Accessibility navigation

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

Lowery, N., Potthast, R. ORCID:, Vahdati, M. and Holderbaum, W. (2012) On discrimination algorithms for ill-posed problems with an application to magnetic tomography. Inverse Problems , 28 (6). 065010. ISSN 1361-6420

Full text not archived in this repository.

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1088/0266-5611/28/6/065010


In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

Item Type:Article
Divisions:Life Sciences > School of Biological Sciences > Department of Bio-Engineering
Science > School of the Built Environment > Energy and Environmental Engineering group
ID Code:28170
Publisher:IOP Science

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation