On the Consistency of Multiclass Classification Methods

Ambuj Tewari, Peter L. Bartlett.

Year: 2007, Volume: 8, Issue: 36, Pages: 1007−1025


Binary classification is a well studied special case of the classification problem. Statistical properties of binary classifiers, such as consistency, have been investigated in a variety of settings. Binary classification methods can be generalized in many ways to handle multiple classes. It turns out that one can lose consistency in generalizing a binary classification method to deal with multiple classes. We study a rich family of multiclass methods and provide a necessary and sufficient condition for their consistency. We illustrate our approach by applying it to some multiclass methods proposed in the literature.