%0 Conference Proceedings
%T Mapping Points Back from the Concept Space with Minimum Mean Squared Error
%+ University of Bialystok
%+ Warsaw University of Technology [Warsaw]
%A Homenda, Wladyslaw
%A Penza, Tomasz
%Z Part 2: Rough Set Methods for Big Data Analytics
%< avec comité de lecture
%( Lecture Notes in Computer Science
%B 15th IFIP International Conference on Computer Information Systems and Industrial Management (CISIM)
%C Vilnius, Lithuania
%Y Khalid Saeed
%Y Władysław Homenda
%I Springer International Publishing
%3 Computer Information Systems and Industrial Management
%V LNCS-9842
%P 67-78
%8 2016-09-14
%D 2016
%R 10.1007/978-3-319-45378-1_7
%Z Computer Science [cs]
%Z Humanities and Social Sciences/Library and information sciencesConference papers
%X 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.
%G English
%Z TC 8
%2 https://inria.hal.science/hal-01637496/document
%2 https://inria.hal.science/hal-01637496/file/419526_1_En_7_Chapter.pdf
%L hal-01637496
%U https://inria.hal.science/hal-01637496
%~ SHS
%~ IFIP-LNCS
%~ IFIP
%~ IFIP-TC
%~ IFIP-TC8
%~ IFIP-CISIM
%~ IFIP-LNCS-9842