MATHEMATICS COLLOQUIUM

 WHEN:
On Thursday, October 11, 2001 at 2.30PM

WHERE:
Durham Science Center, Room 255

WHAT:

Zhenyuan Wang

University of Nebraska at Omaha

will give a talk on

Part II: Classification by Nonlinear Integral Projection Pursuit

Abstract:
A new classifier based on the nonlinear integral projection is presented. The contribution rate of each combination of the feature attributes, including each singleton, toward the classification is represented by a nonadditive measure whose values are regarded as a part of unknown parameters. Its nonadditivity reflects the interaction among the feature attributes toward the classifying attribute. For classification, the weighted Choquet integral with respect to the nonadditive measure serves as an aggregation tool to project the feature space optimally onto a real axis according to an error criterion, and the classifying attribute may be properly numericalized on the axis simultaneously such that it is easy to be classified. Based on given training data consisting of the records of feature attributes and the corresponding records of the classifying attribute, an adaptive genetic algorithm is used to search the values of unknown parameters optimally. This new classifier is tested by recovering the preset parameters from a set of artificial data constructed by these parameters. It also has a good performance on real-world data sets. Beyond discriminating classes, this method can also mine information on the scaling requirement and respective importance of the feature attributes as well as the relationships among them. A comprehensive discussion on the semantic and geometric meaning of the parameters involved in this model is given, and it can be used for short-listing important feature attributes to reduce the complexity (dimension) of the classification problem. This new method also compares favorably with other methods on some well-known real-world data.