Detection of Common-Variance Subspace and Its Application to Classification

• Activity Number: 22 - Testing and Evaluation of High-Dimensional Models
• Type: Topic Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jiae Kim* and Steve MacEachern
• Companies: The Ohio State University and The Ohio State University
• Keywords: LDA; QDA; classification; linear classifier

Abstract

Fisher’s linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) are traditional methods for classification. LDA assumes the same variance-covariance matrices for each class and results in one-dimensional linear classifier. QDA doesn’t require the assumption and produces a quadratic classifier. We introduce a new classifier. We first find linear subspaces with the same variance-covariance and then detect a subspace which is the “most” efficient for classification. Resulting linear subspace can be multidimensional. We present technical details, some of which are how to transform the data, a sequential algorithm that finds the linear subspaces of the same variance-covariance and how to make a use of the efficient subspace for classification. The performance of the new classifiers is compared with state-of-art classifiers on simulated and real data.