Mapping Points Back from the Concept Space with Minimum Mean Squared Error

Władysław Homenda , Tomasz Penza

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 w of concept space, we give explicitly a set of points in feature space that are mapped onto 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.
Author Władysław Homenda ZSMPW
Władysław Homenda,,
- Department of Structural Methods for Knowledge Processing
, Tomasz Penza WMiNI
Tomasz Penza,,
- Faculty of Mathematics and Information Science
Book Saeed Khalid, Homenda Władysław (eds.): Computer Information Systems and Industrial Management, Lecture Notes In Computer Science, vol. 9842, 2016, SPRINGER INT PUBLISHING AG, ISBN 978-3-319-45377-4
Abstract in PolishW pracy rozważane jest odwzorowanie odwrotne do odwzorowania z przestrzeni cech do przestrzeni pojęć. Konstrukcja odwzorowania z przestrzeni cech do przestrzeni pojęć jest oparta o metodę grupowania rozmytego “fuzzy c-means”. Odwzorowanie odwrotne jest konstruowane na podstawie znanej gęstości prawdopodobieństwa w przestrzeni cech.
DOIDOI:10.1007/978-3-319-45378-1_7
URL http://link.springer.com/chapter/10.1007%2F978-3-319-45378-1_7
Languageen angielski
Score (nominal)15
ScoreMinisterial score [Punktacja MNiSW] = 15.0, 26-06-2017, BookChapterSeriesAndMatConf
Ministerial score (2013-2016) [Punktacja MNiSW (2013-2016)] = 15.0, 26-06-2017, BookChapterSeriesAndMatConf
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