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Learning with Algebraic Invariances, and the Invariant Kernel Trick

Király, FJ; Ziehe, A; Müller, K-R; (2014) Learning with Algebraic Invariances, and the Invariant Kernel Trick. arXiv , Article arXiv:1411.7817 [stat.ML]. Green open access

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Abstract

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA.

Type: Article
Title: Learning with Algebraic Invariances, and the Invariant Kernel Trick
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/1411.7817
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; Learning; Statistics Theory
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/1517418
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