Discrimination and Clustering Based on Nonparametric Hypothesis Testing

• Activity Number: 193
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): George von Borries*+ and Haiyan Wang
• Companies: Kansas State University and Kansas State University
• Keywords: High dimension data ; classification and discrimination ; nonparametric hypothesis testing ; support vector machine ; misclassification rate

Abstract

In this paper, we are concerned with the classification and clustering problem in high-dimension, low sample size data. This is an increasingly important topic that can be applied to a range of practical contexts, including gene microarray analysis, chemometrics, and medical image analysis. Classical multivariate methods, which often need to sphere the data by multiplying the root inverse of the covariance matrix, cannot be applied to such cases because there are more parameters than sample sizes. Support vector machine and distance weighted discrimination (Marron and Todd 2002) work well when the dimension is moderately large, but the misclassification rate increases significantly as the dimension increases. Here, we present a classification and clustering method based on nonparametric hypothesis testing developed especially for such a setting. This is an appealing alternative to techniques such as inverse regression as it does not require constant variance or normality. Simulation study will be given to evaluate the performance and an application to a microarray dataset will be illustrated.