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Home > Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 32

Approximate Vanishing Ideal via Data Knotting

March 15, 2023

Authors

Hiroshi Kera

The University of Tokyo


Yoshihiko Hasegawa

The University of Tokyo


Published:

2018-02-08

Proceedings:

Proceedings of the AAAI Conference on Artificial Intelligence, 32

Volume

Issue:

Thirty-Second AAAI Conference on Artificial Intelligence 2018

Track:

AAAI Technical Track: Machine Learning

Downloads:

Download PDF

Abstract:

The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designed to approximately rather than exactly equal zero on the designated data. Although such approximations empirically demonstrate high performance, the sound algebraic structure of the vanishing ideal is lost. The present paper proposes a vanishing ideal that is tolerant to noisy data and also pursued to have a better algebraic structure. As a new problem, we simultaneously find a set of polynomials and data points for which the polynomials approximately vanish on the input data points, and almost exactly vanish on the discovered data points. In experimental classification tests, our method discovered much fewer and lower-degree polynomials than an existing state-of-the-art method. Consequently, our method accelerated the runtime of the classification tasks without degrading the classification accuracy.

DOI:

10.1609/aaai.v32i1.11677


AAAI

Thirty-Second AAAI Conference on Artificial Intelligence 2018


ISSN 2374-3468 (Online) ISSN 2159-5399 (Print)


Published by AAAI Press, Palo Alto, California USA Copyright © 2018, Association for the Advancement of Artificial Intelligence All Rights Reserved.

Topics: AAAI

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