Functional Robust Support Vector Machines for Sparse and Irregular Longitudinal Data

Abstract

Functional and longitudinal data are becoming more and more common in practice. This article focuses on sparse and irregular longitudinal data with a multicategory response. The predictor consists of sparse and irregular observations, potentially contaminated with measurement errors, on the predictor trajectory. To deal with this type of complicated predictor, we borrow the strength of large-margin classifiers in statistical learning for classification of sparse and irregular longitudinal data. In particular, we propose functional robust truncated-hinge-loss support vector machines to perform multicategory classification with the aid of functional principal component analysis. This article has online supplementary material.

Key Words:

• Classification
• Functional principal component analysis
• Multicategory
• Reproducing kernel Hilbert space
• SVM
• Truncated-hinge-loss SVM

ACKNOWLEDGMENTS

The authors thank Professor Richard A. Levine, the associate editor, and two referees for their constructive comments and suggestions that led to significant improvement of the article. The authors also thank Professor Gareth James for sharing the spinal bone mineral density data. The work is partially supported by NSF Grants DMS-0747575 (Liu), DMS-0905561 (Wu), and DMS-1055210 (Wu), and NIH Grant NIH/NCI R01 CA-149569 (Liu and Wu).