DISTANCE AND CLASS SPACE IN THE UNEQ CLASS-MODELING TECHNIQUE

Different estimators of the Mahalanobis distance (such as that based on the Defrise-Gussenhoven correction) are studied and compared with respect to the bias on the distance and the characteristics (sensitivity and specificity) of the class model. Results obtained using estimators with critical values from chi(2)-statistics are compared with those obtained using estimators with critical values from beta-statistics (training set) and Hotelling statistics (evaluation set). Tables are reported for D-statistics (useful for simulating populations of two categories with selectable theoretical sensitivity and specificity) and for critical values of the Mahalanobis distance obtained from beta-statistics. For objects of the training set the estimator of the Mahalanobis distance based on the estimate of the covariance matrix produces models with the optimum sensitivity. The same model has too low a sensitivity for objects of the model category in the evaluation set, but good specificity for objects of outer categories. The estimator with the Defrise-Gussenhoven correction produces enlarged models with too high a sensitivity for objects in the training set, good sensitivity for objects of the model category in the evaluation set and low specificity for objects of outer categories.