Boudjemaa, R; Forbes, A B; Harris, P M; Langdell, S* (2003) Multivariate empirical models and their use in metrology. NPL Report. CMSC 32/03

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Abstract

In this report, we consider classes of the empirical functions available to the metrologist to model multivariate data and discuss the algorithmic requirements for using these models in data approximation. We first review common examples of empirical functions of one variable and describe their generic features relevant to models in higher dimensions. We then review common approaches to modelling multivariate data including approaches specific to data on a regular grid (e.g., tensor product polynomial and splines) and more general approaches (e.g., radial basis functions and sup-port vector machines). For each type of model we highlight their advantages and disadvantages with respect to their applications in modelling metrological data. We also give an example application involving interferometric data. We conclude that i) radial basis functions are likely to become important tools for modelling multivariate systems in metrology, ii) much of the underlying technology of support vector machines – statistical information theory, reproducing kernel Hilbert spaces, etc., – are of potential value to metrology, particularly in situations in which the system under study is imperfectly understood, for example, in biotechnology.

Item Type:	Report/Guide (NPL Report)
NPL Report No.:	CMSC 32/03
Subjects:	Mathematics and Scientific Computing Mathematics and Scientific Computing > Modelling
Last Modified:	02 Feb 2018 13:16
URI:	http://eprintspublications.npl.co.uk/id/eprint/2942

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