Bidirectional discrimination with application to data visualization

• 成果类型: Article
• 署名作者: Huang, Hanwen; Liu, Yufeng; Marron, J. S.
• 署名单位: University of Texas System; University of Texas Health Science Center Houston; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass029
• 发表日期: 2012
• 页码: 851864
• 关键词: high-dimension; geometric representation

摘要

Linear classifiers are very popular, but can have limitations when classes have distinct subpopulations. General nonlinear kernel classifiers are very flexible, but do not give clear interpretations and may not be efficient in high dimensions. We propose the bidirectional discrimination classification method, which generalizes linear classifiers to two or more hyperplanes. This new family of classification methods gives much of the flexibility of a general nonlinear classifier while maintaining the interpretability, and much of the parsimony, of linear classifiers. They provide a new visualization tool for high-dimensional, low-sample-size data. Although the idea is generally applicable, we focus on the generalization of the support vector machine and distance-weighted discrimination methods. The performance and usefulness of the proposed method are assessed using asymptotics and demonstrated through analysis of simulated and real data. Our method leads to better classification performance in high-dimensional situations where subclusters are present in the data.