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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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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| _version_ | 1841524867639279616 |
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| author | Guoxiang Lu |
| author_facet | Guoxiang Lu |
| author_sort | Guoxiang Lu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6fc3b0e5812b49608e2896f0dc69b84e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6fc3b0e5812b49608e2896f0dc69b84e2025-02-03T05:47:10ZengWileyJournal 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 |
| spellingShingle | Guoxiang Lu A Class of New Metrics for n-Dimensional Unit Hypercube Journal of Applied Mathematics |
| title | 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_short | A Class of New Metrics for n-Dimensional Unit Hypercube |
| title_sort | class of new metrics for n dimensional unit hypercube |
| url | http://dx.doi.org/10.1155/2013/942687 |
| work_keys_str_mv | AT guoxianglu aclassofnewmetricsforndimensionalunithypercube AT guoxianglu classofnewmetricsforndimensionalunithypercube |