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SECOND INTERNATIONAL
SYMPOSIUM ON

IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

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Cornell University

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Ithaca, NY, USA

26 - 29 June 2001

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ELECTRONIC PROCEEDINGS

## Philippe Nivlet, Frederique Fournier, Jean-Jacques Royer

# Interval Discriminant Analysis: An Efficient Method to Integrate Errors In Supervised Pattern Recognition

### Abstract

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

** Format. **PDF

**Paper Download **

The paper is availabe in the following sites:

** 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: **

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