NDLI: Using 2-Interactive Measures in Nonlinear Classifications

Content Provider	IEEE Xplore Digital Library
Author	Yan Wu Zhenyuan Wang
Copyright Year	2007
Abstract	Within the classification algorithms based on signed fuzzy measures, an obvious limitation is the complexity of the algorithms due to the large number of interactions among attributes. For a data set with n attributes, the complexity of classification algorithm would be O $(2^{n}).$ But in the practical problems, the higher-order interactions among attributes are often not significant enough to the classification. So sometimes omitting them just sacrifices the accuracy a little but will save a lot of time and energy. Hence, a 2-interactive measure may be used to reduce the calculation complexity into O $(n^{2}).$ In this study, the Mobius Transformation and its reverse - Zeta Transformation are used to calculate the 2-interactions among attributes for the records. A comprehensive discussion on the semantic and geometric meanings of the parameters is given. The weighted Choquet integral with respect to a signed fuzzy measure serves as an aggregation tool to project the feature space onto a real axis to make the classification simple. To implement the classification, we need to determine the values of the signed fuzzy measure and the other parameters. This can be done by running an adaptive genetic algorithm based on a given training data set. The new classifier is tested by recovering the preset parameters from a set of artificial training data generated from these parameters.
Starting Page	348
Ending Page	353
File Size	431316
Page Count	6
File Format	PDF
ISBN	1424412137
DOI	10.1109/NAFIPS.2007.383863
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-06-24
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Genetic algorithms Training data Educational institutions Classification algorithms Testing Fuzzy sets Information science Mathematics Art Weight measurement M bius transformation 2-interactive fuzzy measures Choquet integrals Genetic Algorithm
Content Type	Text
Resource Type	Article

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