A method to enrich experimental datasets by means of numerical simulations in view of classification tasks

Classification tasks are frequent in many applications in science and engineering. A wide variety of statistical learning methods exist to deal with these problems. However, in many industrial applications, the number of available samples to train and construct a classifier is scarce and this has an...

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Bibliographic Details
Published in:ESAIM. Mathematical modelling and numerical analysis 2021-09, Vol.55 (5), p.2259-2291
Main Authors: Lombardi, Damiano, Raphel, Fabien
Format: Article
Language:English
Subjects:
Adaptation
Algorithms
Classification
Datasets
Industrial applications
Investigations
Machine learning
Mathematical models
Mathematics
Metric space
Numerical analysis
Simulation
Statistical methods
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Summary:Classification tasks are frequent in many applications in science and engineering. A wide variety of statistical learning methods exist to deal with these problems. However, in many industrial applications, the number of available samples to train and construct a classifier is scarce and this has an impact on the classifications performances. In this work, we consider the case in which some a priori information on the system is available in form of a mathematical model. In particular, a set of numerical simulations of the system can be integrated to the experimental dataset. The main question we address is how to integrate them systematically in order to improve the classification performances. The method proposed is based on Nearest Neighbours and on the notion of Hausdorff distance between sets. Some theoretical results and several numerical studies are proposed.
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2021060