Noncrossing Ordinal Classification
This work addresses a specific issue in ordinal data classification for applications where class order matters, representing an incremental improvement over existing pooling frameworks.
The paper tackles the problem of ambiguous class predictions in ordinal classification due to boundary crossing by proposing a noncrossing ordinal classification method that imposes constraints to eliminate this issue, showing improved classification performance for ordinal data in simulated and real examples.
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.