Search results for "moments of Order Statistics"

showing 3 items of 3 documents

The fundamental theory of optimal "Anti-Bayesian" parametric pattern classification using order statistics criteria

2013

Author's version of an article in the journal: Pattern Recognition. Also available from the publisher at: http://dx.doi.org/10.1016/j.patcog.2012.07.004 The gold standard for a classifier is the condition of optimality attained by the Bayesian classifier. Within a Bayesian paradigm, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal Bayesian strategy would be to achieve this based on the (Mahalanobis) distance from the corresponding means. The reader should observe that, in this context, the mean, in one sense, is the most central point in the respective distribution. In this paper, we shall show that we can obtain opti…

Mahalanobis distanceVDP::Mathematics and natural science: 400::Mathematics: 410::Statistics: 412Feature vectorOrder statisticBayesian probabilityclassification by moments of order statistics020206 networking & telecommunicationsVDP::Technology: 500::Information and communication technology: 55002 engineering and technologyprototype reduction schemesNaive Bayes classifierBayes' theoremExponential familypattern classificationorder statisticsArtificial IntelligenceSignal Processing0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingComputer Vision and Pattern RecognitionAlgorithmSoftwarereduction of training patternsMathematicsParametric statistics
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“Anti-Bayesian” parametric pattern classification using order statistics criteria for some members of the exponential family

2013

This paper submits a comprehensive report of the use of order statistics (OS) for parametric pattern recognition (PR) for various distributions within the exponential family. Although the field of parametric PR has been thoroughly studied for over five decades, the use of the OS of the distributions to achieve this has not been reported. The pioneering work on using OS for classification was presented earlier for the uniform distribution and for some members of the exponential family, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean. A…

Uniform distribution (continuous)classification by moments of order statisticsBayesian probabilityOrder statisticNonparametric statisticsVDP::Technology: 500::Information and communication technology: 550020206 networking & telecommunications02 engineering and technologyprototype reduction schemesBayes' theorempattern classificationVDP::Mathematics and natural science: 400::Information and communication science: 420Exponential familyArtificial IntelligenceSignal Processing0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingComputer Vision and Pattern RecognitionBeta distributionAlgorithmSoftwareMathematicsParametric statisticsPattern Recognition
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Optimal “anti-Bayesian” parametric pattern classification for the exponential family using Order Statistics criteria

2012

Published version of a chapter in the book: Image Analysis and Recognition. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-31295-3_2 This paper reports some pioneering results in which optimal parametric classification is achieved in a counter-intuitive manner, quite opposed to the Bayesian paradigm. The paper, which builds on the results of [1], demonstrates (with both theoretical and experimental results) how this can be done for some distributions within the exponential family. To be more specific, within a Bayesian paradigm, if we are allowed to compare the testing sample with only a single point in the feature space from each class, the optimal Bayesian strat…

VDP::Mathematics and natural science: 400::Information and communication science: 420::Knowledge based systems: 425classification using Order Statisticsmoments of Order Statistics
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