Bounds on the Bayes classification error based on pairwise riskfunctions
Garber, F.D.
Djouadi, A.
Dept. of Electr. Eng., Ohio State Univ., Columbus, OH;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Mar 1988
Volume: 10,
Issue: 2
On page(s): 281-288
ISSN: 0162-8828
References Cited: 17
CODEN: ITPIDJ
INSPEC Accession Number: 3144004
Digital Object Identifier: 10.1109/34.3891
Current Version Published: 2002-08-06
Abstract
Upper and lower bounds on the Bayes risk for multiple,
composite-hypothesis classification are obtained. Bounds on the Bayes
risk for M simple classes are derived in terms of the risk
functions for (M-1) classes, and so on, until the desired
result depends only on the pairwise (M=2) Bayes risks. A method
of computing upper and lower bounds on the pairwise Bayes risk for
composite classes is developed. Algorithms for computing the upper and
lower bounds for the general M-class case and for
composite-hypothesis classes are presented. Numerical examples of the
application of the bounding techniques to a problem involving the
classification of aircraft are discussed. Results for the bounds and
other performance measures are compared for the most interesting cases
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