hus helpful in many instances to define a set of "features" with different amounts of noise resistance that still provide helpful and adequate spatial information. A "feature" may thus be any combination of detector signals in the detector array. Some of the features may be simple; others may be complicated (such as the reconstructed three-dimensional nitrogen density distribution), and may require imaging techniques. A set of features can be defined by: (1) calculating or estimating certain anticipated features that would normally be present for a set of typical objects (e.g., pieces of luggage) containing explosives; (2) developing calibration techniques using different sets of these features; and (3) testing the performance of the calibration techniques on a test set of data.
Experiments have shown that the variance for any feature is roughly the same for objects with explosives as it is for objects without explosives, even though, of course, the values of the feature may differ between the two classes of objects. It is also true that the distribution of "bombness" (i.e., the likelihood of explosive materials being present) in objects, such as suitcases, is decidedly non-normal. Most suitcases, for example, contain little nitrogen, and are thus quite easy to classify as non-threatening (containing no explosives). However, a significant percentage of the pieces of luggage encountered in airports and similar locations contain sufficient nitrogen and other interfering materials to falsely alarm the detection system, absent some further classification criteria. The distribution of "bombness" thus follows (roughly) the distribution of nitrogen, that is, with most pieces of luggage occurring at low levels of threat but with an extensive tail to the distribution. The addition of a simulated threat shifts the distribution without distorting its shape. This results in the variance for any feature being the same for objects with and without threats, as stated above.
The first (and more conventional) approach used to classify 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 a