Nonlinear multi-output regression on unknown input manifold

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    6 Citations (Scopus)


    Consider unknown smooth function which maps high-dimensional inputs to multidimensional outputs and whose domain of definition is unknown low-dimensional input manifold embedded in an ambient high-dimensional input space. Given training dataset consisting of ‘input-output’ pairs, regression on input manifold problem is to estimate the unknown function and its Jacobian matrix, as well to estimate the input manifold. By transforming high-dimensional inputs in their low-dimensional features, initial regression problem is reduced to certain regression on feature space problem. The paper presents a new geometrically motivated method for solving both interrelated regression problems.

    Original languageEnglish
    Pages (from-to)209-240
    Number of pages32
    JournalAnnals of Mathematics and Artificial Intelligence
    Issue number1-2
    Publication statusPublished - 1 Oct 2017


    • Dimensionality reduction
    • Manifold estimation
    • Manifold learning
    • Regression on feature space
    • Regression on manifolds


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