# Hamming Networks

** Introduction:-**The Hamming network performs the task of pattern association, or classification, based on measuring the

Hamming distance. The network is apattern associate of n-dimensional binary vectors labeled with m-class labels (m-class patterns).

A new vector x' is associated with class pattern xi with the minimum Hamming distance, a Hamming distance being the number of different bits in the two patterns. The Hamming network is similar to the Hopfield network, but it has two layers of connections. The first layer contains connections between all the n inputs, and all the m outputs. The second layer is a fully connected recurrent network with m neurons (similar to the Hopfield network). All nodes use linear threshold activation functions. The first layer of connections is finding the difference between the number n and the Hamming distance between the input pattern x' and each of the m-class patterns used to calculate the connection weights in advance.

The second layer of connections is calculating the maximum of these values for finding the best matched- class pattern.

Using a Hamming network has several advantages: it requires fewer connections than the Hopfield network, and it implements the "optimum minimum error classifier when bit errors are random and independent”, that is, the network always converges and finds the output node with the maximum value.