Confliction of the Convexity and Metric Properties in f-Divergences(<Special Section>Information Theory and Its Applications)
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概要
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We prove that the Variational distance (and its positive multiples) is the only f-divergence that satisfies both the identity of indiscernibles and the triangle inequality. Therefore it is the unique f-divergence which serves as a metric. This point is interpreted as a fundamental confliction of the convexity for f(x) with the metric properties for its associated f-divergence. Therefore, we relax the convexity of f(x) and replace it with other constraints to create new metrics.
- 社団法人電子情報通信学会の論文
- 2007-09-01
著者
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Gulliver T.
Department Of Electrical & Computer Engineering University Of Victoria
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Gulliver T.
Department Of Electrical And Computer Engineering University Of Victoria
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Khosravifard Mohammadali
Department Of Electrical And Computer Engineering Isfahan University Of Technology
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FOOLADIVANDA Dariush
Department of Electrical and Computer Engineering, Isfahan University of Technology
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Fooladivanda Dariush
Department Of Electrical And Computer Engineering Isfahan University Of Technology
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Khosravifard Mohammadali
Dep. Of Electrical And Computer Engineering Isfahan Univ. Of Technol.
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