Propagation (BP) is used as the paradigm of learning for the system. BP is based on the generalized delta rule, mentioned above, and is well documented in the art. Essentially, this rule is a steepest descent method of computing the interconnection weights between neurons of the ANS that minimizes the total squared output error over a set of training vectors. Evaluation of the effectiveness of the ANS network may be judged by simply observing the residual error (as the network can be expected to make errors and have false positives), and/or by simply measuring the PD and PFA rates for a test set of objects.
A performance comparison between an explosive detection system using the discriminant analysis approach and one using an ANS trained by the BP technique is depicted in FIG. 9. The performance of both techniques is evaluated on a test set of objects that is different from the training set. Since the outputs of both techniques produce gray scale values, different thresholds can be applied to get different performance points on the PD PFA tradeoff curve. Each curve in FIG. 9 was generated by changing the thresholds for the decision over the applicable range.
FIG. 9 clearly shows that the ANS approach performs better than the discriminant analysis approach for false alarm rates greater than 1.75%. For example, at the operating point of 95% detection (which is a typical operating point for a viable explosive detection system), the ANS reduces the false alarm rate by around 1.5-2.0%. Advantageously, for an explosive detection system having a high throughput of objects, this results in substantially fewer objects having to be scanned or checked by secondary techniques. At slightly higher detection rates, e.g., 96%, the ANS reduces the difference between the PFA rates still further (even though the value of the PFA goes up for both approaches).
One advantage offered by the BP-trained ANS network over the discriminant analysis approach is that ANS takes relatively less human supervision. As noted above, calibration of the discriminant analysis may require several days of statistical analysis. With the BP technique, only a few hours of set up time are required by a computer literate person, and a day or two of computer time (to train the system).
As seen in FIG. 9, the performance of the ANS network at low false alarm rates (less than 1.75%) is substantially lower than for the discriminant analysis technique. This is believed to be caused by the particular activation function used in the ANS network. (The activation function is that function which defines the relationship between the output of a particular neuron and its input(s).) The sigmoid function was used, and this function is very steep in the middle (i.e., at net input values close to zero). Consequently, most of the output activation values tend to cluster around -0.5 and +0.5. Inevitably, there will be a few non-threatening objects that have similar characteristics to threatening objects. In these instances, the non-threatening objects will also have a value close to +0.5. In order to remove these objects, the threshold would need to be adjusted close to +0.5. However, doing so would cause the detection rate to drop rapidly. Hence, it is believed that a better solution to this problem (of low performance at low PFA rates) is to use a smoother activation function.
The ANS portion of the present invention may be implemented through custom software and/or hardware installed in or coupled to the computer 116 (FIG. 1) or the computer 58 (FIG. 4), hereafter the "host" computer. One implementation, for example, includes an array processor network, or "card", that is installed in or coupled to the host computer. A suitable array processor network that can perform this function is described in U.S. patent application Ser. No. 07/191,207, filed 05/06/88, (assigned to the same assignee as is this application), which patent application is incorporated herein by reference. The advantage of using an array processor of the type described in the referenced patent application is that 