7.1. Introduction

In supervised training, training patterns are provided in input/teacher pairs, [X, T] = {[x⁽¹⁾, t⁽¹⁾], [x⁽²⁾, t⁽²⁾],..., [x^(N), t^(N)]}. In a decision-based network, the teacher's values are exclusively the class membership or class symbols, as opposed to any quantitative or numeric values. Consequently, in training a decision-based neural network (DBNN), the teachers do not know (and need not know) the network's exact quantitative output values. More precisely, a decision-based network receives instruction from the teacher on the correct or preferred decision and performs the training process accordingly. This chapter introduces the (supervised) decision-based learning rule and shows how such a learning rule may be combined with the (unsupervised) EM clustering for training hierarchical networks. The results are several variants of the basic and probabilistic decision-based neural networks (PDBNNs) that show promise for biometric authentication.