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Dual-to-kernel learning with ideals

Király, FJ; Kreuzer, M; Theran, L; (2014) Dual-to-kernel learning with ideals. arXiv.org , Article arXiv:1402.0099 [stat.ML]. Green open access

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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.

Type: Article
Title: Dual-to-kernel learning with ideals
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/1402.0099
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Machine Learning (stat.ML); Learning (cs.LG); Commutative Algebra (math.AC); Algebraic Geometry (math.AG); Statistics Theory (math.ST)
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1517412
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