eprintid: 1517412
rev_number: 19
eprint_status: archive
userid: 608
dir: disk0/01/51/74/12
datestamp: 2016-09-26 01:10:29
lastmod: 2020-02-12 18:56:11
status_changed: 2017-09-04 16:10:57
type: article
metadata_visibility: show
creators_name: Király, FJ
creators_name: Kreuzer, M
creators_name: Theran, L
title: Dual-to-kernel learning with ideals
ispublished: pub
divisions: UCL
divisions: A01
divisions: B04
divisions: C06
divisions: F61
keywords: Machine Learning (stat.ML); Learning (cs.LG); Commutative Algebra (math.AC); Algebraic Geometry (math.AG); Statistics Theory (math.ST)
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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.
date: 2014-02-01
official_url: https://arxiv.org/abs/1402.0099
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1002722
lyricists_name: Kiraly, Franz
lyricists_id: FJKIR17
full_text_status: public
publication: arXiv.org
article_number: arXiv:1402.0099 [stat.ML]
citation:        Király, FJ;    Kreuzer, M;    Theran, L;      (2014)    Dual-to-kernel learning with ideals.                   arXiv.org      , Article arXiv:1402.0099 [stat.ML].        Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1517412/1/Kiraly_1402.0099v1.pdf