<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve is outside this class or not. In opposite to the majority of the literature, two sources of a curve variability are present, namely, the one inherent to curves from the proper class and observations errors’. Therefore, firstly a decision function is trained on historical data, and then, descriptors of each curve to be classified are learned from noisy observations.When the intrinsic variability is Gaussian, a decision threshold can be established from <italic>T</italic> <sup>2</sup> Hotelling distribution and tuned to more general cases. Expansion coefficients in a selected orthogonal series are taken as descriptors and an algorithm for their learning is proposed that follows nonparametric curve fitting approaches. Its fast version is derived for descriptors that are based on the cosine series. Additionally, the asymptotic normality of learned descriptors and the bound for the probability of their large deviations are proved. The influence of this bound on the decision threshold is also discussed.The proposed approach covers curves described as functional data projected onto a finite-dimensional subspace of a Hilbert space as well a shape sensitive description of curves, known as square-root velocity (SRV). It was tested both on synthetic data and on real-life observations of the COVID-19 growth curves.</p>
</abstract>

Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve is outside this class or not. In opposite to the majority of the literature, two sources of a curve variability are present, namely, the one inherent to curves from the proper class and observations errors’. Therefore, firstly a decision function is trained on historical data, and then, descriptors of each curve to be classified are learned from noisy observations.When the intrinsic variability is Gaussian, a decision threshold can be established from T 2 Hotelling distribution and tuned to more general cases. Expansion coefficients in a selected orthogonal series are taken as descriptors and an algorithm for their learning is proposed that follows nonparametric curve fitting approaches. Its fast version is derived for descriptors that are based on the cosine series. Additionally, the asymptotic normality of learned descriptors and the bound for the probability of their large deviations are proved. The influence of this bound on the decision threshold is also discussed.The proposed approach covers curves described as functional data projected onto a finite-dimensional subspace of a Hilbert space as well a shape sensitive description of curves, known as square-root velocity (SRV). It was tested both on synthetic data and on real-life observations of the COVID-19 growth curves.

Learning Novelty Detection Outside a Class of Random Curves with Application to COVID-19 Growth

Department of Control Systems and Mechatronics

Wrocław University of Science and Technology

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Let a class of proper curves is specified by positive examples only. We aim to propose a learning novelty detection algorithm that decides whether a new curve...

Learning Novelty Detection Outside a Class of Random Curves with Application to COVID-19 Growth

Published Online: May 29, 2021

Page range: 195 - 215

Received: Sep 06, 2020

Accepted: Mar 21, 2021

DOI: https://doi.org/10.2478/jaiscr-2021-0012

Keywords
classification, learning, novelty detection, functional data

© 2021 Wojciech Rafajłowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Learning Novelty Detection Outside a Class of Random Curves with Application to COVID-19 Growth

Published Online: May 29, 2021

Page range: 195 - 215

Received: Sep 06, 2020

Accepted: Mar 21, 2021

DOI: https://doi.org/10.2478/jaiscr-2021-0012

Keywordsclassification, learning, novelty detection, functional data

© 2021 Wojciech Rafajłowicz, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
classification, learning, novelty detection, functional data