Local convergence in Fermat's problem

Katz, Irving

doi:10.1007/bf01580224

Cited by 75 publications

(19 citation statements)

References 8 publications

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“…Obtaining a precise value for the complexity of this strategy was more difficult than other spatial distribution strategies. The problem of minimizing W is not a trivial task, and it has a long history (see Drezner and Hamacher, 2002;Katz, 1974;Wesolowsky, 1993). The function, W, is convex so it has a unique minimum in the convex hull of the set of given points.…”

Section: Center Of Minimum Distancementioning

confidence: 99%

On the Complexity and Accuracy of Geographic Profiling Strategies

et al. 2005

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Geographic profilers have access to a repertoire of strategies for predicting a serial offender's home location. These strategies range in complexity-some involve more calculations to implement than others-and the assumption often made is that more complex strategies will outperform simpler strategies. In the present study, we tested the relationship between the complexity and accuracy of 11 strategies. Data were crime site and home locations of 16 UK residential burglars who had committed 10 or more crimes each. The results indicated that strategy complexity was not positively related to accuracy. This was also found to be the case across tasks that ranged in complexity (where complexity was determined by the number of crimes used to make a prediction). Implications for police' policies and procedures, as well as our understanding of human decisionmaking, are discussed.

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Section: Center Of Minimum Distancementioning

confidence: 99%

On the Complexity and Accuracy of Geographic Profiling Strategies

et al. 2005

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“…This algorithm is guaranteed to converge to the optimal solution [27,31], and in most settings converges quadratically [24].…”

Section: Robust Mds: Rmdsmentioning

confidence: 99%

Universal multi-dimensional scaling

Agarwal

Phillips

Venkatasubramanian

2010

Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

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In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied.Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/ 2 ) log n)-dimensional sphere causes only an -distortion in the geodesic distances.

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“…The Weiszfeld method is the standard, and best-known, method for solving problem (1). The convergence of the Weiszfeld method was studied in [18], [17] and [2].…”

Section: Location Of a Single Facilitymentioning

confidence: 99%