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Function parametrization: Difference between revisions
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The fast reconstruction of the system parameters is obtained by computing the inverse of the mapping ''M''. To do so, the parameters ''p'' are varied over a range corresponding to the expected variation in actual experiments, the corresponding ''q'' are obtained, and the set of ''(p,q)'' data are stored in a database. This database is then subjected to a statistical analysis in order to recover the inverse of ''M''. This analysis is typically a [[:Wikipedia:Principal Component Analysis|Principal Component Analysis]]. This procedure is also amenable to a rather detailed error analysis, so that errors in the recovered parameters ''p'' for the interpretation of actual data ''q'' can be obtained. | The fast reconstruction of the system parameters is obtained by computing the inverse of the mapping ''M''. To do so, the parameters ''p'' are varied over a range corresponding to the expected variation in actual experiments, the corresponding ''q'' are obtained, and the set of ''(p,q)'' data are stored in a database. This database is then subjected to a statistical analysis in order to recover the inverse of ''M''. This analysis is typically a [[:Wikipedia:Principal Component Analysis|Principal Component Analysis]]. This procedure is also amenable to a rather detailed error analysis, so that errors in the recovered parameters ''p'' for the interpretation of actual data ''q'' can be obtained. | ||
<ref name=RTP>B.Ph. van Milligen, N.J. Lopes Cardozo, ''Function Parametrization: a fast inverse mapping method'', Comp. Phys. Commun. '''66''' (1991) 243</ref> | <ref name=RTP>[http://dx.doi.org/10.1016/0010-4655(91)90073-T B.Ph. van Milligen, N.J. Lopes Cardozo, ''Function Parametrization: a fast inverse mapping method'', Comp. Phys. Commun. '''66''' (1991) 243]</ref> | ||
== Applications == | == Applications == | ||
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== Alternatives == | == Alternatives == | ||
* Neural networks. Like with FP, most of the computational effort is concentrated in an analysis phase (network ''training''), before the actual application to data. Therefore, this method is fast and suited for real-time applications. With FP, non-linear dependencies are limited by the degree of the polynomial expansions used, whereas neural networks allow more general non-linear dependencies, in principle. | |||
* Neural networks. Like with FP, most of the computational effort is concentrated in an analysis phase (network ''training''), before the actual application to data. Therefore, this method is fast and suited for real-time applications. | * [[Bayesian data analysis]], which allows non-Gaussian error distributions and complex data dependencies. A very powerful method but not fast due to the need for maximization (not suited for real-time applications). | ||
== References == | == References == | ||
<references /> | <references /> | ||