Application of weighted sums of order <i>p</i> to distance estimation

Abstract

<p>Distance functions are employed to estimate actual distances in a transportation network. The ℓ<em>_bp</em>-norm, which is a weighted sum of order <em>p</em>, is a generalization of the weighted ℓ<em>_p</em>-norm, a well-known distance predicting function. We derive some mathematical properties of the new norm and of a goodness-of-fit criterion. These properties are used to develop computational procedures to determine the best-fitting parameter values of the ℓ<em>_bp</em>-norm for a transportation network. We apply the new norm to seventeen geographic regions and find significant improvements in the accuracy of distance estimations over the weighted ℓ<em>_p</em>-norm.</p>