ssify the objects under examination as containing or not containing explosives is referred to as standard decision analysis. The basic technique used in standard decision analysis is linear discriminant analysis. In linear discriminant analysis, a discriminant value is computed by a linear combination of the values of a set of features measured for a piece of luggage. If the discriminant value is greater than some prescribed threshold, e.g., zero, the piece of luggage is classified as containing a threat; otherwise, the piece of luggage is cleared.
Geometrically, the features are axes which define the classification hyperspace. The measurement of any particular piece of luggage (e.g., suitcase) is plotted as a point in this space. The points for suitcases without threats cluster separately from those with threats. The hyperplane that best separates the two clusters may be viewed as a dividing surface that results from the linear discriminant function. In fact, the computed discriminant value is just the normal distance of the hyperplane from the point which represents the piece of luggage, with the sign (positive or negative) representing which "side" of the hyperplane the point is on. Quadratic or other functional forms may be used for the discriminant, which will result in dividing surfaces which are something other than planes.
Application of the usual least squares technique to the classification problem results in the dividing hyperplane being perpendicular to the line that joins the centers of the two clusters. This plane is also halfway between the two centers, if the distance is measured after normalization by the covariance matrix. Any overlap between the two clusters determines the possible tradeoff between detection and false alarm rates. By moving the dividing hyperplane along the line joining the two centers (which is equivalent to changing the threshold the discriminant value must exceed) this tradeoff can be set to any level, from zero false alarm rate (and a low detection rate) to 100% detection and 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 in