Asymptotic properties of multiclass support vector machine under high dimensional settings

Abstract

We proceed with the current comprehension of asymptotic properties of multiclass support vector machine (MSVM) in high-dimensional, low-sample-size (HDLSS) settings. We show that MSVM is biased under HDLSS settings and point out inconsistency problems for MSVM. We propose a bias-corrected MSVM (BC-MSVM) which works well even for HDLSS data set. We give simulation studies and discuss the performance of the BC-MSVM. Finally, we evaluate the performance of the BC-MSVM using microarray data set.

Keywords:

• Discriminant analysis
• HDLSS
• Large d
• Multicategory support vector machine
• Small n

Acknowledgements

I would like to thank two anonymous referees for their constructive comments. I would like to express my sincere gratitude to my supervisor, Professor Makoto Aoshima, for his enthusiastic guidance and helpful support to my research project. I would also like to thank Associate Professor Kazuyoshi Yata for his valuable suggestions. This work was supported by JST SPRING under Grant Number JPMJSP2124.