Graph-Based Sparse Linear Discriminant Analysis for High-Dimensional Classification

• Activity Number: 219 - SLDS 2017 Student Paper Awards Session
• Type: Topic Contributed
• Date/Time: Monday, July 31, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Jianyu Liu* and Guan Yu and Yufeng Liu
• Companies: University of North Carolina at Chapel Hill and State University of New York at Buffalo and University of North Carolina
• Keywords: linear discriminant analysis ; graph ; classification ; unlabeled data

Abstract

Linear discriminant analysis (LDA) is a classic classification technique with great success in practice. Despite its effectiveness in low dimensional problems, extensions for LDA are necessary to classify high dimensional data. Although there exist several LDA extensions in the literature, most do not fully incorporate the structure information of predictors when it is available. In this paper, we introduce a new high dimensional LDA method (GSLDA) that utilizes the graph structure among features. The graph structure could be either given or estimated from the training data. Moreover, we explore the relationship between within-class feature structure and overall feature structure. Based on the relationship, we propose a variant of our method, which can effectively utilize unlabeled data. The new methods are shown to yield more accurate and interpretable classifiers than many existing methods. Some theoretical results are used to further justify the methods.