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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| Format: | Article |
| Language: | English |
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Hindawi Limited
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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doaj-6fc3b0e5812b49608e2896f0dc69b84e2020-11-24T22:22:52ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/942687942687A Class of New Metrics for n-Dimensional Unit HypercubeGuoxiang Lu0School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430077, ChinaWe 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.http://dx.doi.org/10.1155/2013/942687 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Guoxiang Lu |
| spellingShingle |
Guoxiang Lu A Class of New Metrics for n-Dimensional Unit Hypercube Journal of Applied Mathematics |
| author_facet |
Guoxiang Lu |
| author_sort |
Guoxiang Lu |
| title |
A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_short |
A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_full |
A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_fullStr |
A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_full_unstemmed |
A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_sort |
class of new metrics for n-dimensional unit hypercube |
| publisher |
Hindawi Limited |
| series |
Journal of Applied Mathematics |
| issn |
1110-757X 1687-0042 |
| publishDate |
2013-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2013/942687 |
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