On the directional bias of the lbp-norm

Abstract The weighted sum of order p , the l bp -norm, is a generalization of the well-known l p -norm used in predicting distances in a transportation network. The properties of the directional bias function and the unit balls for the l bp -norm are of theoretical and practical interest. We investigate these properties and compare them with the properties of the l p -norm's directional bias function and the unit balls. We find that the l bp -norm is better at capturing the nonlinearity in a transportation network than the weighted l p -norm. It is also shown that, in contrast to the weighted l p -norm, where the optimal parameter p value is confined to the interval (1,2), for the l bp -norm the parameter p can have an optimal value greater than 2.

[1]  John B. Westwood.  A Transport Planning Model for Primary Distribution , 1977 .

[2]  Peter J. Kolesar,et al.  Determining the Relation between Fire Engine Travel Times and Travel Distances in New York City , 1975, Oper. Res..

[3]  Nicos Christofides,et al.  Distribution management : mathematical modelling and practical analysis , 1971 .

[4]  N. Archer.  Characterizing World Wide Web search strategies , 1996 .

[5]  Robert F. Love,et al.  Comparison of the properties and the performance of the criteria used to evaluate the accuracy of distance predicting functions , 1996 .

[6]  A. Montazemi,et al.  An Empirical Investigation of CBI in Support of Mastery Learning , 1995 .

[7]  Kalyan Moy Gupta,et al.  Empirical evaluation of retrieval in case-based reasoning systems using modified cosine matching function , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[8]  Kalyan Moy Gupta,et al.  An adaptive agent for case description in diagnostic CBR systems , 1996 .

[9]  Jack Brimberg,et al.  Estimating travel distances by the weightedlp norm , 1991 .

[10]  Jack Brimberg,et al.  The effect of axis rotation on distance estimation , 1995 .

[11]  Jason Schwandt,et al.  Electronic data interchange: an overview of its origins, status and future , 1997 .

[12]  J. Perreur,et al.  Note---On the Weber Problem with Rectangular Distance: A Comment , 1973 .

[13]  Yufei Yuan,et al.  Web-based collective bargaining support system: a valid process support tool for remote negotiation , 1998 .

[14]  Alan T. Murray,et al.  Cluster Discovery Techniques for Exploratory Spatial Data Analysis , 1998, Int. J. Geogr. Inf. Sci..

[15]  R. Love,et al.  Application of a Weighted Sum of Order p to Distance Estimation , 1998 .

[16]  R. Love,et al.  Mathematical Models of Road Travel Distances , 1979 .

[17]  Jack Brimberg,et al.  Directional bias of the lp-norm , 1993 .

[18]  HALIT ÜSTER,et al.  Application of a weighted sum of order p to distance estimation , 1998 .

[19]  Jiang Chen,et al.  Discrete Lot Streaming In Two-Machine Flow Shops , 1999 .

[20]  Paul Stephenson,et al.  Subset-Restricted Interchange for Dynamic Min-Max Scheduling Problems , 2000, SIAM J. Discret. Math..

[21]  Paul Sparrow,et al.  Evaluating levels of strategic integration and devolvement of human resource management in India , 1997 .

[22]  Harish C. Jain,et al.  Workplace Substance Testing—An Exploratory Study , 1998 .

[23]  Kalyan Moy Gupta,et al.  A framework for retrieval in case-based reasoning systems , 1997, Ann. Oper. Res..

[24]  J. Estes,et al.  Geographic Information Systems: An Introduction , 1990 .

[25]  Kalyan Moy Gupta,et al.  A connectionist approach for similarity assessment in case-based reasoning systems , 1997, Decis. Support Syst..

[26]  George Steiner,et al.  Approximation methods for discrete lot streaming in flow shops , 1997, Oper. Res. Lett..

[27]  Pierre Hansen,et al.  Procedures for the reduction of errors in road network data , 1974 .

[28]  Harish C. Jain,et al.  Bill 40 amendments to Ontario Labour Relations Act: an overview and evaluation , 1993 .

[29]  R. Love,et al.  Properties of ordinary and weighted sums of order $p$ used for distance estimation , 1995 .

[30]  Rolf Klein,et al.  Voronoi Diagrams in the Moscow Metric (Extended Abstract) , 1987, WG.

[31]  Isik U. Zeytinoglu,et al.  Global diversity in employment relationships: a typology of flexible employment , 1996 .

[32]  Christopher K. Bart,et al.  Mission statement rationales and organizational alignment in the not-for-profit health care sector. , 1998 .