Integrative linear discriminant analysis with guaranteed error rate improvement

• Published in: Biometrika Vol. 105; no. 4; pp. 917 - 930
• Main Authors: LI, QUEFENG, LI, LEXIN
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.12.2018; Oxford Publishing Limited (England)
• Subjects: Alzheimer's disease; Classification; Data analysis; Discriminant analysis; Empirical analysis; Medical imaging; Neuroimaging; Neurology; Outliers (statistics); Integrative analysis; Multi-type data; Linear discriminant analysis; Bayes error; High-dimensional classification; Regularization
• ISSN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asy047

Multiple types of data measured on a common set of subjects arise in many areas. Numerous empirical studies have found that integrative analysis of such data can result in better statistical performance in terms of prediction and feature selection. However, the advantages of integrative analysis have mostly been demonstrated empirically. In the context of two-class classification, we propose an integrative linear discriminant analysis method and establish a theoretical guarantee that it achieves a smaller classification error than running linear discriminant analysis on each data type individually. We address the issues of outliers and missing values, frequently encountered in integrative analysis, and illustrate our method through simulations and a neuroimaging study of Alzheimer’s disease.