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Sufficient Statistics for Divergence and the Probability of MisclassificationOne particular aspect is considered of the feature selection problem which results from the transformation x=Bz, where B is a k by n matrix of rank k and k is or = to n. It is shown that in general, such a transformation results in a loss of information. In terms of the divergence, this is equivalent to the fact that the average divergence computed using the variable x is less than or equal to the average divergence computed using the variable z. A loss of information in terms of the probability of misclassification is shown to be equivalent to the fact that the probability of misclassification computed using variable x is greater than or equal to the probability of misclassification computed using variable z. First, the necessary facts relating k-dimensional and n-dimensional integrals are derived. Then the mentioned results about the divergence and probability of misclassification are derived. Finally it is shown that if no information is lost (in x = Bz) as measured by the divergence, then no information is lost as measured by the probability of misclassification.
Document ID
19730020848
Acquisition Source
Legacy CDMS
Document Type
Other
Authors
Quirein, J.
(Houston Univ. TX, United States)
Date Acquired
August 7, 2013
Publication Date
November 1, 1972
Publication Information
Publication: Varied Statist. Probl. and Test, Vol. 2 28
Subject Category
Mathematics
Report/Patent Number
REPT-14
Accession Number
73N29580
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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