# How to devise multicategory classifiers employing linear discriminant functions?

1. We might reduce the problem to $$c$$ two-class problems, where the $$i^{th}$$ problem is solved by a linear discriminant function that separates points assigned to $$w_i$$ from those not assigned to $$w_1$$.

2. A more extravagant approach would be to use $$\frac{c(c-1)}{2}$$ linear discriminants, one for every pair of classes.

For these two methods, I don't understand how they divide the area. If we remove all the lines in Figure 9.3, how should we start?

• What you wrote in (1) and (2) sounds like what is going on in that picture. So if you understand those, then you understand the ideas. Or is it that you're trying to understand what those two points are saying? Also, shere did that figure come from? Feb 20 '20 at 1:45
• The figure is from Chapter 9 Linear Discriminant Functions. At the beginning, we are given 4 regions. Without the lines done in the figure, I want to know how we should start to divide. Feb 20 '20 at 2:30