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Distance and class space in the UNEQ class‐modeling technique
Author(s) -
Forina M.,
Lanteri S.,
Sarabia L.
Publication year - 1995
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180090202
Subject(s) - mahalanobis distance , mathematics , estimator , sensitivity (control systems) , statistics , covariance , set (abstract data type) , class (philosophy) , pattern recognition (psychology) , artificial intelligence , computer science , electronic engineering , engineering , programming language
Abstract 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 χ 2 ‐statistics are compared with those obtained using estimators with critical values from β‐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 β‐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.