 Jan 20185 Jan 2018

    Conference

    Conference2018 International Symposium on Artificial Intelligence and Mathematics, ISAIM 2018
    Country/TerritoryUnited States
    CityFort Lauderdale
    Period3/01/185/01/18

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