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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Mapping Points Back from the Concept Space with Minimum Mean Squared Error
verfasst von : Wladyslaw Homenda, Tomasz Penza
Erschienen in: Computer Information Systems and Industrial Management
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Abstract
In this article we present a method to map points from the concept space, associated with the fuzzy c–means algorithm, back to the feature space. We assume that we have a probability density function f defined on the feature space (e.g. a normalized density of a data set). For a given point \(\varvec{w}\) of concept space, we give explicitly a set of points in feature space that are mapped onto \(\varvec{w}\) and we give a formula for a reverse mapping to the feature space which results in minimum mean squared error, with respect to density f, of the operation of mapping a point of feature space into the concept space and back. We characterize the circumstances under which points can be mapped back into the feature space unambiguously and provide a formula for the inverse mapping.