The set logical variables forms stack topped

the current input presentation. When no more resets occur, resonance is said to have occurred, and the input has finally been assigned a class. The ART-1 classification algorithm can be summarized as one that solves the combinatorial optimization problem stated as follows:

maximize| I ∧ T∝ | / (β + | T∝ | )
w.r.t. ∝

which leads to the template property expressed in equation (1). When a class is first established, all connection-weight values in its template are 1s. Many of these are changed to 0s via the learning process as the network assigns input patterns to the class.

The next subsection presents a preprocessing network that converts a single real-valued input into a multicomponent pattern containing binary-valued components. The resulting coded pattern is well suited for the processing of an ART-1 network.

not true of the usual binary-coded-decimal format used in digital computers, in which 0 and 1 are coefficients of powers of 2. The codings used here are referred to as stack numerals and are similar to “thermometer codes” where a real number is mapped into an interval defined by real-valued minimum and maximum values. This interval is quantized into m subintervals, one of which contains the real input value. Associated with each subinterval is a logical variable. The stack numeral is constructed by setting all of the logical variables for subintervals less than or equal to the one containing the real-valued input to TRUE (or 1) and those above to FALSE or UNCERTAIN (0). If the interval is thought of as being a vertical structure, the set of logical variables forms a stack of 1s topped by 0s, totaling m components high. The precision of representation is set by the choice of the max, min, and m stack parameters and can be easily matched to the accuracy of a measured input value.

Figure 1. (a) A simple example of a neural implementation of a stack numeral. The complement stack has a different connectivity. (b) The activation function

for the stack units with threshold δ.