Linear Dimension Reduction for Multiple Heteroscedastic Multivariate Normal Populations

• 作者: Dean M. Young Johanna S. van Zyl Phil D. Young Songthip T. Ounpraseuth Tyler W. Nelson
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: Linear TRANSFORMATION BAYES Classification FEATURE Extraction PROBABILITY of MISCLASSIFICATION
• 年，卷（期）: 2015,（4）
• 页码范围: 311-333
• 页数: 23页
• 分类号: O1

摘要

For the case where all multivariate normal parameters are known, we derive a new linear dimension reduction (LDR) method to determine a low-dimensional subspace that preserves or nearly preserves the original feature-space separation of the individual populations and the Bayes probability of misclassification. We also give necessary and sufficient conditions which provide the smallest reduced dimension that essentially retains the Bayes probability of misclassification from the original full-dimensional space in the reduced space. Moreover, our new LDR procedure requires no computationally expensive optimization procedure. Finally, for the case where parameters are unknown, we devise a LDR method based on our new theorem and compare our LDR method with three competing LDR methods using Monte Carlo simulations and a parametric bootstrap based on real data.