Corpus ID: 8012764

Dual-to-kernel learning with ideals

@article{Kirly2014DualtokernelLW,
  title={Dual-to-kernel learning with ideals},
  author={F. Kir{\'a}ly and M. Kreuzer and Louis Theran},
  journal={ArXiv},
  year={2014},
  volume={abs/1402.0099}
}
  • F. Király, M. Kreuzer, Louis Theran
  • Published 2014
  • Mathematics, Computer Science
  • ArXiv
  • In this paper, we propose a theory which unifies kernel learning and symbolic algebraic methods. We show that both worlds are inherently dual to each other, and we use this duality to combine the structure-awareness of algebraic methods with the efficiency and generality of kernels. The main idea lies in relating polynomial rings to feature space, and ideals to manifolds, then exploiting this generative-discriminative duality on kernel matrices. We illustrate this by proposing two algorithms… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 29 REFERENCES
    Nonlinear dimensionality reduction by locally linear embedding.
    • 12,555
    • PDF
    A training algorithm for optimal margin classifiers
    • 9,325
    • PDF
    Nonlinear Component Analysis as a Kernel Eigenvalue Problem
    • 7,261
    • PDF
    Kernel Methods for Pattern Analysis
    • 2,700
    • PDF
    The Nature of Statistical Learning Theory
    • 36,400
    • Highly Influential
    • PDF
    Learning with kernels
    • 7,408
    • PDF
    Generalized principal component analysis (GPCA)
    • 933
    • PDF
    The singular value decomposition for polynomial systems
    • 225
    • PDF
    Group theoretical methods in machine learning
    • 75
    • PDF
    The Construction of Multivariate Polynomials with Preassigned Zeros
    • 175