In a statistical pattern recognition context, probabilistic algorithms like -par ametric or nonparametric- discriminant analysis are designed to classify, when p ossible, objects into predefined classes. Because these methods require precise input data, they cannot propagate uncertainties in the classifying process. In r eal case studies, this could lead to drastic misinterpretations of objects. We h ave thus developed an extension of these methods to directly propagate imprecise interval-form data. The computations are based on interval arithmetic, which ap pears to be an efficient tool to handle intervals. They consist in calculating s uccessively interval conditional probability density functions and interval post erior probabilities, whose definitions are closely associated with the imprecise probability theory. The algorithms eventually assign any object to a subset of classes, consistent with the data and its uncertainties. The resulting classifyi ng model is thus less precise, but much more realistic than the standard one. Th e efficiency of this algorithm is tested on a synthetic case study.
Keywords. Discriminant Analysis, Interval Arithmetic, Imprecise Probabilities
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Authors addresses:
Philippe Nivlet
1-4, avenue de Bois Préau
92852 RUEIL-MALMAISON Cedex
FRANCE
Frederique Fournier
1-4, avenue de Bois Préau
92852 RUEIL-MALMAISON Cedex
FRANCE
Jean-Jacques Royer
rue du Doyen Marcel Roubault
BP 40
54501 VANDOEUVRE-LES-NANCY
FRANCE
E-mail addresses:
| Philippe Nivlet | philippe.nivlet@ifp.fr |
| Frederique Fournier | frederique.fournier@ifp.fr |
| Jean-Jacques Royer | Jean-Jacques.Royer@ensg.inpl-nancy.fr |