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http://hdl.handle.net/11375/5572| Title: | On the directional bias of the ℓ<sub><i>bp</i></sub>-norm |
| Authors: | Üster, Halit Love, Robert F. McMaster University, Michael G. DeGroote School of Business |
| Keywords: | Distances;Directional Bias;Transportation;Business;Business |
| Publication Date: | Apr-1998 |
| Series/Report no.: | Research and working paper series (Michael G. DeGroote School of Business) 428 |
| Abstract: | <p>The Weighted Sum of Order <em>p</em>, the ℓ<em><sub>bp</sub></em>-norm, is a generalization of the well-known ℓ<em><sub>p</sub></em>-norm used in predicting distances in a transportation network. The properties of the directional bias function and the unit balls for the ℓ<em><sub>bp</sub></em>-norm are of theoretical and practical interest. We investigate these properties and compare them with the properties of the ℓ<em><sub>p</sub></em>-norm's directional bias function and the unit balls. We find that the ℓ<em><sub>bp</sub></em>-norm is better at capturing the nonlinearity in a transportation network than the weighted ℓ<em><sub>p</sub></em>-norm. It is also shown that, in contrast to the weighted ℓ<em><sub>p</sub></em>-norm, where the optimal parameter <em>p</em> value is confined to the interval (1, 2), for the ℓ<em><sub>bp</sub></em>-norm the parameter <em>p</em> can have an optimal value greater than 2.</p> |
| Description: | <p>26 p. : ; Includes bibliographical references: p. 24-26. ; In the title [bp] is a subscript.</p> |
| URI: | http://hdl.handle.net/11375/5572 |
| Identifier: | dsb/32 1031 4944052 |
| Appears in Collections: | DeGroote School of Business Working Paper Series |
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|---|---|---|---|
| fulltext.pdf | 655.6 kB | Adobe PDF | View/Open |
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