to several different groups or subsets. A calibration may then be performed on all but one group of subset, and then tested on this last subset. Each subset in turn is then used as the test subset in a manner similar to that used in jackknife analysis. The difference between the performance of the calibration on itself and on the test subset provides a measure of robustness. A large difference indicates poor robustness. The number of classification groups and features in each group may then be chosen and adjusted as required until the calibration becomes robust.
An (ANS) may be described as a collection of simple processors (neurons) that are connected in a massively parallel network. In one embodiment of an ANS, each neuron accepts inputs from several others with a different weight applied to each link. If the sum of the weighted inputs exceeds some present value, the neuron "fires" and sends its output signal to other neurons. Some neurons (the input layer) connect directly to the available inputs to the ANS. Other neurons (the output layer) connect to the desired output signal (which, in the case of an explosive detection system, comprise output signals ranging from "no threat" to "must be a threat"). Training or calibration objects are presented in the form of the input signals corresponding to a desired output, and the weights in the network are adjusted according to a learning rule until the network predicts the correct desired output. The weights are then frozen, and the trained ANS is then used on a test set of data to identify threats. Advantageously, the training step requires no operator intervention once the data is assembled; the network is simply allowed to iterate to a solution. If the proper network architecture has been established, the ANS can be trained with far less operator involvement than with the discriminant analysis approach described above.
It is seen that an ANS is simply one form of a parallel distributed network (PDN) made up of processing elements (PE's) that are interconnected via information channels called interconnects. Where these PE's perform a simple function, such as "on" if the weighted inputs thereto exceed a prescribed threshold, and "off" if not, these PE's may be referred to as "neurons." Each PE or neuron may have multiple input signals, but typically only one output signal (although this output signal may be connected to several different locations within the ANS). The PE's are arranged in several different layers. A first or input layer of PE's is generally characterized by each PE having an input that comprises one of the input signals to the PDN. An output layer of PE's is characterized by each PE providing one of the output signals of the PDN. The output signals from each PE in the input layer comprise the input signals to the PE's of other layers, either in a feedforward or feedback interconnect, and these interconnections, as indicated, may be weighted by an appropriate factor. For simple PDN applications, two layers of PE's may be sufficient, in which case the PDN comprises only an input layer and an output layer. For more complex applications, one or more hidden layers of PE's may be required intermediate the input and output layers. The complexity of the PDN is largely governed by the number of layers of PE's. The general structure of a three-layer PDN or ANS, for example, is illustrated in FIG. 6. This particular three-layer ANS is further discussed below.
Parallel distributed networks are described in the art. See, e.g., Rumelhart, et al., Parallel Distributed Processing, Vol. I (MIT Press, 1986). In general terms, such systems are characterized as including: (1) a set of processing units or elements; (2) a state of activation (i.e., the current state of the element); (3) an output function for each element (i.e., a function that defines the output signal as some function of the input signals); (4) a pattern of connectivity among the processing elements; (5) a propagation rule for propagating patterns of activities (signals) through the pattern of connectivities; (