Dual-to-kernel learning with ideals
Machine Learning
2014-02-04 v1 Machine Learning
Commutative Algebra
Algebraic Geometry
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1402.0099,
title = {Dual-to-kernel learning with ideals},
author = {Franz J. Király and Martin Kreuzer and Louis Theran},
journal= {arXiv preprint arXiv:1402.0099},
year = {2014}
}
Comments
15 pages, 1 figure