# SVM Three Way Classification

I would like to verify the following methodology for using SVMs for three way classification. That is, the response $Y$ can be either $\{-1, 0, 1\}$:

First train an SVM to distinguish between $\{-1,1\}$ and $\{0\}$. Then train an SVM to distinguish between $\{-1,1\}$. For each instance $X$, first use the first SVM, and if it is not $\{0\}$, classify it using the second SVM.

My main questions are:

1. Whether this type of thing is common
2. Whether I can possibly get better results by using other combinations, e.g., first distinguishing between $\{-1, 0\}$ and then $\{0, 1\}$?

The most common approach is one-vs-all classification, which involves making $n$ models for $n$ classes. In your case that would be 1 vs (0, 1), 0 vs (-1, 1) and -1 vs (0, 1). Another common approach is all-vs-all, which requires $n(n-1)$ models and is hence more computationally demanding.