Dual-to-kernel learning with ideals

Franz J. Király; Martin Kreuzer; Louis Theran

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arXiv · 1402.0099

Dual-to-kernel learning with ideals

Franz J. Király·Martin Kreuzer·Louis Theran

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Abstract

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, IPCA and AVICA, for simultaneous manifold and feature learning, and test their accuracy on synthetic and real world data.

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BibTeX RIS

Franz J. Király, Martin Kreuzer, Louis Theran. 2014-02-01. Dual-to-kernel learning with ideals. https://arxiv.org/abs/1402.0099

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