Xi

FIGURE 7.3-2 The ADALINE's decision boundaries used to separate the ¬ęs from the os.

Three-layer ANNs with multiple output neurons can be made from ADALINES. The w3 weights of the output layer can be optimized or trained by use of the Widrow-Hoff LMS algorithm, described below. A back-propagation algorithm is generally required to train the w2 and Wj weights of the hidden layers (Widrow and Winter, 1988).

The LMS training algorithm for a single MADALINE adjusts w to minimize the mean squared error (MSE) of the classifier. The MSE can be written in matrix notation (Hecht-Nielsen, 1990):

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