A Class of New Metrics for n-Dimensional Unit Hypercube
We study the metric on the n-dimensional unit hypercube. We introduce a class of new metrics for the space, which is information theoretically motivated and has close relation to Jensen-Shannon divergence. These metrics are obtained by discussing a function FDα(P,Q) with the parameter α. We come to...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/942687 |
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| Summary: | We study the metric on the n-dimensional unit hypercube. We introduce a class of new metrics for the space, which is information theoretically motivated and has close relation to Jensen-Shannon divergence. These metrics are obtained by discussing a function FDα(P,Q) with the parameter α. We come to the conclusion that the sufficient and necessary condition of the function being a metric is 0<α≤1/2. Finally, by computing basic examples of codons, we show some numerical comparison of the new metrics to the former metric. |
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| ISSN: | 1110-757X 1687-0042 |