nd a commensurately higher false alarm rate. In addition, the value of the discriminant implies a "sureness" for the decision. This value may be used in some kind of Bayesian analysis or may simply map onto the tradeoff curve as the PD/PFA point that would result if the threshold were set at that value.
Unfortunately, in practice, the development of the discriminant is a complicated problem. First, a classification of the detector data set must be made so that pieces of luggage which result in similar instrument responses are grouped together. For example, large heavy suitcases are analyzed as one group. Next, the set of features to be used in each group must be chosen. The computation of the discriminant coefficient is relatively straightforward once the features are chosen. A variety of computer programs are commercially available for performing this computation. Some adjustments must be made to improve performance by allowing some regions of the decision space to have special decisions made. These are situations where a "by hand" technique takes advantage of the fact that the distribution of the objects under investigation is non-normal. Finally, the resulting calibration is tested on a set of data not used in the calibration and, eventually, on-line during the supervised tests. Experience using this technique has revealed that a separate calibration must usually be developed for the bulk and sheet explosives due to their different measured response in the system. Unfortunately, a significant amount of time, e.g., several days of statistical analysis, is typically required in order to correctly perform this discriminant development and calibration.
It is preferred that the robustness of this calibration procedure be tested, and that based on such test, adjustments be made as required in order to provide a robust calibration. Testing robustness may be performed by taking a large data set (obtained from passing a large number of pieces of luggage through a detection system as herein described) and breaking it into 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 