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Biplots of fuzzy coded data
- Source :
- Fuzzy Sets and Systems. 183:57-71
- Publication Year :
- 2011
- Publisher :
- Elsevier BV, 2011.
-
Abstract
- WOS: 000295444200004<br />A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure-of-fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data<br />BBVA Foundation; Ministry of Science and Innovation [MTM2008-00642, MTM2009-09063]<br />The second author thanks the BBVA Foundation for financial support in this research, as well as the Ministry of Science and Innovation Grants MTM2008-00642 and MTM2009-09063. The reports of two referees on the first version of this paper led to significant improvements and are hereby acknowledged with thanks.
- Subjects :
- Multivariate statistics
Biplot
Logic
Multiple Correspondence Analysis
Defuzzification
jel:C88
computer.software_genre
Fuzzy logic
Correspondence analysis
Fuzzy Coding
Artificial Intelligence
Multiple correspondence analysis
Singular value decomposition
Multivariate Data
Indicator Matrix
Mathematics
Principal Component Analysis
defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis
business.industry
Pattern recognition
jel:C19
Measure-Of-Fit
Principal component analysis
Data mining
Artificial intelligence
business
computer
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 183
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi.dedup.....43dc3c121c191836570de00d65ce7edf