Statistics and Its Interface

Volume 10 (2017)

Number 2

Noncrossing ordinal classification

Pages: 187 – 198



Xingye Qiao (Department of Mathematical Sciences, Binghamton University, State University of New York, Binghamton, N.Y., U.S.A.)


Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the results from binary classifiers together. An inherent difficulty of this framework is that the class prediction can be ambiguous due to boundary crossing. To fix this issue, we propose a noncrossing ordinal classification method which materializes the framework by imposing noncrossing constraints. An asymptotic study of the proposed method is conducted. We show by simulated and data examples that the proposed method can improve the classification performance for ordinal data without the ambiguity caused by boundary crossings.


classification, mixed integer programming, multivariate analysis, statistical computing, support vector machine

Published 31 October 2016