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 | |
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 Polish | W 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. |
DOI | DOI:10.1007/978-3-319-45378-1_7 |
URL | http://link.springer.com/chapter/10.1007%2F978-3-319-45378-1_7 |
Language | en angielski |
Score (nominal) | 15 |
Score | = 15.0, 04-09-2019, BookChapterSeriesAndMatConfByConferenceseries = 15.0, 04-09-2019, BookChapterSeriesAndMatConfByConferenceseries |
Publication indicators | = 0; = 0 |
Citation count* |
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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