Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition

276 Supervised Classification Part 1

classifiers have two disadvantages. They are designed for two-class problems

and their outputs, unlike feed-forward neural networks, do not model posterior

class membership probabilities in a natural way.

A common way to overcome the two-class restriction is to determine all

possible two-class results and then use a voting scheme to decide on the class

label (Wu et al., 2004). That is, for K c lasses, we train K(K − 1)/2 SVM’s

on each of the po ssible pairs (i, j) ∈ K ⊗ K. For a new observation g and the

SVM for (i, j), let

µ

ij

(g) = Pr(ℓ = i | ℓ = i or j, g) =

Pr(ℓ = i | g)

Pr(ℓ = i or j | g)

. (6.73)

The last equality ...